[
  {
    "expression": "450 * 63",
    "correct_answer": 28350,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "95 + 26 * 38 - 22 * 59",
    "correct_answer": -215,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "12 + 29 - 15",
    "correct_answer": 26,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "25 * 26",
    "correct_answer": 650,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "90 * 445 + 791 + 89 - 803",
    "correct_answer": 40127,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "37 + 88 * 15 - 50 * 22",
    "correct_answer": 257,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "135 % 7",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "2524 - 1719",
    "correct_answer": 805,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "2 - 22 - 28 - 26 - 16 + 30 + 9 - 12 - 28 + 30 - 5 + 24 + 23 - 12 - 10 - 20 - 2 - 15 - 5 + 13 - 16 - 30 - 30 - 12",
    "correct_answer": -158,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "366 * 29",
    "correct_answer": 10614,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "2231 - 5229",
    "correct_answer": -2998,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "213 - 522 * 584 + 32 * 263",
    "correct_answer": -296219,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "7853 + 9907",
    "correct_answer": 17760,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "499 % 18",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "5 + 9 + 8 + 1 - 3 - 4 + 2 - 9 + 2 + 9 - 3 - 6 + 5 - 9 - 1 + 3 - 8 - 4 + 2 - 9 - 1 + 3 + 1 + 7 - 5 - 9 + 8 + 9 - 8 - 6 - 2 + 8 + 6 + 9 - 9 - 1",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "867 * 20",
    "correct_answer": 17340,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "840 * 432",
    "correct_answer": 362880,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "6 - 6 - 5 + 3 + 1 + 3 + 8 + 5 - 6 - 4 + 6 - 8 - 1 + 3 + 7 + 5 - 7",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "9 - 12 - 17 - 30 - 11 + 25 - 16 - 25 - 20 - 13 - 1 + 5 - 13 + 24 - 25 - 28 + 9 + 5 + 18 + 18 - 7 + 17 + 17 + 12 - 26 - 1",
    "correct_answer": -86,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "9 - 2 + 5 + 13 - 7 - 29 + 3 - 17 - 17 - 7 + 5 - 21 - 29 + 20 + 22 + 23 + 10 + 23 + 16 - 26 + 2",
    "correct_answer": -4,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "46 * 16",
    "correct_answer": 736,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "661 * 16",
    "correct_answer": 10576,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "4470 - 9105",
    "correct_answer": -4635,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "17 - 86",
    "correct_answer": -69,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "43 * 35",
    "correct_answer": 1505,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "171 + 290 * 25 * 583 + 114",
    "correct_answer": 4227035,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2 + 9 - 2 - 8 - 7 + 8 + 8 - 9 - 8 - 8 + 1 + 3 + 2 - 9 - 6 + 6 - 2 - 9 + 1",
    "correct_answer": -28,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "181 % 3",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "564 - 182 + 157 + 271 - 167",
    "correct_answer": 643,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "71 + 26 * 66 - 25 * 56",
    "correct_answer": 387,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "(84 + 23) * (87 - 69)",
    "correct_answer": 1926,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "32 + 26",
    "correct_answer": 58,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "41 * 77",
    "correct_answer": 3157,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "21 + 59",
    "correct_answer": 80,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "3887 - 4836",
    "correct_answer": -949,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "70 - 47 + 68",
    "correct_answer": 91,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "21 + 40",
    "correct_answer": 61,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "581 * 33",
    "correct_answer": 19173,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "354 * 261",
    "correct_answer": 92394,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "21 + 31",
    "correct_answer": 52,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "57 * 84",
    "correct_answer": 4788,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "135 - 801 * 347 - 764 * 835",
    "correct_answer": -915752,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "719 * 936 + 823 + 175 + 129",
    "correct_answer": 674111,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "10 - 1 - 4 - 2 + 7 + 16 + 19 - 29 + 14 + 8 - 8 + 13 + 22 + 18 + 12 - 4 - 9 - 9 + 13 - 12 + 8",
    "correct_answer": 82,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "96 * 97",
    "correct_answer": 9312,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "458 - 496",
    "correct_answer": -38,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "1 - 2 + 7 - 7 - 7 + 9 + 5 - 4 + 5 + 5 + 1 + 7 + 8 + 9 - 6 + 2 + 2 + 5 - 7 + 3",
    "correct_answer": 36,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "9 + 4 - 5 + 8 - 9 + 9 + 8 + 5 + 7 + 4 + 7 + 6 + 4 + 7 + 3 + 4 + 4 + 9 + 6 + 2 - 2 + 7 + 4 + 2 + 9 - 6 - 7 + 7 - 5 + 1",
    "correct_answer": 102,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "223 * 990",
    "correct_answer": 220770,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "59 * 38",
    "correct_answer": 2242,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "55 + 41 - 86",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "40 + 73 * 73 - 96 * 45",
    "correct_answer": 1049,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "(74 + 94) * (47 - 83)",
    "correct_answer": -6048,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "35 * 18",
    "correct_answer": 630,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "737 * 847",
    "correct_answer": 624239,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "373 - 549",
    "correct_answer": -176,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "533 * 82",
    "correct_answer": 43706,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "1062 - 2029",
    "correct_answer": -967,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "5 + 9 - 7 - 3 + 6 - 8 - 5 + 7 + 3 + 7 + 5 + 9 + 2 + 5 + 6 + 1 - 6 + 3 - 7 - 7 + 4 - 3 - 7 + 5 - 6 + 4 - 1 - 8 - 5 - 1 + 4 + 7 - 3 + 5 + 8 + 3",
    "correct_answer": 31,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "305 * 908",
    "correct_answer": 276940,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "405 - 640",
    "correct_answer": -235,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "5873 - 2388",
    "correct_answer": 3485,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "11 + 8 + 1 + 6 - 16 + 1 - 23 + 22 - 9 + 28 + 20 + 18 + 8 + 15 + 9 + 22 - 7 - 10 + 27 + 16 + 19 + 21 - 22 - 24",
    "correct_answer": 141,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "804 * 710",
    "correct_answer": 570840,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "927 * 119 - 715 + 508 * 916",
    "correct_answer": 574926,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "4 + 7 + 5 - 2 + 5 - 4 + 7 + 5 + 4 + 8 + 7 - 8 + 1 - 4 + 5 - 1 - 7 + 8 + 6 + 9 - 2 - 8",
    "correct_answer": 45,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "6 - 4 + 9 + 8 + 5 + 8 - 7 + 9 - 9 + 5 + 9 + 3 + 8 - 2 - 4 - 7 + 4 + 3",
    "correct_answer": 44,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "48 * 91",
    "correct_answer": 4368,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "16 - 27 - 28 + 3 - 30 - 11 + 1 + 23 - 23 - 20 - 24 - 24 + 17 + 5 - 19 + 30 + 13 + 30 - 19 + 3 - 21 - 1 + 13 - 18",
    "correct_answer": -111,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(18 + 83) * (15 - 36)",
    "correct_answer": -2121,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "84 + 6",
    "correct_answer": 90,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "28 * 30",
    "correct_answer": 840,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "82 + 59",
    "correct_answer": 141,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "96 + 56 - 23",
    "correct_answer": 129,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "5102 - 2350",
    "correct_answer": 2752,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "5646 + 6533",
    "correct_answer": 12179,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "6 + 6 - 1 - 2 + 8 + 9 - 9 + 9 - 3 + 7 - 8 + 5 + 4 + 7 + 4 + 5 + 3 + 4 + 3 - 5 + 4 + 2 + 1 - 8 + 4 - 3 + 8 - 8 - 6 - 6 - 5 - 9 - 6 + 6 - 9 + 4",
    "correct_answer": 21,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "265 * 22",
    "correct_answer": 5830,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "8 - 2 + 6 + 2 + 3 - 8 + 2 + 8 + 4 + 8 - 5 + 3 - 7 - 5 - 9 + 9 + 4 + 8",
    "correct_answer": 29,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "615 * 47",
    "correct_answer": 28905,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "2624 - 3704",
    "correct_answer": -1080,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "(67 + 93) * (44 - 17)",
    "correct_answer": 4320,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "3 - 23 + 1 + 15 - 5 + 14 - 14 - 18 + 21 + 6 - 10 + 28 + 7 - 1 - 7 - 22 + 9 + 24 - 10 + 5 - 2 + 12 + 28",
    "correct_answer": 61,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "680 % 4",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "7703 - 9056",
    "correct_answer": -1353,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "476 % 17",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "747 - 330 * 636 * 595 * 559",
    "correct_answer": -69807136653,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(83 + 31) * (40 - 81)",
    "correct_answer": -4674,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "580 + 70 + 350 - 492 * 630",
    "correct_answer": -308960,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "29 - 82 + 25",
    "correct_answer": -28,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "(45 + 62) * (23 - 56)",
    "correct_answer": -3531,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "523 - 285 * 958 - 600 + 44",
    "correct_answer": -273063,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2 + 7 + 3 + 5 - 5 - 2 - 2 - 9 + 2 + 1 + 5 - 1 - 3 + 5 + 3 + 3 + 7 + 6 - 5 - 3 - 1 - 5 - 8 - 8 - 7 - 4 - 7 + 6 - 4 + 8 - 8 - 5 - 1 + 3 - 6 - 6",
    "correct_answer": -34,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(27 + 73) * (58 - 41)",
    "correct_answer": 1700,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "317 - 101 + 725 + 860 * 752",
    "correct_answer": 647661,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(81 + 27) * (47 - 21)",
    "correct_answer": 2808,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "16 + 8 + 24 + 26 - 8 + 1 - 24 - 21 - 15 + 19 + 23 + 19 + 24 + 11 - 28 + 29 - 19 - 2 - 16 - 30 - 12 - 1 + 19 - 29",
    "correct_answer": 14,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "45 - 45 + 94",
    "correct_answer": 94,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "(92 + 99) * (44 - 39)",
    "correct_answer": 955,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "96 - 75",
    "correct_answer": 21,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "31 * 68",
    "correct_answer": 2108,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "71 - 22",
    "correct_answer": 49,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "31 * 27",
    "correct_answer": 837,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "4092 - 4782",
    "correct_answer": -690,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "830 % 17",
    "correct_answer": 14,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "59 + 77 * 31 - 71 * 51",
    "correct_answer": -1175,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "43 * 95",
    "correct_answer": 4085,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "108 * 168",
    "correct_answer": 18144,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "865 % 3",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "116 * 35",
    "correct_answer": 4060,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "17 - 20 + 19 + 3 - 24 + 22 + 22 + 21 + 11 - 10 + 24 + 12 - 27 + 28 - 16 + 12 - 24 - 19 - 22 - 7 - 15",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "2923 - 4882",
    "correct_answer": -1959,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "5 - 7 + 4 + 6 + 2 - 2 - 9 + 6 - 7 + 4 - 1 + 3 - 9 + 9 + 4 + 7 - 2 - 5 + 2 + 3 + 2",
    "correct_answer": 15,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "6 + 4 - 3 - 2 - 6 - 7 + 5 - 4 + 3 + 6 + 4 + 5 + 5 + 8 - 1 + 9",
    "correct_answer": 32,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "2 + 9 - 7 + 1 + 4 + 2 - 5 - 5 + 5 + 1 - 5 - 7 - 7 + 6 + 1 + 3 - 6 - 7 + 3 - 7 - 3 + 3 + 1 - 4 + 5 + 1 + 5 + 7 - 5 + 6 - 4 + 6 - 4 + 6 - 2 + 5 + 6 - 3 + 1",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "10 + 24 * 81 - 76 * 21",
    "correct_answer": 358,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "4 + 5 - 7 + 5 - 7 - 9 + 4 + 3 + 4 - 5 - 3 + 7 - 5 + 8 - 1 + 4",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "3 - 4 - 24 + 6 - 21 + 21 - 3 + 15 - 16 - 19 - 5 + 22 - 17 - 29 - 10 - 22 + 19 - 23 + 18 + 26 + 1 + 18 + 1 - 4 - 6 - 22",
    "correct_answer": -75,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "30 + 24 - 21 - 21 - 23 - 30 + 10 - 18 + 16 + 3 - 15 - 6 + 27 + 1 + 27 + 23 - 29 + 28 - 1 + 30 - 10 + 26 - 12 - 6 - 12",
    "correct_answer": 41,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "557 * 99",
    "correct_answer": 55143,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "6443 - 7224",
    "correct_answer": -781,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "29 - 26",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "995 % 14",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "85 - 56",
    "correct_answer": 29,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "48 * 481 - 894 * 591 - 933",
    "correct_answer": -506199,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(27 + 80) * (70 - 93)",
    "correct_answer": -2461,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "863 * 973 * 678 - 378 + 828",
    "correct_answer": 569316372,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "40 * 88",
    "correct_answer": 3520,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "4 - 5 - 24 - 1 + 29 - 11 + 16 - 8 + 7 + 10 - 4 - 22 + 13 - 9 - 20 - 24 + 8 + 27 + 16 + 15 + 24 - 12 - 14 + 5",
    "correct_answer": 20,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "3321 + 6707",
    "correct_answer": 10028,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "6 - 5 + 4 - 2 - 5 - 1 + 8 + 3 - 3 + 6 - 9 + 6 + 5 - 2 + 9 - 1 - 7 - 3 + 1",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "229 * 26",
    "correct_answer": 5954,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "33 - 59 + 33",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "8 + 9 - 1 + 2 - 1 + 5 + 9 - 4 + 7 + 2 + 5 - 3 - 6 - 5 + 2 - 8 + 4 + 2 - 6 - 3 + 8 + 1 - 5 - 3 - 1 - 8 - 8 + 8 - 1 - 5 + 9 - 3 + 2 + 6 - 6 - 5 + 5",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "508 * 368",
    "correct_answer": 186944,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "4 + 5 - 6 + 1 + 8 + 3 + 1 - 6 + 2 + 7 - 3 + 3 - 8 - 3 - 3 + 3 + 4 + 2 - 1 - 7 + 1 - 1 - 9 + 7 + 4 + 2 + 7 - 3 + 1 - 6 + 8 - 9",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "45 * 43",
    "correct_answer": 1935,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "1201 + 5006",
    "correct_answer": 6207,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "47 + 75 * 89 - 72 * 38",
    "correct_answer": 3986,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "562 % 8",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "2 + 13 + 11 - 11 - 11 - 4 + 28 - 19 + 15 + 21 + 22 - 1 - 21 - 17 + 29 + 9 + 22 - 16 - 29 - 14 + 23 - 20 + 27 + 28 + 12",
    "correct_answer": 99,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "407 * 327",
    "correct_answer": 133089,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "72 * 76",
    "correct_answer": 5472,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "57 - 16",
    "correct_answer": 41,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "6 + 8 - 7 + 6 + 8 - 5 - 6 + 7 + 5 + 9 - 8 + 3 - 5 - 3 + 4 - 2 - 9 - 3 + 6",
    "correct_answer": 14,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "43 + 57 * 23 - 23 * 87",
    "correct_answer": -647,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "55 * 65",
    "correct_answer": 3575,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "12 + 11 + 24 - 29 + 16 + 22 + 14 - 24 - 19 - 13 - 20 + 23 - 12 - 22 - 21 + 3 - 7 - 1 - 23 - 26 - 20 + 15 - 23 - 23 + 7 - 19 + 17",
    "correct_answer": -138,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "59 + 2 - 93",
    "correct_answer": -32,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "72 - 48 + 15",
    "correct_answer": 39,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "(12 + 77) * (92 - 32)",
    "correct_answer": 5340,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "620 % 10",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "42 + 10 * 21 - 54 * 12",
    "correct_answer": -396,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "9 + 5 - 1 - 3 + 23 + 14 - 20 + 26 - 21 - 26 + 2 - 13 - 5 - 14 + 7 + 8 + 26 + 9 + 2 + 3 + 19 + 8 + 29 + 4 - 26 + 22",
    "correct_answer": 87,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "531 * 90",
    "correct_answer": 47790,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "45 - 1 + 24",
    "correct_answer": 68,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "268 * 145 - 297 - 888 * 24",
    "correct_answer": 17251,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "682 + 925 * 983 + 663 + 735",
    "correct_answer": 911355,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "114 + 233 + 525 + 861 * 824",
    "correct_answer": 710336,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "9 + 5 + 7 + 4 + 1 + 5 - 4 + 5 + 7 + 5 - 5 + 1 - 6 + 3 + 1 + 8 + 6 + 9 - 1 + 2 + 9 + 2 - 5 + 5 + 8 + 3 + 1 + 1 - 9 + 6 + 4 - 5 - 1 - 6 - 1 + 6 + 9 + 9",
    "correct_answer": 98,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "18 - 13 - 12 + 15 - 2 + 27 - 24 - 25 - 7 + 14 - 16 - 12 + 21 - 9 + 18 - 18 + 12 - 1 - 24 + 2 + 24 - 4 + 26 + 4 + 26",
    "correct_answer": 40,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "911 * 284",
    "correct_answer": 258724,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "91 + 16 * 63 - 31 * 15",
    "correct_answer": 634,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "311 + 507 + 820 * 155 + 441",
    "correct_answer": 128359,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "545 - 471 + 254 * 635 * 48",
    "correct_answer": 7741994,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "3 + 4 + 1 + 3 - 8 - 1 - 4 + 5 - 7 + 7 - 9 + 3 - 2 + 1 + 5 - 6 - 5 - 1 + 6 + 8 - 3 - 1 + 9 + 2 + 4 + 2 + 8 - 7 + 9",
    "correct_answer": 26,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "654 * 494 * 183 * 62 * 308",
    "correct_answer": 1129011051168,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "53 * 44",
    "correct_answer": 2332,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "5 + 8 - 9 - 6 + 3 - 8 - 9 + 8 + 1 - 9 + 3 + 3 + 2 - 9 - 9 + 3 - 1 + 7 + 1 + 7 - 4",
    "correct_answer": -13,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "29 + 4",
    "correct_answer": 33,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "2 + 7 + 1 - 9 - 6 + 7 - 4 - 9 + 8 - 5 + 6 - 1 - 4 + 4 + 3 - 2 + 7 + 3 - 3 + 1 + 3",
    "correct_answer": 9,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "151 * 789",
    "correct_answer": 119139,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "390 - 554",
    "correct_answer": -164,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "4591 - 4844",
    "correct_answer": -253,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "5 + 4 - 2 - 2 - 7 + 7 + 6 - 1 + 8 + 5 + 2 - 6 - 4 + 5 - 1 + 5 + 7 - 9 + 1 + 1 - 2 - 7 + 5 + 6 - 9 - 8 + 7 + 8 - 2 + 2 - 1 + 3 - 6 + 7 + 2",
    "correct_answer": 29,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "729 * 86",
    "correct_answer": 62694,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "10 + 3 + 11 - 14 + 20 + 26 + 8 - 2 - 29 + 25 - 4 - 23 + 21 - 28 + 27 - 27 - 27 - 8 + 8 + 11 - 25 + 6 + 16 - 21",
    "correct_answer": -16,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "19 + 26 - 20 + 11 - 2 + 22 + 17 + 20 - 3 - 5 - 1 + 23 - 16 - 23 + 26 + 25 - 8 + 21 + 21 - 12 - 20 - 21 + 30 + 11 - 22",
    "correct_answer": 119,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "3823 - 4244",
    "correct_answer": -421,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "21 - 48",
    "correct_answer": -27,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "333 - 438",
    "correct_answer": -105,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "8 - 4 - 5 + 9 - 7 + 5 + 8 + 8 + 7 + 6 - 1 + 8 + 3 - 9 - 2 - 3 + 9 - 4 + 9 + 9 - 9 + 8 - 5 - 4 - 4 - 5 - 6 - 7 - 1 - 7 + 7 - 5 + 4",
    "correct_answer": 20,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "6 + 85",
    "correct_answer": 91,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "2 + 7 + 4 - 9 - 3 + 7 + 7 + 7 - 2 - 9 + 7 + 3 + 1 + 2 + 5 - 6 + 7 - 6 - 7",
    "correct_answer": 17,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "4921 - 9108",
    "correct_answer": -4187,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "34 * 75",
    "correct_answer": 2550,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "2 - 3 + 5 - 6 + 3 + 4 + 8 + 1 - 6 - 8 + 3 + 9 + 1 + 4 + 9 + 5 - 3 + 4 - 3 + 5 + 7 + 8 + 4 - 4 + 9 + 1 - 3 + 3 - 1 + 9 + 5",
    "correct_answer": 72,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "31 + 49 * 42 - 71 * 74",
    "correct_answer": -3165,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "76 * 87",
    "correct_answer": 6612,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "4949 + 9185",
    "correct_answer": 14134,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "6 - 12 + 13 - 14 - 30 - 9 - 19 - 10 + 25 - 9 + 3 + 6 + 28 + 28 - 28 + 21 - 9 - 25 + 30 - 25 - 24",
    "correct_answer": -54,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "504 * 61",
    "correct_answer": 30744,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "6 - 8 + 7 - 2 + 5 + 1 - 1 - 8 - 4 - 7 - 9 - 7 + 9 + 6 + 7 - 8 - 5 + 2 - 9 + 9 + 2 - 3 - 4 + 3 + 3 - 3 - 2 - 8 - 9 - 3 + 5 + 6",
    "correct_answer": -29,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "5 + 9 + 5 - 3 + 2 - 7 - 3 - 4 + 8 - 9 - 5 - 5 - 3 - 2 - 6 - 6 - 8 + 4",
    "correct_answer": -28,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "85 - 16",
    "correct_answer": 69,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "45 - 83",
    "correct_answer": -38,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "33 + 75 * 47 - 31 * 27",
    "correct_answer": 2721,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "1197 - 6916",
    "correct_answer": -5719,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "3281 + 4385",
    "correct_answer": 7666,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "135 * 391",
    "correct_answer": 52785,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "5991 + 1110",
    "correct_answer": 7101,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "285 % 8",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "18 + 13 + 17 + 4 + 12 + 5 + 18 - 2 - 25 - 22 - 19 + 6 - 15 - 16 - 26 + 6 + 20 - 11 + 7 - 27 + 7 - 23",
    "correct_answer": -53,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "6675 + 1157",
    "correct_answer": 7832,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "40 + 73",
    "correct_answer": 113,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "72 * 91",
    "correct_answer": 6552,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "5 + 7 + 9 - 4 + 8 + 1 - 2 - 5 - 9 + 1 - 5 + 1 - 4 + 9 - 2 - 7 + 6 + 4 + 7 - 4 + 1 + 5 - 5 + 7 + 7 + 3 + 5 - 9 + 2 - 3 - 1 - 2",
    "correct_answer": 26,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "348 * 173",
    "correct_answer": 60204,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "559 % 3",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "315 + 897 - 932 - 928 * 697",
    "correct_answer": -646536,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(26 + 40) * (71 - 74)",
    "correct_answer": -198,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "3230 + 5922",
    "correct_answer": 9152,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "2 - 4 - 29 - 28 - 5 - 24 + 28 + 26 - 30 + 6 - 11 + 22 - 2 + 25 + 6 - 14 - 12 + 19 - 2 - 2 + 25",
    "correct_answer": -4,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "209 * 29",
    "correct_answer": 6061,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "161 * 390",
    "correct_answer": 62790,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "871 % 9",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "8 - 8 - 7 + 9 + 2 + 5 + 8 + 7 - 8 + 2 - 7 - 8 - 8 + 4 + 5 + 7 + 6 + 6 + 8 - 5 + 5 + 4 + 1 + 7 - 3 - 2 + 6 + 9 - 1 - 2 - 6 + 9 + 1",
    "correct_answer": 54,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "853 * 27",
    "correct_answer": 23031,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "55 * 75",
    "correct_answer": 4125,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "22 + 22 - 1 + 28 - 6 + 23 + 18 - 5 - 6 + 13 + 12 + 21 + 29 + 3 + 4 - 14 - 19 - 24 + 6 - 6 + 16 + 4 - 13 + 17",
    "correct_answer": 144,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "82 + 34",
    "correct_answer": 116,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(72 + 91) * (98 - 69)",
    "correct_answer": 4727,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "897 % 14",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "171 - 303",
    "correct_answer": -132,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "922 * 75",
    "correct_answer": 69150,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "1544 - 4320",
    "correct_answer": -2776,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "81 + 83 - 43",
    "correct_answer": 121,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "36 + 60",
    "correct_answer": 96,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "72 + 2",
    "correct_answer": 74,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "56 + 36 * 33 - 15 * 82",
    "correct_answer": 14,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "75 * 39",
    "correct_answer": 2925,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "766 * 589 * 708 + 588 * 76",
    "correct_answer": 319475880,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "9 - 27 - 14 + 30 - 20 - 26 - 24 - 22 + 26 - 3 - 2 - 8 + 1 + 1 - 13 - 11 - 13 - 15 - 14 - 12 + 29 + 24 - 19",
    "correct_answer": -123,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "91 + 81 * 67 - 57 * 88",
    "correct_answer": 502,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "5 + 7 - 4 + 7 + 8 + 3 + 1 + 6 + 3 - 6 - 4 + 7 + 9 - 9 + 4 - 7 + 9 - 1 - 3 + 7 + 9 + 2 + 2 + 2 - 2 + 4 - 3 - 4 + 2 - 8 + 1 + 4 + 5 + 9 - 6 - 1 - 6 - 5 + 8",
    "correct_answer": 55,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "9115 + 9369",
    "correct_answer": 18484,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "51 * 41",
    "correct_answer": 2091,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "9 - 2 - 3 - 7 - 3 + 8 - 9 + 4 + 1 + 2 - 4 + 9 - 9 + 5 - 6 + 4 + 2 + 1 + 8 + 6 - 5 + 7 - 5 + 9 + 4 + 4 - 6 + 7 + 8 + 3",
    "correct_answer": 42,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "28 + 55 * 47 - 69 * 28",
    "correct_answer": 681,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "955 * 232",
    "correct_answer": 221560,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "446 - 653",
    "correct_answer": -207,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "40 * 90",
    "correct_answer": 3600,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "24 * 24",
    "correct_answer": 576,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "9 - 9 + 3 - 9 + 6 - 1 + 6 - 9 + 5 + 2 - 5 - 3 - 7 + 5 - 7 + 9 + 8 + 5 - 1 + 6 - 2 - 9 + 2 - 2 + 6 + 2 - 4 + 2 + 5 - 9 - 2 - 9 + 9 - 9 - 2 + 1 + 7 + 6",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "894 % 12",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "2 + 6 - 7 - 9 - 7 + 4 + 5 + 2 - 4 - 2 - 3 - 7 + 1 + 9 - 7 - 6 + 3 + 4 - 1 + 8 - 5 - 8 - 3 - 3 - 1 + 5 + 2 - 8 + 4 + 7 + 6 - 4 - 4 - 1 - 3 + 7 - 3 + 9",
    "correct_answer": -12,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "54 - 84 + 13",
    "correct_answer": -17,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "807 * 586",
    "correct_answer": 472902,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "545 * 77",
    "correct_answer": 41965,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "11 - 94",
    "correct_answer": -83,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "82 * 404 * 350 - 43 - 446",
    "correct_answer": 11594311,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "594 * 32",
    "correct_answer": 19008,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "86 - 96 + 90",
    "correct_answer": 80,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "(81 + 32) * (91 - 89)",
    "correct_answer": 226,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "4718 - 5184",
    "correct_answer": -466,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "20 + 88 - 61",
    "correct_answer": 47,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "465 + 19 + 770 - 786 * 706",
    "correct_answer": -553662,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "51 + 77 * 11 - 59 * 82",
    "correct_answer": -3940,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "79 - 69",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "157 - 222 * 496 + 353 * 965",
    "correct_answer": 230690,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "4 - 2 - 2 + 5 + 8 + 4 + 6 - 9 - 2 + 6 + 2 + 7 + 1 - 5 - 4 - 8 + 7 - 5 + 1 - 5 - 3 + 2 - 7 + 5 + 6 + 5 - 2 - 7 - 4 - 8 - 6 + 1 - 1 + 1 - 7 + 1",
    "correct_answer": -15,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "274 + 394 + 63 * 255 + 610",
    "correct_answer": 17343,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "29 + 13 - 20 + 24 - 28 - 13 + 21 + 5 + 26 + 26 + 26 - 6 - 17 - 10 - 29 + 2 + 12 + 21 + 11 + 17 - 28 + 7 + 20",
    "correct_answer": 109,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "147 * 524 * 490 - 675 - 198",
    "correct_answer": 37742847,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(67 + 68) * (52 - 88)",
    "correct_answer": -4860,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "51 + 76",
    "correct_answer": 127,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "45 * 23",
    "correct_answer": 1035,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "902 + 699 * 454 + 28 + 414",
    "correct_answer": 318690,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "727 * 43",
    "correct_answer": 31261,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "46 * 721 - 777 * 754 + 276",
    "correct_answer": -552416,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "457 - 639",
    "correct_answer": -182,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "(79 + 49) * (63 - 53)",
    "correct_answer": 1280,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "168 % 10",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "173 - 352",
    "correct_answer": -179,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "7 + 3 - 3 + 7 + 2 + 3 - 7 - 6 - 9 - 5 - 2 - 9 - 1 - 8 - 2 + 7 - 4 - 2 + 7 - 4",
    "correct_answer": -26,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "3692 - 4996",
    "correct_answer": -1304,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "101 % 14",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "1 - 2 + 3 + 2 + 9 + 4 - 9 - 2 + 7 + 7 + 1 - 2 - 8 - 7 - 8 - 5 + 7 + 1 + 6",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "3 - 3 - 9 - 1 + 9 - 7 + 7 + 3 - 8 + 3 + 1 + 4 + 2 + 1 + 5 + 7 + 7 + 8 + 9 + 3 - 3",
    "correct_answer": 41,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "17 + 19 - 1 - 21 + 16 - 12 - 8 - 22 - 29 + 12 + 21 + 25 + 10 - 30 + 9 - 23 + 23 + 17 + 14 + 3 - 19 - 20 - 8",
    "correct_answer": -7,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "867 * 671",
    "correct_answer": 581757,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "(48 + 66) * (42 - 96)",
    "correct_answer": -6156,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "94 + 40 * 50 - 24 * 87",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "83 * 86",
    "correct_answer": 7138,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "27 - 26 - 28 - 19 + 15 - 20 + 4 + 22 - 25 - 1 + 16 - 30 + 18 + 30 + 17 + 10 - 23 - 29 - 14 + 29 - 2 + 28 + 26",
    "correct_answer": 25,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "5026 + 5835",
    "correct_answer": 10861,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "677 - 853 - 526 * 453 - 562",
    "correct_answer": -239016,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "746 * 91",
    "correct_answer": 67886,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "57 + 90 - 63",
    "correct_answer": 84,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "4 - 1 + 6 - 5 - 4 + 6 - 8 - 4 - 9 + 3 - 6 + 6 + 2 - 2 + 8 - 4 + 3 - 5 - 6 + 2 - 3 - 6 - 7 - 9 + 2 - 6 + 4 + 9 - 7",
    "correct_answer": -37,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "78 + 82",
    "correct_answer": 160,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "596 - 166 * 329 - 347 + 565",
    "correct_answer": -53800,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "3 + 7 - 5 + 5 + 2 - 8 - 5 - 2 - 3 + 3 + 7 - 8 - 2 + 5 - 6 - 3 + 6 + 7 - 7 + 6 + 4 + 9 + 9 - 9 + 7 + 7 - 4 + 4 - 4 + 1 - 8 + 2 + 6 + 3 - 3 - 9 + 7 + 4",
    "correct_answer": 28,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "874 - 455 + 336 + 659 - 876",
    "correct_answer": 538,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "8 - 3 - 5 - 9 + 8 - 1 + 8 - 7 + 4 + 8 - 1 - 5 + 8 + 5 + 3 - 3 + 7 - 3 + 2",
    "correct_answer": 24,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "34 * 890 - 334 + 273 + 127",
    "correct_answer": 30326,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "633 * 225",
    "correct_answer": 142425,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "90 - 55",
    "correct_answer": 35,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "28 + 8",
    "correct_answer": 36,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "27 * 41",
    "correct_answer": 1107,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "2163 - 9655",
    "correct_answer": -7492,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "1480 - 6488",
    "correct_answer": -5008,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "19 + 7 - 30 - 4 + 28 + 16 + 28 - 14 - 4 + 20 - 8 - 28 - 2 + 19 + 9 - 4 - 22 - 15 + 22 - 4 - 14 - 2",
    "correct_answer": 17,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "391 * 93",
    "correct_answer": 36363,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "21 + 1 + 11 + 22 + 18 - 2 + 21 + 12 + 23 - 12 - 29 - 30 + 10 - 19 + 25 + 28 + 9 + 14 + 13 + 12 + 23 + 20 - 15 + 3 + 25",
    "correct_answer": 204,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "390 * 86",
    "correct_answer": 33540,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "221 * 39",
    "correct_answer": 8619,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "49 - 5",
    "correct_answer": 44,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "565 * 368 - 336 * 154 - 833",
    "correct_answer": 155343,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "31 * 90",
    "correct_answer": 2790,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "31 - 34",
    "correct_answer": -3,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "48 * 63",
    "correct_answer": 3024,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "3 + 5 - 8 + 3 - 9 + 3 - 4 - 1 - 5 + 1 + 4 + 3 + 5 + 5 - 2 + 9 - 1 + 8 - 6 - 6 + 6 + 7 + 8 + 2 + 4 - 1 - 7 + 4 + 3 - 7 - 3 + 8 + 8 + 2 - 9 - 1 - 7 + 8 + 8",
    "correct_answer": 40,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "78 * 81",
    "correct_answer": 6318,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "887 + 720 + 714 + 324 + 224",
    "correct_answer": 2869,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "5 - 4 - 5 - 9 + 4 + 1 + 4 + 2 - 8 - 7 + 7 + 5 + 6 - 7 - 8 - 1 + 1 + 6 - 8 - 7 + 2 - 6 - 8 + 7 - 8 + 2 + 9 - 4 + 2 + 6",
    "correct_answer": -21,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "2 + 5 + 14 - 15 - 4 - 2 + 1 - 6 - 6 + 11 + 22 - 7 + 24 - 15 + 6 + 18 - 30 + 10 - 16 + 9 - 4 - 8 + 20 - 12",
    "correct_answer": 17,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "4 + 6 + 1 - 6 + 7 - 7 - 2 + 9 + 1 + 9 + 5 - 9 - 5 - 4 - 3 + 2 + 9 + 8 + 1 - 7 - 5 + 2 - 9 + 1 - 5 - 3 + 9 + 1 - 8 + 2",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "73 - 83 + 82",
    "correct_answer": 72,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "36 + 76 - 8",
    "correct_answer": 104,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "81 + 76",
    "correct_answer": 157,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "753 * 690",
    "correct_answer": 519570,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "33 + 50 * 39 - 17 * 75",
    "correct_answer": 708,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "996 + 294 - 381 - 742 - 851",
    "correct_answer": -684,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "496 - 125 - 500 + 876 - 299",
    "correct_answer": 448,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "908 * 58",
    "correct_answer": 52664,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(57 + 30) * (95 - 98)",
    "correct_answer": -261,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "510 * 53",
    "correct_answer": 27030,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "364 * 18",
    "correct_answer": 6552,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "468 * 985",
    "correct_answer": 460980,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "52 + 91 - 82",
    "correct_answer": 61,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "181 * 30",
    "correct_answer": 5430,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "1402 + 8909",
    "correct_answer": 10311,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "11 + 32",
    "correct_answer": 43,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "634 * 63",
    "correct_answer": 39942,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "339 * 304",
    "correct_answer": 103056,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "6 - 6 - 5 - 3 + 8 + 9 - 2 - 7 + 8 + 7 - 1 - 7 + 1 - 3 - 9 - 2 - 9 + 8 + 3 - 6 - 4 + 4 - 8 - 1 - 5 + 3 + 5 - 4 - 9",
    "correct_answer": -29,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "3 + 3 - 1 - 6 - 3 + 2 - 7 + 7 - 1 - 3 - 9 - 7 - 6 - 3 - 8 + 6 - 7 - 4 + 3 + 4 + 4 + 5 + 1 + 8 - 8 - 3 - 9 - 6 + 3 + 2 - 1 - 7 - 8 - 2 - 5 + 9",
    "correct_answer": -54,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "5 - 8 - 6 - 8 + 1 + 6 + 8 + 8 - 3 + 5 - 2 - 9 + 2 + 9 - 5 - 8",
    "correct_answer": -5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "18 - 9 + 10 - 25 + 9 + 18 - 23 + 9 + 2 + 25 - 4 + 30 - 16 + 8 - 29 + 22 + 19 + 28 - 8 + 21 + 6 - 29 + 5",
    "correct_answer": 87,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "4 - 2 + 8 - 5 - 7 + 9 - 4 - 1 + 6 - 3 + 9 - 4 + 4 - 3 + 8 + 2 - 2 + 4 + 1 + 7 - 7 + 8 - 6 - 8 - 9 - 6 + 8 + 6 + 1 + 9 + 1 - 8 - 7 + 1 + 9",
    "correct_answer": 23,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "663 % 12",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "1 - 2 - 1 + 1 + 4 + 8 - 1 - 5 - 9 + 3 + 4 + 5 - 9 - 3 - 1 + 4 - 5 + 8 + 2 + 7 - 9 + 1 + 2 - 3 + 7 - 6 - 5 - 5 - 1 + 4 + 2 - 6",
    "correct_answer": -8,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "17 * 31",
    "correct_answer": 527,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "334 * 41",
    "correct_answer": 13694,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "52 + 71",
    "correct_answer": 123,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "77 * 31",
    "correct_answer": 2387,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "1718 - 4320",
    "correct_answer": -2602,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "178 - 285",
    "correct_answer": -107,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "46 * 17",
    "correct_answer": 782,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "22 * 29",
    "correct_answer": 638,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "16 + 18 - 7 - 20 + 18 + 21 - 30 + 12 + 10 + 13 + 22 - 29 + 26 + 10 - 16 - 23 - 10 - 4 + 4 + 21 + 2",
    "correct_answer": 54,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "539 * 39",
    "correct_answer": 21021,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "1 + 6 - 2 + 5 - 6 + 8 - 7 - 8 - 6 - 5 + 4 + 2 - 7 - 9 + 7 + 9 + 5 - 5 - 4 - 6 - 7 - 7 + 4 - 7 + 9 + 3 + 8 + 9 - 9 + 5 - 7 + 9 + 5",
    "correct_answer": -3,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "735 * 344",
    "correct_answer": 252840,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "479 * 15",
    "correct_answer": 7185,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "21 * 46",
    "correct_answer": 966,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "194 - 744 + 636 - 652 - 366",
    "correct_answer": -932,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "460 - 428 * 893 - 67 - 556",
    "correct_answer": -382367,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "40 + 30 * 40 - 86 * 87",
    "correct_answer": -6242,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "223 - 288",
    "correct_answer": -65,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "87 + 95",
    "correct_answer": 182,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(51 + 22) * (47 - 75)",
    "correct_answer": -2044,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "90 * 545 + 100 * 493 * 769",
    "correct_answer": 37960750,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "39 - 82 + 55",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "483 - 716",
    "correct_answer": -233,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "926 * 250 * 465 - 603 + 439",
    "correct_answer": 107647336,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "82 * 79",
    "correct_answer": 6478,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "8 - 3 - 1 - 8 - 5 - 4 - 5 - 7 + 5 - 4 - 3 + 6 - 8 + 4 + 4 + 9 + 4 + 8 + 6",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "25 + 8 + 14 + 4 + 30 + 26 + 27 - 25 + 25 + 1 - 6 + 23 + 26 + 22 - 17 - 28 + 24 - 11 + 20 - 26 + 9 - 10 + 27",
    "correct_answer": 188,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "1 - 8 + 2 + 5 + 2 + 7 + 5 - 7 - 6 + 5 + 4 + 8 - 2 + 6 - 4 + 8 - 7 + 8 - 1 - 4 + 5",
    "correct_answer": 27,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "190 + 577 * 403 - 205 - 722",
    "correct_answer": 231794,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "890 + 921 - 947 - 656 * 910",
    "correct_answer": -596096,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "42 * 35",
    "correct_answer": 1470,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(84 + 82) * (48 - 48)",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "82 - 97",
    "correct_answer": -15,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "724 * 978 * 565 + 823 * 816",
    "correct_answer": 400732248,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "459 + 435 - 261 - 359 + 527",
    "correct_answer": 801,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2 - 10 + 15 - 9 - 24 - 30 + 5 - 22 + 4 - 14 + 21 + 1 - 20 - 18 + 10 + 20 + 19 - 3 - 21 + 5 + 5 - 14 - 17 - 20 + 25 + 30",
    "correct_answer": -60,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "25 + 26 - 13 + 28 + 24 - 3 - 13 + 25 + 9 + 18 + 30 - 10 + 10 + 21 + 15 - 14 - 2 + 22 + 22 + 22 - 12 + 21 + 16 + 26 + 4 + 12 + 17",
    "correct_answer": 326,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(91 + 53) * (86 - 52)",
    "correct_answer": 4896,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "956 * 89",
    "correct_answer": 85084,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "99 * 82",
    "correct_answer": 8118,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "6077 + 2294",
    "correct_answer": 8371,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "30 - 21 - 30 - 20 - 18 - 14 + 12 + 21 + 14 + 8 + 16 + 15 + 4 - 12 + 4 + 24 - 25 + 11 + 7 - 26 + 23 + 24",
    "correct_answer": 47,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "485 * 507 - 456 + 672 + 216",
    "correct_answer": 246327,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(17 + 98) * (62 - 84)",
    "correct_answer": -2530,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "235 * 444",
    "correct_answer": 104340,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "260 - 314",
    "correct_answer": -54,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "11 + 30 - 30 + 11 + 28 - 30 + 18 + 22 + 25 + 22 + 19 - 17 + 2 - 24 - 16 + 19 - 11 - 24 - 8 - 3 - 14",
    "correct_answer": 30,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "856 + 908 + 908 * 541 * 415",
    "correct_answer": 203861384,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "274 - 988 - 192 - 81 + 960",
    "correct_answer": -27,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(31 + 72) * (46 - 63)",
    "correct_answer": -1751,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "920 % 8",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "5 - 4 - 9 - 5 + 9 - 9 + 7 - 3 + 3 - 7 - 8 + 2 + 1 - 4 - 5 + 9 - 7 - 6 - 9 - 6 + 5",
    "correct_answer": -41,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "302 - 521",
    "correct_answer": -219,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "8 + 4 - 3 + 6 + 3 + 7 - 9 + 8 - 3 - 2 + 1 - 4 - 4 + 6 - 8 + 6 + 4",
    "correct_answer": 20,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "828 + 478 * 118 + 634 * 853",
    "correct_answer": 598034,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "56 - 351 * 583 + 227 + 665",
    "correct_answer": -203685,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "270 - 357",
    "correct_answer": -87,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "68 + 28 - 49",
    "correct_answer": 47,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "726 + 981 * 334 - 443 + 709",
    "correct_answer": 328646,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "43 * 52",
    "correct_answer": 2236,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "46 * 52",
    "correct_answer": 2392,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "438 * 20",
    "correct_answer": 8760,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "765 % 11",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "5 + 3 + 4 + 6 + 5 + 8 + 3 - 6 + 1 + 7 + 2 + 3 - 6 + 3 + 5 - 6 + 7 - 3 - 6 + 7 + 4 - 3 - 3 - 5 + 3 + 7 - 5 - 1 + 9 + 4 + 2 - 9 + 1 - 9 - 4 + 3",
    "correct_answer": 36,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "299 + 340 + 771 * 570 + 400",
    "correct_answer": 440509,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(58 + 79) * (46 - 46)",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "77 * 99",
    "correct_answer": 7623,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "13 - 57 + 13",
    "correct_answer": -31,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "382 + 456 * 518 + 877 * 870",
    "correct_answer": 999580,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "99 - 83",
    "correct_answer": 16,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "18 - 2 - 28 - 6 - 25 + 20 - 9 - 20 + 29 + 25 - 22 - 3 - 20 + 14 - 8 + 9 + 28 + 23 + 28 + 18 + 18",
    "correct_answer": 87,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "760 * 257",
    "correct_answer": 195320,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "34 + 85",
    "correct_answer": 119,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "4 + 7 - 5 + 5 - 9 - 6 + 5 - 7 + 6 + 8 + 8 + 1 + 2 - 3 - 8 - 7 - 4 + 3 - 7 + 8 + 3 + 4 + 9 - 4 + 2 + 7 - 2 - 1 - 5 + 7 - 1 - 4 + 3",
    "correct_answer": 19,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "4 - 4 + 4 - 8 + 7 + 9 - 9 - 8 - 2 + 7 - 6 - 5 - 5 + 3 - 6 - 5 + 1 + 4 - 6 - 2 + 4 + 1 + 6 + 2 - 9 - 1 + 1 - 9 + 1 + 2 + 1 + 2 - 7 + 6 - 4 + 4 + 2",
    "correct_answer": -25,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(49 + 14) * (84 - 61)",
    "correct_answer": 1449,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "18 + 23 * 64 - 15 * 25",
    "correct_answer": 1115,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "957 + 605 + 146 * 820 - 637",
    "correct_answer": 120645,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2228 - 1357",
    "correct_answer": 871,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "410 - 515",
    "correct_answer": -105,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "21 + 1 + 14 - 10 - 9 + 4 - 26 + 4 - 28 + 20 + 28 + 6 + 29 - 20 + 10 + 3 + 3 - 9 - 11 + 20 + 30 + 16 - 11",
    "correct_answer": 85,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "70 * 97",
    "correct_answer": 6790,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "30 + 34 * 62 - 34 * 70",
    "correct_answer": -242,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "936 - 846 * 247 * 72 - 29",
    "correct_answer": -15044357,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "57 - 67",
    "correct_answer": -10,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "3932 - 1579",
    "correct_answer": 2353,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "17 - 15 + 16 - 18 + 8 - 25 - 24 - 14 - 14 - 20 + 20 - 19 - 6 + 8 - 23 + 7 + 9 + 16 + 7 + 19 - 11 - 13",
    "correct_answer": -75,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "913 - 570 * 644 + 580 + 60",
    "correct_answer": -365527,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "33 * 78",
    "correct_answer": 2574,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "857 * 155",
    "correct_answer": 132835,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "7 - 15 + 11 - 9 + 26 + 13 + 21 - 9 - 18 - 18 + 14 + 9 + 30 + 14 - 13 - 11 - 5 + 19 - 7 + 2 - 4 - 22",
    "correct_answer": 35,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "33 * 44",
    "correct_answer": 1452,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "25 + 39 * 39 - 70 * 88",
    "correct_answer": -4614,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "33 * 37",
    "correct_answer": 1221,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "2225 - 2990",
    "correct_answer": -765,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "14 + 22 - 4 - 25 + 4 + 17 + 15 - 18 + 22 + 8 + 26 - 27 + 5 - 12 - 14 - 6 - 29 + 3 - 8 - 13 - 16",
    "correct_answer": -36,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "1 - 6 - 9 + 2 - 1 - 6 + 4 + 4 + 8 + 8 - 9 - 2 + 7 - 7 + 6 + 5 + 8 - 6 - 6 - 1 - 6 - 4 + 7 + 2 + 5 - 5 + 9 - 6 + 6 + 6 - 1 - 9 + 9 + 2 + 6 - 2 + 3 + 6",
    "correct_answer": 28,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "752 * 68",
    "correct_answer": 51136,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "882 * 53 + 507 + 66 * 331",
    "correct_answer": 69099,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "43 * 39",
    "correct_answer": 1677,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "28 + 4 + 13 + 11 + 25 - 28 + 23 + 27 + 27 - 18 + 4 + 27 + 7 - 18 + 22 + 9 + 23 - 21 - 30 + 10 - 5 + 24 - 6 + 8 + 5 + 23 + 25",
    "correct_answer": 219,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(81 + 36) * (58 - 86)",
    "correct_answer": -3276,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "(35 + 56) * (91 - 82)",
    "correct_answer": 819,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "69 + 94",
    "correct_answer": 163,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "17 + 10 + 10 - 10 + 13 + 6 - 24 + 9 + 11 + 17 - 11 - 1 + 6 + 14 + 13 - 11 + 16 + 3 - 23 - 6 + 10 - 2 + 19 - 30",
    "correct_answer": 56,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "8 + 6 + 2 - 5 + 6 + 3 + 9 + 5 + 1 + 9 + 3 + 6 - 1 - 1 + 1 + 7 + 6 + 1 - 4 - 5",
    "correct_answer": 57,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "409 * 106",
    "correct_answer": 43354,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "982 % 4",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "42 * 40",
    "correct_answer": 1680,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "215 - 619 + 135 - 868 - 752",
    "correct_answer": -1889,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "126 - 285",
    "correct_answer": -159,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "3 + 7 - 7 + 9 + 7 + 9 - 5 + 9 + 9 + 3 + 4 + 5 - 3 + 6 - 8 - 5 + 7 + 6 - 6 + 3 - 3 - 1 - 9 + 6 - 8 - 5 - 2 - 2 + 2 - 9 - 2 + 1 - 5 - 8",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "17 - 22 - 22 + 26 - 22 + 30 - 13 - 17 + 6 + 14 + 10 + 4 - 9 - 15 + 15 - 5 - 11 + 23 + 18 + 18 + 27 - 6 - 25 + 30 + 9 - 20",
    "correct_answer": 60,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "36 - 59",
    "correct_answer": -23,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "313 - 427",
    "correct_answer": -114,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "41 + 16",
    "correct_answer": 57,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "63 - 181 - 418 - 318 * 774",
    "correct_answer": -246668,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "101 - 301",
    "correct_answer": -200,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "46 - 74 + 38",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "73 + 98 - 75",
    "correct_answer": 96,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "94 * 45",
    "correct_answer": 4230,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "113 * 313",
    "correct_answer": 35369,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "4 - 2 - 7 + 3 - 8 + 9 - 5 - 2 + 3 + 8 + 1 - 4 + 9 + 4 + 3 + 2 - 8 - 4 - 9 + 2 - 6 - 4 - 3 + 1 - 4 - 5 + 3 + 3 + 8 - 3 + 2 + 4 + 3 + 7 + 1 + 7 + 1 - 4",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "597 - 761 - 441 - 993 + 306",
    "correct_answer": -1292,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1 + 2 - 3 + 4 - 6 + 5 + 5 - 9 - 6 - 7 - 8 - 2 - 4 - 1 + 3 - 3 - 8 + 4 + 1 + 4 - 1 + 1 + 8 + 5 + 8 - 4 + 6 - 1 + 5",
    "correct_answer": -1,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "919 * 29",
    "correct_answer": 26651,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "271 * 680 - 410 * 801 + 777",
    "correct_answer": -143353,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1462 - 6761",
    "correct_answer": -5299,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "42 * 51",
    "correct_answer": 2142,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "203 * 842",
    "correct_answer": 170926,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "2082 - 4680",
    "correct_answer": -2598,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "35 * 42",
    "correct_answer": 1470,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "513 + 495 + 177 + 241 + 428",
    "correct_answer": 1854,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "8272 + 9006",
    "correct_answer": 17278,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "5403 + 2934",
    "correct_answer": 8337,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "1 - 7 - 8 + 8 + 5 - 3 + 2 - 7 + 9 - 6 + 8 - 7 + 8 - 9 - 1 - 8 - 4 - 1 + 9 + 7 + 5",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "1225 + 5295",
    "correct_answer": 6520,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "579 * 483 + 591 + 214 - 862",
    "correct_answer": 279600,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "42 + 85 * 55 - 70 * 24",
    "correct_answer": 3037,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "5 + 5 + 1 - 6 + 7 - 3 + 2 + 8 + 2 - 5 + 5 + 1 - 5 - 4 - 6 - 2 + 3",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "8460 + 4389",
    "correct_answer": 12849,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "20 - 10 + 38",
    "correct_answer": 48,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "840 * 387 - 200 - 655 + 105",
    "correct_answer": 324330,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "959 - 949 + 318 + 968 + 314",
    "correct_answer": 1610,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "552 * 49",
    "correct_answer": 27048,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(69 + 91) * (95 - 76)",
    "correct_answer": 3040,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "8 - 22",
    "correct_answer": -14,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "17 * 42",
    "correct_answer": 714,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(37 + 75) * (52 - 92)",
    "correct_answer": -4480,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "63 - 29",
    "correct_answer": 34,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "16 + 4 - 24 + 21 + 2 + 12 + 6 - 22 + 9 - 21 - 26 + 21 - 24 + 27 - 18 + 22 - 11 + 4 - 27 - 4 - 22",
    "correct_answer": -55,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "1951 - 4242",
    "correct_answer": -2291,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "734 * 45 - 334 - 161 * 469",
    "correct_answer": -42813,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "3 - 6 - 8 - 7 + 5 + 5 + 5 + 5 - 6 + 6 - 7 + 7 + 7 + 7 - 3 + 5 + 4 + 5 + 6 - 7 - 6 - 4 + 9 + 5 + 4 - 8 - 8 - 1 - 7 + 8 + 7",
    "correct_answer": 25,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "37 * 28",
    "correct_answer": 1036,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "65 - 40",
    "correct_answer": 25,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "582 * 86",
    "correct_answer": 50052,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "119 * 29",
    "correct_answer": 3451,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "4136 - 6863",
    "correct_answer": -2727,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "(18 + 80) * (21 - 73)",
    "correct_answer": -5096,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "13 + 19 - 9 + 14 + 26 + 21 - 16 + 20 + 21 + 3 + 6 - 3 + 7 - 17 + 6 + 1 + 8 + 12 + 7 + 30 - 8",
    "correct_answer": 161,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "5 + 7 + 7 - 6 + 1 + 6 - 4 + 3 - 9 + 3 + 9 + 2 + 1 + 9 - 3 + 1 + 7",
    "correct_answer": 39,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "224 % 4",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "(71 + 53) * (46 - 54)",
    "correct_answer": -992,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "815 * 39",
    "correct_answer": 31785,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "870 % 17",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "9 + 98",
    "correct_answer": 107,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "99 + 81 - 64",
    "correct_answer": 116,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "17 + 23 * 78 - 16 * 16",
    "correct_answer": 1555,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "26 + 29 - 29 + 10 + 19 - 21 - 27 - 30 - 16 + 7 + 2 - 10 - 27 - 1 + 8 - 19 + 3 + 4 + 6 + 25 - 25 + 16 + 20 - 24",
    "correct_answer": -54,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "4 - 9 + 6 + 2 - 6 + 3 - 8 + 4 - 4 + 2 + 8 + 9 + 6 - 5 + 6 - 1 - 1 + 1 - 3 + 2 + 4 + 2 - 9 - 1 - 1 + 6 - 2 - 9 + 5 - 2",
    "correct_answer": 9,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "424 + 804 - 912 + 96 - 560",
    "correct_answer": -148,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "412 * 636",
    "correct_answer": 262032,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "7718 + 1391",
    "correct_answer": 9109,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "342 * 133 * 599 - 150 + 866",
    "correct_answer": 27246830,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1323 - 2841",
    "correct_answer": -1518,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "8 + 5 + 3 - 2 - 8 - 6 + 2 + 8 - 4 + 2 + 6 + 7 - 3 - 3 - 2 + 9 + 4 + 4 - 3 + 5 + 8 - 1 + 8 - 8 + 9 - 3 - 6 - 1 + 8 - 2 - 2 - 1 - 9",
    "correct_answer": 32,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(67 + 51) * (55 - 24)",
    "correct_answer": 3658,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "1 - 10 + 1 - 1 + 4 + 4 - 11 - 11 - 19 + 5 - 24 + 25 + 22 + 22 - 20 - 14 + 5 - 16 + 26 - 23 - 23 - 16 - 16 - 30 + 28 - 7 + 15",
    "correct_answer": -83,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(48 + 56) * (83 - 54)",
    "correct_answer": 3016,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "549 * 850",
    "correct_answer": 466650,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "63 + 92 - 57",
    "correct_answer": 98,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "61 + 66 * 76 - 96 * 86",
    "correct_answer": -3179,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "2 - 1 + 1 + 7 + 9 - 1 - 9 + 6 + 4 + 9 - 2 - 2 + 5 + 6 + 8 + 7 - 7 + 3 + 8 + 8 - 2",
    "correct_answer": 59,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "503 * 251",
    "correct_answer": 126253,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "313 * 70",
    "correct_answer": 21910,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "732 - 888 + 736 - 288 - 98",
    "correct_answer": 194,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "497 * 773",
    "correct_answer": 384181,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "790 * 636 * 283 * 590 * 246",
    "correct_answer": 20637532072800,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "553 * 90",
    "correct_answer": 49770,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "6 - 3 - 9 - 9 - 6 - 8 + 1 - 7 + 7 + 4 - 2 + 8 + 1 - 2 + 9 - 1 + 6 + 9 + 8 - 5 - 7 - 9 + 7 - 9 + 5 - 7 - 8 - 1 - 7",
    "correct_answer": -29,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "74 - 87",
    "correct_answer": -13,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "85 * 91",
    "correct_answer": 7735,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "39 - 132 + 514 * 623 * 380",
    "correct_answer": 121684267,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "813 * 14",
    "correct_answer": 11382,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "2336 - 2557",
    "correct_answer": -221,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "45 * 66",
    "correct_answer": 2970,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "186 - 736 * 39 + 844 + 237",
    "correct_answer": -27437,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "571 * 50",
    "correct_answer": 28550,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "3321 - 5014",
    "correct_answer": -1693,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "64 - 935 + 557 - 490 - 534",
    "correct_answer": -1338,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "8 + 6 + 1 + 16 - 18 + 28 - 18 - 20 - 17 - 13 - 10 - 24 + 6 + 9 - 24 - 21 - 28 - 2 + 19 + 22 + 15 + 24",
    "correct_answer": -41,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "614 % 8",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "850 % 6",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "10 + 40 - 60",
    "correct_answer": -10,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "138 % 13",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "932 + 214 - 696 + 39 * 159",
    "correct_answer": 6651,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "267 * 17",
    "correct_answer": 4539,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "460 % 13",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "144 - 201",
    "correct_answer": -57,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "79 + 95",
    "correct_answer": 174,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "41 * 73",
    "correct_answer": 2993,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "1 + 9 + 4 - 5 + 1 - 9 + 9 - 8 + 1 + 7 - 8 - 6 - 6 + 2 - 3 + 6 + 7 + 6 - 2 - 8 - 6 + 3 + 3 + 1 - 2 + 8 + 5 - 5 - 6 + 4 - 2 - 4 + 3 - 9",
    "correct_answer": -9,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "3588 + 8230",
    "correct_answer": 11818,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "(49 + 82) * (25 - 43)",
    "correct_answer": -2358,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "594 * 762 + 965 * 544 * 858",
    "correct_answer": 450868308,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "32 * 18",
    "correct_answer": 576,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "15 - 52 + 3",
    "correct_answer": -34,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "67 + 83 * 82 - 71 * 43",
    "correct_answer": 3820,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "83 - 20",
    "correct_answer": 63,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "9 + 12 + 7 + 22 + 11 + 29 - 29 - 30 - 11 + 16 + 29 - 18 - 6 + 10 + 13 + 17 - 17 + 26 + 15 - 12 + 8 - 1 + 23 - 18",
    "correct_answer": 105,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "89 + 68 * 22 - 77 * 43",
    "correct_answer": -1726,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "24 - 11 - 8 + 29 + 3 + 10 + 8 + 29 - 18 + 6 - 2 - 24 - 26 + 22 + 1 + 27 + 17 - 8 - 10 + 23 + 22 + 30 + 5 + 17",
    "correct_answer": 166,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "5055 - 5877",
    "correct_answer": -822,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "16 - 7 + 20 - 5 + 18 + 19 - 29 - 13 + 28 - 14 - 7 + 12 - 3 - 29 - 23 - 12 + 18 + 12 - 25 - 4 + 13 + 26",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "7516 - 4568",
    "correct_answer": 2948,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "7 + 2 - 7 - 4 + 2 + 3 - 1 + 6 + 5 - 6 - 3 - 9 + 7 - 5 + 4 - 2 + 1 - 5 + 6 - 6",
    "correct_answer": -5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "3444 - 5487",
    "correct_answer": -2043,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "16 - 13 - 22 + 6 - 22 - 28 + 27 - 14 - 1 + 19 - 8 + 2 + 24 + 16 + 13 + 12 - 28 - 14 + 13 + 18 - 16",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "9 + 6 + 7 - 5 + 2 + 4 + 1 - 3 + 5 - 4 + 4 + 4 + 4 + 5 - 1 - 8 - 7 + 4",
    "correct_answer": 27,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "45 * 87",
    "correct_answer": 3915,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "97 - 57",
    "correct_answer": 40,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "963 * 28",
    "correct_answer": 26964,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "428 * 838",
    "correct_answer": 358664,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "3 + 15 - 22 - 9 - 26 - 19 - 30 + 7 - 6 + 27 + 15 - 10 + 18 + 8 + 19 + 30 - 4 - 27 - 23 - 16 - 15 + 14 - 19 - 5 - 19 + 24",
    "correct_answer": -70,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "3 + 3 + 1 + 1 + 8 + 8 - 9 - 4 - 7 + 8 + 9 - 2 - 4 - 5 - 7 - 8 - 5 - 9 + 6 - 6 - 6 - 4 + 4 - 3 + 1 + 6 - 1 + 6 - 6 - 9 + 5",
    "correct_answer": -26,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "186 + 657 - 936 + 850 * 477",
    "correct_answer": 405357,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "488 * 851",
    "correct_answer": 415288,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "984 * 70",
    "correct_answer": 68880,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "27 * 23",
    "correct_answer": 621,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "5040 + 9123",
    "correct_answer": 14163,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "273 - 425",
    "correct_answer": -152,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "9019 + 9646",
    "correct_answer": 18665,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "319 * 976",
    "correct_answer": 311344,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "446 * 877",
    "correct_answer": 391142,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "248 * 31",
    "correct_answer": 7688,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "37 * 34",
    "correct_answer": 1258,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "325 * 43",
    "correct_answer": 13975,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "7895 - 6986",
    "correct_answer": 909,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "596 * 327 - 473 - 810 * 496",
    "correct_answer": -207341,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "9 + 5 + 2 - 2 + 4 - 1 + 6 - 8 - 3 - 9 - 1 + 7 - 6 - 9 + 8 + 1",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "479 * 972 * 901 * 162 + 603",
    "correct_answer": 67958156259,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "39 * 47",
    "correct_answer": 1833,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "31 * 15",
    "correct_answer": 465,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "4 + 15 - 24 - 25 - 9 - 21 - 24 - 18 - 15 + 15 + 29 + 26 - 13 - 28 - 21 - 25 + 30 + 27 + 27 - 24 - 17 - 18 + 11 + 7 + 18 - 10",
    "correct_answer": -83,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "81 + 25 * 73 - 81 * 40",
    "correct_answer": -1334,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "296 * 42",
    "correct_answer": 12432,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "2010 + 4641",
    "correct_answer": 6651,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "88 - 30",
    "correct_answer": 58,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "4 + 80 - 72",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "672 - 732 - 495 * 976 + 692",
    "correct_answer": -482488,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "9 - 5 - 9 + 1 + 9 - 8 + 7 - 8 + 3 + 2 + 6 - 1 + 5 - 7 - 3 + 7 - 2 + 1",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "896 * 179 * 35 * 655 * 326",
    "correct_answer": 1198637843200,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "87 + 40",
    "correct_answer": 127,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "2211 - 8357",
    "correct_answer": -6146,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "299 * 68",
    "correct_answer": 20332,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "567 + 720 * 187 + 695 * 767",
    "correct_answer": 668272,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "444 - 608",
    "correct_answer": -164,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "29 - 1 - 18 - 14 - 3 - 9 - 5 - 5 - 10 - 2 - 19 + 16 + 4 - 4 + 15 + 8 - 6 + 15 - 23 - 22 + 8",
    "correct_answer": -46,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "28 - 99 + 18",
    "correct_answer": -53,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "670 * 42",
    "correct_answer": 28140,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "480 * 89",
    "correct_answer": 42720,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "19 + 17 - 70",
    "correct_answer": -34,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "426 + 818 + 290 - 852 * 492",
    "correct_answer": -417650,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "276 - 450",
    "correct_answer": -174,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "434 + 386 - 412 * 977 + 239",
    "correct_answer": -401465,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "293 - 555 - 801 + 697 + 289",
    "correct_answer": -77,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "529 * 234 * 940 * 357 * 883",
    "correct_answer": 36679913492040,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "233 - 335",
    "correct_answer": -102,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "7 + 72",
    "correct_answer": 79,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "37 * 46",
    "correct_answer": 1702,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "19 + 10 + 5 + 23 + 2 + 9 - 13 - 14 - 21 + 24 + 19 + 5 + 10 + 28 - 11 + 18 - 25 + 4 + 20 - 7 - 13 + 24 - 8 + 7",
    "correct_answer": 115,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "61 - 67",
    "correct_answer": -6,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "6432 - 8052",
    "correct_answer": -1620,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "854 * 35",
    "correct_answer": 29890,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "717 * 79",
    "correct_answer": 56643,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "355 % 6",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "2 - 7 + 7 + 1 + 2 - 8 + 2 + 7 + 9 + 9 + 1 - 7 + 5 - 6 + 3 - 9 + 6 + 5 - 4 + 3 + 8 + 7 + 8 + 1 + 4 - 2 + 6 - 8 + 2 - 9",
    "correct_answer": 38,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "17 + 29 + 30 + 30 + 11 - 9 - 15 - 14 + 19 - 8 + 24 - 14 - 15 - 27 + 5 - 5 - 4 - 22 + 23 + 29 - 19 - 18 - 19 - 7 - 24",
    "correct_answer": -3,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "97 + 99",
    "correct_answer": 196,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "69 + 70 * 99 - 39 * 70",
    "correct_answer": 4269,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "133 * 74",
    "correct_answer": 9842,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "95 * 32",
    "correct_answer": 3040,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "8 + 9 - 1 - 1 - 5 + 7 - 8 - 3 - 7 - 5 - 2 - 2 - 9 - 5 - 7 + 9 - 7 - 8 + 1 + 6 + 2 - 2 + 7 + 7 - 9 + 3 - 9 - 6 + 6 - 8 + 7 - 1",
    "correct_answer": -33,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "31 * 26",
    "correct_answer": 806,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "957 + 83 + 763 * 510 - 29",
    "correct_answer": 390141,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "46 * 21",
    "correct_answer": 966,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "88 * 67",
    "correct_answer": 5896,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "3 + 5 + 5 - 3 + 7 + 4 + 4 + 5 + 8 + 8 + 6 + 9 + 3 + 7 - 4 + 7 + 5 - 9 + 5 + 4 + 8 + 2 + 3 - 8 - 6 + 1 - 2 + 1 + 8 + 2 + 6 - 8",
    "correct_answer": 86,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "646 * 714",
    "correct_answer": 461244,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "10 + 57",
    "correct_answer": 67,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "78 + 20 - 43",
    "correct_answer": 55,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "362 * 930",
    "correct_answer": 336660,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "6 + 8 + 5 + 9 - 2 - 1 - 4 + 8 + 1 + 4 + 1 - 9 - 7 - 7 + 4 - 8 - 1 + 9 + 9 - 3",
    "correct_answer": 22,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "201 * 98",
    "correct_answer": 19698,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "17 + 65 - 76",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "378 * 80",
    "correct_answer": 30240,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "8 + 1 + 2 + 8 + 1 + 7 + 4 - 3 + 7 - 3 + 8 + 5 + 3 - 9 - 8 - 5 + 8 + 6 - 8 - 3 + 8 + 2 + 6 - 2 - 8 - 4 - 3 + 7 + 7 + 7 - 9 + 9 + 2",
    "correct_answer": 51,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "43 + 10",
    "correct_answer": 53,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "72 + 102 + 846 * 918 * 934",
    "correct_answer": 725370726,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "34 + 14 * 41 - 72 * 13",
    "correct_answer": -328,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "525 * 864",
    "correct_answer": 453600,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "860 * 734 - 501 - 653 * 618",
    "correct_answer": 227185,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "426 - 606",
    "correct_answer": -180,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "(15 + 44) * (25 - 18)",
    "correct_answer": 413,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "847 - 132 * 534 + 599 - 875",
    "correct_answer": -69917,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2768 - 3628",
    "correct_answer": -860,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "251 * 989",
    "correct_answer": 248239,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "50 * 31",
    "correct_answer": 1550,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "398 - 533",
    "correct_answer": -135,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "947 * 10",
    "correct_answer": 9470,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "969 - 925 - 920 + 230 * 848",
    "correct_answer": 194164,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "377 * 778",
    "correct_answer": 293306,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "9 - 3 - 6 + 5 + 2 + 9 - 5 + 4 + 7 - 9 + 6 + 2 - 6 + 1 - 6 - 3 - 2 + 2 + 7 - 1 - 4 + 8 + 3 + 1 - 7 + 1 + 8 - 2 - 5 - 6 - 4",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "58 - 47 + 66",
    "correct_answer": 77,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "9 - 3 - 6 + 28 - 29 - 16 - 11 + 16 + 26 - 17 - 25 - 20 + 25 - 4 - 13 + 2 - 14 - 5 + 29 + 24 + 30",
    "correct_answer": 26,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "15 - 20 - 29 + 25 + 8 + 5 - 1 + 5 + 8 + 23 - 4 + 1 + 11 + 20 + 16 + 9 - 1 - 8 - 30 - 14 + 15 - 26 + 21 + 13 + 24",
    "correct_answer": 86,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(30 + 13) * (91 - 88)",
    "correct_answer": 129,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "24 - 9 + 22 - 30 - 8 + 18 - 9 - 1 - 2 + 21 - 13 - 3 - 12 + 26 + 14 + 25 + 27 + 22 + 16 - 11 + 4 - 12 - 29 + 6",
    "correct_answer": 86,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "379 - 514",
    "correct_answer": -135,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "78 * 78",
    "correct_answer": 6084,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "187 * 215",
    "correct_answer": 40205,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "(78 + 30) * (72 - 69)",
    "correct_answer": 324,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "4674 - 6434",
    "correct_answer": -1760,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "(10 + 96) * (27 - 95)",
    "correct_answer": -7208,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "393 * 86",
    "correct_answer": 33798,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "43 * 32",
    "correct_answer": 1376,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "176 - 556 + 134 - 424 + 796",
    "correct_answer": 126,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "454 - 691",
    "correct_answer": -237,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "801 * 44",
    "correct_answer": 35244,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "3 + 16 - 23 - 4 - 11 - 30 - 2 + 25 - 20 + 1 + 20 - 1 - 14 + 26 - 21 - 6 - 8 - 20 - 3 - 26 - 8",
    "correct_answer": -106,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "2 - 6 - 3 - 7 - 8 + 1 - 3 - 1 - 2 + 3 - 5 + 6 + 3 - 2 + 1 - 4 + 4 + 4 + 8 + 1 + 1 + 6 + 7 + 6 - 5 + 2 + 6 + 5 - 8 + 3 - 5",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "27 + 54 * 47 - 30 * 90",
    "correct_answer": -135,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "(79 + 88) * (22 - 16)",
    "correct_answer": 1002,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "14 - 2",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "3755 + 8492",
    "correct_answer": 12247,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "169 % 19",
    "correct_answer": 17,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "4490 + 3480",
    "correct_answer": 7970,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "7524 + 6228",
    "correct_answer": 13752,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "(36 + 66) * (64 - 35)",
    "correct_answer": 2958,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "50 + 89",
    "correct_answer": 139,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(43 + 89) * (28 - 17)",
    "correct_answer": 1452,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "7815 + 2406",
    "correct_answer": 10221,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "15 - 3 - 17 + 15 - 11 - 18 + 23 - 7 + 5 + 1 + 10 - 8 - 8 - 11 - 5 + 16 - 3 - 29 + 17 + 28 + 3 - 27 - 3 + 3 + 15 - 14 - 16",
    "correct_answer": -29,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "960 + 770 * 865 * 316 * 752",
    "correct_answer": 158274794560,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "636 + 69 * 595 * 654 - 99",
    "correct_answer": 26850507,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "16 + 20 * 90 - 52 * 29",
    "correct_answer": 308,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "50 - 581 * 538 + 995 - 204",
    "correct_answer": -311737,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "4434 - 8183",
    "correct_answer": -3749,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "4 + 7 + 6 + 7 + 5 - 8 + 5 + 4 + 2 + 7 + 8 - 3 + 8 + 2 + 9 + 9 + 5 + 2 - 3 - 5 - 7",
    "correct_answer": 64,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "44 + 87 - 77",
    "correct_answer": 54,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "18 + 55",
    "correct_answer": 73,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(72 + 10) * (51 - 25)",
    "correct_answer": 2132,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "41 + 79 * 70 - 77 * 73",
    "correct_answer": -50,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "1505 + 4613",
    "correct_answer": 6118,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "59 + 54",
    "correct_answer": 113,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(67 + 32) * (88 - 83)",
    "correct_answer": 495,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "7 - 3 - 7 + 4 - 9 - 4 - 9 - 7 + 4 + 8 + 2 - 2 - 9 + 7 + 8 - 7 + 2 + 2 - 9 - 4 + 3",
    "correct_answer": -23,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "13 + 77 * 75 - 40 * 53",
    "correct_answer": 3668,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "2 + 3 + 1 + 7 + 9 + 4 - 2 + 9 + 1 - 1 + 4 - 8 + 1 + 5 + 1 - 8 + 4 - 8 - 8 + 9 - 2 - 7 - 3 - 6 - 1 + 5 - 5 - 8 - 6 - 1 + 2 + 8 - 6",
    "correct_answer": -5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "8 - 9 + 9 - 7 + 5 + 2 + 9 - 9 - 5 - 1 - 6 + 4 - 3 + 1 + 6 + 6 + 1 + 6 - 1 + 7 + 4 - 3",
    "correct_answer": 24,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "725 * 277 - 77 * 440 * 756",
    "correct_answer": -25412455,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "126 % 8",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "74 + 6",
    "correct_answer": 80,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "43 * 26",
    "correct_answer": 1118,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(68 + 57) * (67 - 69)",
    "correct_answer": -250,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "133 * 684 + 194 + 291 * 261",
    "correct_answer": 167117,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "87 * 60",
    "correct_answer": 5220,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "29 * 28",
    "correct_answer": 812,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "61 * 91",
    "correct_answer": 5551,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "28 + 25 + 22 - 22 + 17 - 1 - 22 - 6 + 11 - 23 - 5 - 27 + 14 - 9 + 4 - 22 + 2 + 30 + 20 + 22 - 4 - 5 - 4 - 26 + 4 - 4",
    "correct_answer": 19,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "69 - 55",
    "correct_answer": 14,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "59 + 19 * 73 - 48 * 92",
    "correct_answer": -2970,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "32 * 36",
    "correct_answer": 1152,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "379 * 717 * 996 - 701 - 833",
    "correct_answer": 270654494,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1 + 8 + 9 - 5 + 3 + 4 - 6 - 5 - 6 + 3 - 6 + 8 - 8 + 2 - 4 + 9 - 5 + 8 + 3 + 5 + 2 + 7 - 6 - 8 - 1 - 2 + 3 + 4 - 9 + 7 + 9 + 8 + 2 - 9 - 9 + 4 + 8",
    "correct_answer": 28,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "258 * 480",
    "correct_answer": 123840,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "158 * 32",
    "correct_answer": 5056,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "642 + 471 * 388 * 710 + 479",
    "correct_answer": 129752201,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "8851 - 7566",
    "correct_answer": 1285,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "5942 - 4366",
    "correct_answer": 1576,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "496 % 6",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "41 * 24",
    "correct_answer": 984,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "3525 + 7932",
    "correct_answer": 11457,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "56 * 98",
    "correct_answer": 5488,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "2195 - 1273",
    "correct_answer": 922,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "628 * 170 * 985 + 937 * 601",
    "correct_answer": 105721737,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "93 + 66 * 70 - 47 * 16",
    "correct_answer": 3961,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "630 % 7",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "376 - 441",
    "correct_answer": -65,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "388 - 426",
    "correct_answer": -38,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "407 * 138",
    "correct_answer": 56166,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "3881 - 5254",
    "correct_answer": -1373,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "2615 + 5239",
    "correct_answer": 7854,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "30 + 82 * 94 - 46 * 19",
    "correct_answer": 6864,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "7 + 7 - 2 - 4 + 8 + 7 - 8 + 2 - 4 - 1 + 3 - 3 + 5 - 9 - 4 + 1 + 4 + 4 - 5 - 2 - 2 + 5 + 3 - 9 + 5 + 1 + 5 + 6 + 5 - 6",
    "correct_answer": 19,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "4 - 3 + 1 - 9 + 6 - 7 + 6 - 5 + 2 - 1 + 2 + 3 - 7 + 6 - 8 - 6 - 7 + 4 - 1",
    "correct_answer": -20,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "236 % 4",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "277 * 599",
    "correct_answer": 165923,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "1 - 3 + 12 + 23 - 1 - 30 - 18 - 6 - 12 - 15 - 4 - 30 + 16 - 14 + 16 + 23 + 20 + 26 + 18 + 10 + 9 + 1 - 4 - 6",
    "correct_answer": 32,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "82 + 69 * 73 - 74 * 83",
    "correct_answer": -1023,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "785 * 64 + 544 - 778 + 524",
    "correct_answer": 50530,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "95 + 36",
    "correct_answer": 131,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "3 - 1 - 1 + 3 - 7 + 5 + 1 + 9 + 1 - 6 + 4 - 2 - 5 + 5 - 3 + 7 - 1 + 2 - 2 + 1 + 3 - 6 - 1 - 5 - 8 + 5 - 4 + 6 + 1 - 2 + 2 - 5 + 4 - 9",
    "correct_answer": -6,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "190 * 290",
    "correct_answer": 55100,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "3 + 4 + 2 + 1 + 6 + 7 - 2 - 5 - 3 - 6 - 3 + 4 - 7 + 5 - 5 - 8 - 7 + 7",
    "correct_answer": -7,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "461 * 95",
    "correct_answer": 43795,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(43 + 34) * (81 - 54)",
    "correct_answer": 2079,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "456 * 295",
    "correct_answer": 134520,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "13 + 2 + 27 - 11 - 21 + 5 + 9 - 29 - 30 + 26 - 2 + 29 + 4 + 20 - 1 + 12 - 16 + 28 - 7 - 2 - 2 + 14",
    "correct_answer": 68,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "76 * 70",
    "correct_answer": 5320,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "5503 + 4683",
    "correct_answer": 10186,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "473 * 61",
    "correct_answer": 28853,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "981 * 97",
    "correct_answer": 95157,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "22 - 29 + 9 - 21 - 7 + 2 - 16 + 26 - 14 - 8 - 16 - 22 - 5 + 16 - 14 + 19 + 19 + 13 - 22 - 19 - 1 + 26 + 11 + 12",
    "correct_answer": -19,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "263 - 345 + 603 * 923 + 978",
    "correct_answer": 557465,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "910 % 7",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "39 * 24",
    "correct_answer": 936,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "4 + 8 + 9 - 3 + 3 + 1 + 6 + 7 - 7 + 9 - 1 - 1 - 3 - 6 - 7 - 4 - 2 + 4 - 6 - 8 + 5 - 2 + 3 + 8 + 4 + 7 + 4 + 9 + 1 + 1 + 7 + 2 + 7 + 2 + 4",
    "correct_answer": 65,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "755 * 53",
    "correct_answer": 40015,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "29 + 14 + 14 - 23 + 23 + 9 - 7 + 26 - 16 + 7 - 7 - 21 - 8 - 28 + 6 - 22 + 24 - 1 + 6 + 15 - 29 + 9 - 12 - 3 - 5 - 2 + 19",
    "correct_answer": 17,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "74 + 25",
    "correct_answer": 99,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "33 * 50",
    "correct_answer": 1650,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "55 * 54",
    "correct_answer": 2970,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(82 + 29) * (27 - 16)",
    "correct_answer": 1221,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "7 + 1 + 3 + 6 - 3 + 5 - 3 - 4 - 1 + 6 + 3 + 5 - 1 - 8 + 5 + 4 - 6 - 4 + 2 - 8",
    "correct_answer": 9,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "71 + 16 * 96 - 16 * 64",
    "correct_answer": 583,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "143 % 14",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "(79 + 64) * (49 - 73)",
    "correct_answer": -3432,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "7 + 5 - 8 + 3 + 6 - 3 - 9 - 8 - 9 - 3 + 5 - 5 + 9 + 5 + 5 - 4 + 2 - 9 - 8 + 3 + 7 + 3",
    "correct_answer": -6,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "177 - 732 + 456 - 926 - 51",
    "correct_answer": -1076,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "26 - 28 - 12 + 2 - 13 - 24 - 28 + 29 - 9 - 24 - 3 - 29 + 24 - 20 + 25 - 24 + 16 + 17 - 23 + 28 - 3 + 27 - 8 - 22 + 25 - 14",
    "correct_answer": -65,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "40 * 50",
    "correct_answer": 2000,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "28 + 67 * 54 - 88 * 31",
    "correct_answer": 918,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "52 * 52",
    "correct_answer": 2704,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "30 - 13 - 23 + 26 - 22 - 3 - 21 + 2 + 24 + 22 - 22 + 24 - 4 + 22 - 29 + 23 - 22 + 26 + 12 - 20 + 24 + 5 - 2 - 16",
    "correct_answer": 43,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "398 % 16",
    "correct_answer": 14,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "88 + 77",
    "correct_answer": 165,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "540 * 431",
    "correct_answer": 232740,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "545 * 684 + 97 - 156 * 420",
    "correct_answer": 307357,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "28 * 25",
    "correct_answer": 700,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "9796 - 4063",
    "correct_answer": 5733,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "1254 - 4089",
    "correct_answer": -2835,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "8 + 2 - 4 - 5 + 8 + 7 + 6 + 6 + 6 + 9 - 1 + 7 + 5 + 3 - 4 - 6 - 7 + 6",
    "correct_answer": 46,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "700 * 35",
    "correct_answer": 24500,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "475 - 531 - 575 - 403 + 241",
    "correct_answer": -793,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "204 * 46",
    "correct_answer": 9384,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "379 % 17",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "255 * 269 - 403 * 664 * 381",
    "correct_answer": -101883957,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "310 - 323",
    "correct_answer": -13,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "24 + 31 * 99 - 60 * 81",
    "correct_answer": -1767,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "4273 + 9939",
    "correct_answer": 14212,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "48 * 45",
    "correct_answer": 2160,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "19 + 1 - 21 + 2 + 28 - 5 - 23 + 22 + 17 - 12 - 15 - 28 + 26 - 3 - 22 - 5 + 17 + 29 - 4 - 14 - 10 - 1 + 15 - 21 - 20 + 13 + 19",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "74 * 62",
    "correct_answer": 4588,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "5 + 4 + 3 - 9 + 4 - 1 + 2 - 3 - 6 - 9 + 6 + 9 - 4 + 8 - 6 - 9 + 2 - 7 + 2",
    "correct_answer": -9,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "50 - 44",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "5 - 1 - 8 + 4 - 6 - 2 - 8 - 2 - 6 + 2 + 9 + 7 + 1 + 3 - 6 - 2 - 7 - 6 - 7 + 3 - 7 - 1",
    "correct_answer": -35,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "98 + 27",
    "correct_answer": 125,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "49 * 36",
    "correct_answer": 1764,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "675 * 82",
    "correct_answer": 55350,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "672 * 302",
    "correct_answer": 202944,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "231 * 16",
    "correct_answer": 3696,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "351 - 708 + 420 * 657 - 102",
    "correct_answer": 275481,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "4 - 6 - 7 - 5 - 9 - 4 - 7 + 9 + 9 - 5 + 2 - 5 + 1 - 3 + 3 - 8 - 4 - 7 + 1 + 2 - 7 + 1 - 9 - 9 + 4 + 4 + 3 + 5 + 1 + 1",
    "correct_answer": -45,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "10 - 28 - 3 - 4 + 27 - 11 + 8 + 15 + 16 - 13 + 3 - 16 + 16 - 14 + 8 + 6 - 15 + 28 - 22 - 20 - 5 + 15 + 28 + 9 - 18 + 6",
    "correct_answer": 26,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "356 % 9",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "67 - 47 + 80",
    "correct_answer": 100,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "56 + 17",
    "correct_answer": 73,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "3734 + 7024",
    "correct_answer": 10758,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "3248 + 1185",
    "correct_answer": 4433,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "(27 + 31) * (23 - 93)",
    "correct_answer": -4060,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "168 - 395",
    "correct_answer": -227,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "326 * 715 * 930 + 941 + 450",
    "correct_answer": 216775091,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "19 + 84",
    "correct_answer": 103,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "1862 + 3938",
    "correct_answer": 5800,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "10 + 3 - 7 + 6 - 22 + 25 + 17 + 3 + 15 + 10 + 30 - 23 + 1 - 25 + 17 - 17 - 18 - 9 - 7 + 5 + 27 - 6 - 28 - 16 + 7",
    "correct_answer": -2,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "88 * 73",
    "correct_answer": 6424,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "9499 + 4621",
    "correct_answer": 14120,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "42 - 44",
    "correct_answer": -2,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "93 * 99",
    "correct_answer": 9207,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "59 * 47",
    "correct_answer": 2773,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "10 + 86 * 98 - 69 * 17",
    "correct_answer": 7265,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "322 - 497",
    "correct_answer": -175,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "44 * 24",
    "correct_answer": 1056,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(24 + 33) * (38 - 81)",
    "correct_answer": -2451,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "3289 - 4277",
    "correct_answer": -988,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "9 - 61 + 57",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "732 * 67",
    "correct_answer": 49044,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "887 % 16",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "451 - 147 - 742 + 509 * 592",
    "correct_answer": 300890,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "9336 + 1042",
    "correct_answer": 10378,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "283 * 30 * 490 - 32 * 396",
    "correct_answer": 4147428,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "134 * 86",
    "correct_answer": 11524,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "20 - 9 + 17 + 14 + 18 - 15 + 10 - 7 - 2 - 5 - 9 + 1 - 12 + 16 + 5 + 16 - 20 + 26 - 30 + 25 + 24 - 8 - 24 + 7 - 19 + 1",
    "correct_answer": 40,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "19 - 8 - 4 + 1 - 13 - 16 + 12 - 23 - 14 + 18 + 7 + 14 - 13 + 17 - 15 - 5 + 27 - 8 - 8 - 13 + 6 + 25",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "661 % 19",
    "correct_answer": 15,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "13 + 16 + 26 - 23 + 6 + 29 - 4 + 12 - 5 + 2 + 13 + 25 - 19 - 9 + 4 - 23 + 11 + 14 - 18 - 6 - 27 + 29",
    "correct_answer": 66,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "825 * 130 + 878 * 828 - 434",
    "correct_answer": 833800,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "375 * 70",
    "correct_answer": 26250,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(90 + 78) * (30 - 21)",
    "correct_answer": 1512,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "38 + 5",
    "correct_answer": 43,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "194 + 912 * 652 + 538 - 600",
    "correct_answer": 594756,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "6 + 8 - 7 - 4 + 4 + 8 + 8 - 2 + 4 + 6 - 1 + 6 + 1 + 2 + 4 + 5 + 5 - 9 - 2",
    "correct_answer": 42,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "35 - 65",
    "correct_answer": -30,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "755 * 73",
    "correct_answer": 55115,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "88 - 82",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "616 * 445",
    "correct_answer": 274120,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "48 + 37",
    "correct_answer": 85,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "306 * 51 + 166 - 390 - 393",
    "correct_answer": 14989,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "22 + 10 * 77 - 53 * 77",
    "correct_answer": -3289,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "1 - 1 - 6 + 4 - 7 + 4 + 8 - 4 + 3 - 6 - 3 + 9 - 3 + 4 + 3 + 4 - 4 - 8 + 1 + 5 + 4 + 1 + 8 + 4 - 4 - 9 + 9 + 5 + 2 - 8 + 1 + 4 - 9 - 6 + 2 - 7",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "168 - 403",
    "correct_answer": -235,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "630 * 238",
    "correct_answer": 149940,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "34 * 53",
    "correct_answer": 1802,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "6161 + 7438",
    "correct_answer": 13599,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "810 % 18",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "88 - 69",
    "correct_answer": 19,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(19 + 48) * (73 - 56)",
    "correct_answer": 1139,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "399 + 54 - 944 * 589 + 893",
    "correct_answer": -554670,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(86 + 92) * (13 - 93)",
    "correct_answer": -14240,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "(50 + 95) * (10 - 46)",
    "correct_answer": -5220,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "145 * 937",
    "correct_answer": 135865,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "15 - 2 - 5 - 3 + 24 + 10 + 28 - 15 + 22 + 15 - 2 + 18 - 29 - 8 - 12 + 5 - 20 - 13 + 24 + 22 - 11 - 4 + 26 + 11 - 1",
    "correct_answer": 95,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "81 + 94 * 90 - 81 * 72",
    "correct_answer": 2709,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "(30 + 18) * (84 - 31)",
    "correct_answer": 2544,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "52 * 70",
    "correct_answer": 3640,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "26 * 19",
    "correct_answer": 494,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "823 * 945 - 321 - 745 * 101",
    "correct_answer": 702169,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "161 * 464",
    "correct_answer": 74704,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "66 * 36",
    "correct_answer": 2376,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "845 * 143",
    "correct_answer": 120835,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "277 - 300",
    "correct_answer": -23,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "244 * 811",
    "correct_answer": 197884,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "3 + 8 + 7 - 5 - 6 - 1 + 6 + 3 - 5 - 1 + 2 - 2 + 4 - 4 + 3 - 5 + 2 + 4 - 1 - 7 + 9 - 8 + 6 + 7 - 7 + 1 - 7 + 7 - 9 + 6 + 6 + 3 + 7 - 7 - 4",
    "correct_answer": 15,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "308 * 552 + 968 + 536 * 794",
    "correct_answer": 596568,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "79 - 73",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "241 * 371",
    "correct_answer": 89411,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "3111 - 3783",
    "correct_answer": -672,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "622 * 76",
    "correct_answer": 47272,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "157 - 748 - 683 + 149 * 150",
    "correct_answer": 21076,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "226 - 307",
    "correct_answer": -81,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "7 + 9 - 6 - 5 + 4 - 5 - 2 - 9 - 2 - 2 + 8 + 4 - 6 - 5 - 2 + 4 + 2 + 8 + 6 - 4 - 6 - 4 - 8 + 9 + 7 + 6 - 5 - 3 + 2 + 2 + 6 - 7 - 2",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "30 + 45 * 47 - 93 * 89",
    "correct_answer": -6132,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "35 - 40",
    "correct_answer": -5,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "503 * 169 * 481 - 927 - 483",
    "correct_answer": 40886957,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "16 + 59",
    "correct_answer": 75,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "7563 + 7098",
    "correct_answer": 14661,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "6 + 6 + 2 - 1 + 5 + 9 - 1 - 1 + 6 + 7 + 1 + 2 + 3 - 1 - 4 + 1 + 4 - 7",
    "correct_answer": 37,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "6 + 7 - 9 - 5 - 4 + 9 + 3 - 1 + 5 - 3 - 8 - 5 + 4 - 4 + 1 - 2 + 3 - 7 - 3 + 2 + 8 + 1 - 9 - 7 + 7 + 2 + 8 - 3 - 7 - 2 + 7 + 8 + 2 + 2 + 9 + 8",
    "correct_answer": 23,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "472 * 894",
    "correct_answer": 421968,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "3 + 7 + 5 - 8 + 3 - 1 + 3 - 3 + 3 + 9 + 1 - 8 + 5 + 6 - 7 - 6 + 6 + 1 - 8 + 7",
    "correct_answer": 18,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "4572 - 4871",
    "correct_answer": -299,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "9 - 36 + 99",
    "correct_answer": 72,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "1 - 2 - 4 - 1 - 8 - 5 - 8 - 2 + 1 + 1 - 2 - 5 - 9 - 6 + 9 + 5 + 2",
    "correct_answer": -33,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "547 % 15",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "646 * 49",
    "correct_answer": 31654,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "495 % 13",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "36 * 44",
    "correct_answer": 1584,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(35 + 55) * (78 - 99)",
    "correct_answer": -1890,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "576 + 426 + 505 * 427 + 249",
    "correct_answer": 216886,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "913 * 825",
    "correct_answer": 753225,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "71 * 78",
    "correct_answer": 5538,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "11 - 23 + 3 - 12 + 22 - 8 - 3 + 5 + 14 + 18 - 11 + 13 + 22 + 1 + 12 + 21 + 9 + 9 + 14 - 11 + 17 - 23",
    "correct_answer": 100,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "29 - 17 - 23 - 14 - 13 - 20 + 18 + 23 + 15 + 26 - 8 - 15 + 20 - 30 - 10 + 23 - 30 + 7 + 24 + 18 + 29 + 4 - 2 + 29 + 7",
    "correct_answer": 90,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "3328 - 4084",
    "correct_answer": -756,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "5 - 5 + 5 - 3 - 9 - 1 - 5 - 7 + 1 - 9 - 3 + 4 + 4 - 9 - 9 + 8 + 2 + 4",
    "correct_answer": -27,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "8 + 22 + 28 + 18 - 26 + 18 - 18 + 29 + 4 - 25 + 17 - 10 + 23 - 2 - 11 - 30 + 5 + 4 + 15 - 23 + 17 + 1 - 28 - 14",
    "correct_answer": 22,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "3 - 5 + 9 - 2 - 4 - 7 + 9 + 6 + 2 + 6 + 3 + 9 + 1 + 8 - 7 + 7 + 5 + 3 + 8 + 2 - 4 + 8 - 5 - 3 + 2 - 2 + 7 - 1 + 3 + 3 - 1 + 9",
    "correct_answer": 72,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "77 - 66 + 96",
    "correct_answer": 107,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "27 + 52 * 24 - 21 * 27",
    "correct_answer": 708,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "76 + 18 * 47 - 50 * 30",
    "correct_answer": -578,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "386 - 635",
    "correct_answer": -249,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "24 + 12 - 11 + 19 + 7 - 16 + 23 - 26 - 18 + 15 - 17 + 27 + 2 - 22 + 6 + 20 + 13 - 12 - 7 + 26 + 15 - 5 + 27",
    "correct_answer": 102,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "29 * 42",
    "correct_answer": 1218,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "14 + 11 + 26 - 19 - 22 + 12 - 11 - 16 - 24 + 25 - 15 + 7 + 30 - 22 - 7 - 21 - 7 + 8 - 3 - 16 + 2 - 29 + 6 - 20 + 17",
    "correct_answer": -74,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "8996 + 6362",
    "correct_answer": 15358,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "952 * 939",
    "correct_answer": 893928,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "828 % 8",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "708 * 771",
    "correct_answer": 545868,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "31 * 670 * 45 + 688 * 717",
    "correct_answer": 1427946,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "30 + 12 - 3 - 5 + 16 - 27 + 4 - 1 + 25 - 30 - 18 - 17 - 9 - 24 - 4 + 16 - 12 - 14 - 7 + 10 + 11 - 11",
    "correct_answer": -58,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "4 - 6 + 42",
    "correct_answer": 40,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "29 * 48",
    "correct_answer": 1392,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "81 - 80",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "77 + 57 * 55 - 74 * 92",
    "correct_answer": -3596,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "6 - 7 - 2 - 4 - 3 - 6 - 8 + 7 - 5 + 4 + 9 - 2 + 4 + 1 - 3 - 2 + 1 - 7 + 6 + 3 - 4 + 4 - 2 + 4 + 9 - 1 + 1 + 1 - 3 + 5 + 6 - 6 - 4 - 9 + 2 - 5 - 4 + 3 - 6",
    "correct_answer": -17,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "378 * 99",
    "correct_answer": 37422,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "201 * 423",
    "correct_answer": 85023,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "18 + 22 + 12 + 6 - 3 + 26 - 11 - 12 + 26 - 26 - 28 + 20 - 14 - 8 - 21 - 22 - 24 + 29 - 1 + 30 + 25 - 26 - 28 + 25",
    "correct_answer": 15,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "989 % 4",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "59 - 39 + 26",
    "correct_answer": 46,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "740 * 402 * 443 - 621 + 84",
    "correct_answer": 131783103,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "259 * 875",
    "correct_answer": 226625,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "235 * 23",
    "correct_answer": 5405,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "305 + 991 + 121 + 292 + 723",
    "correct_answer": 2432,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "6 - 7 - 8 + 9 - 8 - 1 + 2 + 5 + 3 - 2 + 6 - 1 - 9 + 4 + 1 - 2 + 9 - 9 - 9 + 1 + 9 - 5 - 3 + 4 + 8 - 5 - 2 - 2 + 3 + 1 - 4 + 8 - 9 + 1 + 2 + 2 + 8",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "5 - 24 - 5 - 22 + 10 - 20 - 13 - 12 - 19 + 15 - 25 - 8 - 10 + 26 - 27 - 19 + 10 + 5 - 21 + 13 + 2 + 28",
    "correct_answer": -111,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "392 + 614 - 867 + 167 - 93",
    "correct_answer": 213,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "6 + 10 - 27 - 22 - 1 + 10 - 10 - 9 + 1 + 14 - 7 - 7 - 5 - 12 + 13 + 18 - 5 + 24 + 27 - 7 - 4 + 12 + 27 - 19 + 9 - 28",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "818 * 649",
    "correct_answer": 530882,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "183 % 4",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "981 * 51",
    "correct_answer": 50031,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "93 * 47",
    "correct_answer": 4371,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "8 - 6 + 25 - 20 - 24 + 30 - 30 + 27 + 5 - 13 - 23 + 17 + 30 + 1 + 3 + 23 + 8 - 4 - 15 - 11 - 21 - 21 + 29 + 6 + 18",
    "correct_answer": 42,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "85 * 39",
    "correct_answer": 3315,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "4 - 10 + 21 + 27 + 19 - 17 + 26 + 11 - 25 - 30 + 22 + 11 - 27 + 4 + 30 - 15 + 6 + 2 - 16 - 10 + 16 + 19 + 23 + 16 - 16 + 28 + 1",
    "correct_answer": 120,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "51 * 53",
    "correct_answer": 2703,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "76 + 28 - 30",
    "correct_answer": 74,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "2506 - 6432",
    "correct_answer": -3926,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "7 - 6 + 9 - 6 + 2 - 3 - 8 + 5 + 1 - 8 - 3 + 8 - 7 + 3 - 8 + 6 - 2 + 2 + 2 + 1 - 3 - 8 - 1 + 7 + 5 + 9 + 7 + 6 + 5",
    "correct_answer": 22,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(13 + 56) * (88 - 72)",
    "correct_answer": 1104,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "40 + 31",
    "correct_answer": 71,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "68 + 36 * 38 - 57 * 30",
    "correct_answer": -274,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "13 + 29 - 18 - 1 - 26 - 22 + 7 - 30 + 18 - 22 - 25 - 13 + 22 - 2 + 17 - 10 - 13 - 13 - 20 + 23 + 14 - 22 - 7 + 17 - 29",
    "correct_answer": -113,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "421 * 50",
    "correct_answer": 21050,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "15 + 30 + 23 - 5 + 12 - 19 - 11 + 22 + 10 + 3 + 14 + 6 - 27 - 28 + 20 + 2 - 23 - 27 - 7 + 9 - 13 - 10",
    "correct_answer": -4,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(73 + 64) * (25 - 12)",
    "correct_answer": 1781,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "527 * 123 - 71 * 275 - 529",
    "correct_answer": 44767,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "375 * 33",
    "correct_answer": 12375,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "5 + 8 + 9 - 1 + 1 + 7 + 6 + 8 - 8 + 1 + 1 - 8 + 2 - 9 + 4 + 2 + 2 + 7 - 9 + 2 - 8 + 7 + 9 + 4 + 2 - 1 + 1 + 9 + 4 + 9 + 6 - 8 + 9 - 6 - 4 + 9",
    "correct_answer": 72,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "5 + 2 - 9 + 8 + 9 - 1 + 9 - 6 + 7 + 3 + 1 + 3 + 3 + 4 - 8 - 7 - 2 - 5 + 7 - 9 - 1 + 6 - 3 + 2 + 6 + 1 + 7 + 9 - 6 - 3 - 5 + 1",
    "correct_answer": 28,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "22 - 10 - 9 - 9 + 11 + 15 + 29 + 4 + 30 - 18 + 24 + 17 - 30 - 11 - 24 - 27 + 25 - 24 + 18 + 21 + 11 + 4 - 18 - 16 - 26",
    "correct_answer": 9,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "464 * 29",
    "correct_answer": 13456,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "192 * 80",
    "correct_answer": 15360,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "2 + 2 - 7 - 1 + 2 - 3 - 3 - 4 - 9 - 8 + 1 - 9 + 6 - 2 + 9 + 5 + 1 + 9 + 4 - 2 - 4 - 2 - 9 + 6 - 9 + 5 - 3 + 5 + 1 - 5 + 1 + 4 + 4 + 7 + 6 + 5 - 5 + 7",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "98 - 446 * 193 * 620 * 654",
    "correct_answer": -34902907342,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(17 + 92) * (17 - 73)",
    "correct_answer": -6104,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "89 + 73 * 53 - 43 * 77",
    "correct_answer": 647,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "3325 - 6187",
    "correct_answer": -2862,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "848 * 927",
    "correct_answer": 786096,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "3 + 2 + 7 + 7 + 4 - 3 + 3 + 6 + 2 - 8 + 3 + 8 - 6 - 4 + 9 + 4 + 3 + 3 - 9 - 9 - 8 - 6 + 7 + 2 - 4 - 6 - 2 - 6 - 8 + 8 + 2 + 9 - 1 - 6",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "976 * 58",
    "correct_answer": 56608,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "409 - 615",
    "correct_answer": -206,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "17 - 2 + 46",
    "correct_answer": 61,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "326 * 720",
    "correct_answer": 234720,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "986 % 13",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "930 % 7",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "27 - 6 + 19 + 9 + 6 + 21 + 15 - 6 + 13 + 11 + 15 - 28 - 30 - 22 + 4 + 20 - 7 + 7 + 1 + 19 + 29 - 22",
    "correct_answer": 95,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "499 * 49",
    "correct_answer": 24451,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(56 + 80) * (54 - 52)",
    "correct_answer": 272,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "3 - 23 - 30 - 17 + 1 - 19 - 13 - 28 - 29 + 8 - 21 - 18 + 18 - 21 + 25 - 16 - 22 - 14 - 28 + 30 + 15 + 11 + 9 + 12 + 19",
    "correct_answer": -148,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "421 * 55",
    "correct_answer": 23155,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "33 - 26 + 23",
    "correct_answer": 30,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "2749 - 5125",
    "correct_answer": -2376,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "3298 + 4065",
    "correct_answer": 7363,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "70 - 60",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "923 * 21",
    "correct_answer": 19383,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "4 - 4 + 6 - 6 - 9 - 8 - 1 + 6 + 7 + 2 - 4 + 2 + 9 + 8 + 6 - 4 - 1 + 9 - 9 - 9 + 1 - 1 + 5 + 8 - 2 + 9 - 7 - 3 + 2 + 6 - 7 + 4 - 1 - 6 + 7",
    "correct_answer": 19,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "85 + 10 * 43 - 59 * 51",
    "correct_answer": -2494,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "641 * 141",
    "correct_answer": 90381,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "52 + 91 * 21 - 73 * 38",
    "correct_answer": -811,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "1304 - 4141",
    "correct_answer": -2837,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "5 - 5 - 2 - 2 - 8 - 9 + 9 + 4 + 7 + 4 + 5 - 9 + 2 - 5 - 7 + 7 + 1 - 2 + 1 - 3 + 6",
    "correct_answer": -1,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "7 - 34",
    "correct_answer": -27,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "15 - 22 - 24 + 16 - 2 - 3 - 28 + 1 - 16 + 25 - 20 + 10 + 29 + 2 - 11 + 22 - 29 - 30 + 27 + 15 - 21 - 16 - 13 + 9 + 5 - 10",
    "correct_answer": -69,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "465 + 698 - 371 * 857 - 376",
    "correct_answer": -317160,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "36 * 22",
    "correct_answer": 792,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "96 * 77",
    "correct_answer": 7392,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "15 + 12 * 61 - 91 * 87",
    "correct_answer": -7170,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "315 * 31",
    "correct_answer": 9765,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "100 * 843",
    "correct_answer": 84300,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "36 + 71 * 55 - 82 * 75",
    "correct_answer": -2209,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "620 * 826",
    "correct_answer": 512120,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "757 - 797 * 305 + 195 + 930",
    "correct_answer": -241203,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "186 * 93",
    "correct_answer": 17298,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "751 * 10",
    "correct_answer": 7510,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "1 - 53",
    "correct_answer": -52,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "777 * 42",
    "correct_answer": 32634,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "51 - 83",
    "correct_answer": -32,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "293 + 64 + 125 - 711 + 519",
    "correct_answer": 290,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "781 * 537",
    "correct_answer": 419397,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "4 + 9 - 6 + 2 - 4 - 7 - 4 - 5 - 5 - 1 + 3 + 4 + 9 - 7 + 7 + 1 + 7 + 2 - 4 - 6 + 1 + 2 - 1 + 5 - 2 + 6 - 7 + 9 - 8 + 3 + 6",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "6963 + 7274",
    "correct_answer": 14237,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "14 - 90",
    "correct_answer": -76,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "121 - 204",
    "correct_answer": -83,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "(49 + 72) * (86 - 28)",
    "correct_answer": 7018,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "377 - 551",
    "correct_answer": -174,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "790 * 14",
    "correct_answer": 11060,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "42 + 32",
    "correct_answer": 74,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "894 * 60",
    "correct_answer": 53640,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "210 * 119",
    "correct_answer": 24990,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "(88 + 48) * (38 - 20)",
    "correct_answer": 2448,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "599 * 67",
    "correct_answer": 40133,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "19 - 21 + 30 + 4 - 19 - 14 + 2 + 3 + 18 - 18 + 20 - 9 - 30 - 19 + 4 + 21 + 1 + 27 + 19 - 12 - 14 - 21 + 5 - 19 + 27 + 18",
    "correct_answer": 22,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "5 + 9 - 7 + 4 - 4 + 2 + 2 - 3 - 8 - 6 - 3 + 3 + 1 - 3 - 9 + 9 + 1 + 3 - 3 - 4 - 6 + 5 + 8 - 2 - 3 + 1 + 7 + 5 - 8 - 7 - 7",
    "correct_answer": -18,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "27 - 86",
    "correct_answer": -59,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "388 - 474",
    "correct_answer": -86,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "533 * 474",
    "correct_answer": 252642,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "6706 + 8801",
    "correct_answer": 15507,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "181 * 87",
    "correct_answer": 15747,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "1 + 9 - 4 - 1 + 8 - 1 - 4 - 3 + 8 + 2 + 9 + 6 - 8 + 7 + 1 + 2 - 1 + 5 - 5 + 8 + 1 - 8 - 8 - 2 - 7 + 8 - 6 + 7 + 7 + 8 - 1 + 7",
    "correct_answer": 45,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "22 - 80 + 59",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "(42 + 90) * (86 - 77)",
    "correct_answer": 1188,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "688 % 10",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "468 - 617",
    "correct_answer": -149,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "915 * 10",
    "correct_answer": 9150,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "5 + 21 + 13 + 9 - 28 + 5 + 25 + 3 - 9 + 9 - 21 - 2 - 20 + 18 + 2 - 17 + 5 + 4 + 30 + 7 + 24 + 19 - 4 + 29 - 25",
    "correct_answer": 102,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "62 + 14 - 31",
    "correct_answer": 45,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "6 + 1 - 8 + 6 + 5 + 7 + 5 + 3 + 6 - 5 + 6 + 5 - 7 - 2 + 4 + 3 - 2 - 6 - 7 + 6 - 3 - 8 - 7 - 5 - 5 + 1 + 9 - 3 + 6 - 4 - 5 - 5 + 7 - 3 + 9 + 1",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "84 * 31",
    "correct_answer": 2604,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "592 + 640 + 862 - 208 - 863",
    "correct_answer": 1023,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2313 - 3383",
    "correct_answer": -1070,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "238 * 592",
    "correct_answer": 140896,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "901 + 111 - 672 + 352 + 135",
    "correct_answer": 827,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "33 + 62",
    "correct_answer": 95,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "757 % 5",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "929 * 479 * 823 + 380 + 463",
    "correct_answer": 366228436,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "890 % 13",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "325 - 441",
    "correct_answer": -116,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "9 + 2 - 8 + 7 + 7 - 4 + 5 + 8 + 3 + 6 - 5 - 3 - 7 + 3 + 1 + 5 + 8 - 9 + 7 + 6 + 7 + 7 + 8 + 7 + 6 + 7 + 9 - 4 - 4",
    "correct_answer": 84,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "9954 - 5016",
    "correct_answer": 4938,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "3846 - 3885",
    "correct_answer": -39,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "13 + 72 - 87",
    "correct_answer": -2,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "1906 - 2603",
    "correct_answer": -697,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "42 + 87 * 58 - 79 * 98",
    "correct_answer": -2654,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "21 - 5 - 17 - 21 - 30 - 29 - 10 - 12 - 4 - 6 + 15 - 8 - 9 + 21 + 8 - 23 - 27 - 12 - 28 + 27 - 11 - 24",
    "correct_answer": -184,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "288 * 12",
    "correct_answer": 3456,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "16 + 32",
    "correct_answer": 48,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "975 - 419 * 497 - 627 * 506",
    "correct_answer": -524530,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(89 + 26) * (27 - 63)",
    "correct_answer": -4140,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "737 * 72",
    "correct_answer": 53064,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "2276 + 7108",
    "correct_answer": 9384,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "22 + 19 + 12 + 2 + 3 - 13 - 3 + 2 - 8 - 3 - 25 + 13 - 5 + 10 + 16 - 14 + 17 - 1 + 23 + 8 - 14 + 18",
    "correct_answer": 79,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "522 * 55",
    "correct_answer": 28710,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "375 - 590",
    "correct_answer": -215,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "7 - 7 + 29 - 1 + 20 - 1 + 28 + 1 - 5 - 25 - 12 - 9 + 12 - 26 - 26 + 26 + 14 + 17 + 11 - 4 + 28 + 27 + 2 - 27 + 17 - 3 + 26",
    "correct_answer": 119,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "107 * 58",
    "correct_answer": 6206,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "943 % 5",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "164 * 934 * 69 * 740 * 906",
    "correct_answer": 7085976903360,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "311 - 405",
    "correct_answer": -94,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "93 * 49",
    "correct_answer": 4557,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "6900 + 1908",
    "correct_answer": 8808,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "88 + 18 - 81",
    "correct_answer": 25,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "83 * 61",
    "correct_answer": 5063,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "506 * 23",
    "correct_answer": 11638,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "134 + 557 - 888 + 407 - 941",
    "correct_answer": -731,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "62 - 52 + 55",
    "correct_answer": 65,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "5 + 1 + 6 - 5 - 7 + 6 - 8 + 3 - 2 + 5 + 1 - 6 - 8 + 7 + 2 + 2 + 6 + 2",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "1 - 6 + 8 - 4 + 9 + 9 - 6 + 3 - 4 - 8 + 1 + 1 + 7 + 2 + 7 + 7 + 1 + 7 - 7 + 5 - 6 - 6 - 5 - 4 - 6 - 7 - 1 + 9 - 5 + 9",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "50 * 37",
    "correct_answer": 1850,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "16 + 28 - 17 - 6 - 24 - 17 + 24 + 19 - 28 - 1 + 29 - 21 - 28 + 24 + 13 + 17 - 12 + 18 + 27 + 14 + 25",
    "correct_answer": 100,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "68 - 78",
    "correct_answer": -10,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "3280 - 5961",
    "correct_answer": -2681,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "5 + 2 - 2 + 8 + 3 - 8 + 8 + 9 - 5 + 7 - 8 - 3 + 3 + 1 - 5 + 5 + 2 - 4 + 1 + 6 + 2 + 8 - 7 - 9 + 7 - 6 - 8 - 9 - 2 - 4 - 5 + 9 - 5 + 7 + 2 - 9 - 1 - 5",
    "correct_answer": -10,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "19 - 9 - 10 - 1 + 27 - 23 + 12 - 11 + 7 + 16 - 14 + 21 + 28 + 17 - 19 + 21 - 7 - 28 - 21 - 11 + 6 + 19",
    "correct_answer": 39,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "9395 + 7685",
    "correct_answer": 17080,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "523 * 31",
    "correct_answer": 16213,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "2 + 8 - 7 - 4 + 3 + 1 - 9 - 3 + 8 - 1 - 1 - 2 - 7 + 1 + 4 + 4 + 9 + 3 + 4 - 4 + 1 + 2 + 7 + 9 - 2 - 6 + 5 + 6 + 7 + 9 - 9 + 2 + 4 + 9 + 6 + 2",
    "correct_answer": 61,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "23 * 36",
    "correct_answer": 828,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "78 * 590 - 496 - 224 + 824",
    "correct_answer": 46124,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "31 - 175 + 753 - 490 + 458",
    "correct_answer": 577,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "57 + 45 * 47 - 12 * 28",
    "correct_answer": 1836,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "904 * 537 + 695 + 733 - 958",
    "correct_answer": 485918,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "613 * 544",
    "correct_answer": 333472,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "19 + 77 - 1",
    "correct_answer": 95,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "795 % 17",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "920 % 7",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "40 + 83 * 13 - 72 * 25",
    "correct_answer": -681,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "356 * 98",
    "correct_answer": 34888,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "3848 + 1509",
    "correct_answer": 5357,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "8 + 4 - 6 + 7 - 8 + 6 + 2 + 5 - 1 - 9 + 8 + 8 - 3 - 7 + 7 - 6 + 5 + 2 + 5 + 7 - 2 - 8 - 6 + 4 + 5 + 5 - 6 + 1 - 9 + 3 + 4 + 3 + 4",
    "correct_answer": 32,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "36 - 93",
    "correct_answer": -57,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(33 + 13) * (19 - 10)",
    "correct_answer": 414,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "434 - 536",
    "correct_answer": -102,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "9 + 2 - 6 + 3 - 4 - 2 - 5 - 2 - 1 - 4 - 2 + 7 - 3 + 3 + 3 - 6 - 4 - 1 + 2 + 9 - 8 + 5",
    "correct_answer": -5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "10 - 12 + 17 + 13 - 15 + 29 + 8 + 28 + 11 - 5 - 13 - 8 - 1 + 26 - 20 - 28 - 9 - 14 + 23 + 28 - 10 - 28 - 17 + 25 + 14",
    "correct_answer": 52,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "734 * 977",
    "correct_answer": 717118,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "(32 + 98) * (48 - 83)",
    "correct_answer": -4550,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "6 + 22 + 6 - 24 + 17 - 15 + 25 - 6 + 18 - 18 + 17 - 19 - 27 - 3 - 22 + 20 - 24 - 11 - 22 - 10 - 9 + 5 + 27",
    "correct_answer": -47,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "8728 - 9674",
    "correct_answer": -946,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "6 + 2 + 7 + 6 - 6 + 1 + 3 + 3 + 5 - 7 - 8 + 2 - 2 - 9 - 1 - 2 - 3 - 9 + 1 + 7 - 1 - 2 - 4 + 8 - 5 - 8 - 1 - 7 + 7 + 3 - 6 + 5",
    "correct_answer": -15,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "3 - 7 + 7 - 8 + 9 - 7 - 9 + 2 - 8 + 2 - 6 + 7 - 8 - 8 - 1 + 4 + 2 + 6 - 9 + 3",
    "correct_answer": -26,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(41 + 47) * (25 - 72)",
    "correct_answer": -4136,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "21 * 21",
    "correct_answer": 441,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "2 - 6 - 6 - 2 + 1 - 6 - 7 + 7 - 8 - 3 + 9 - 1 - 6 + 8 + 8 - 5 + 2 + 8",
    "correct_answer": -5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "9 - 9 + 18 - 27 + 29 - 7 - 14 - 18 - 30 + 30 + 13 + 6 + 7 + 22 - 14 - 24 + 10 - 11 - 21 + 8 - 17 + 24 + 27 + 15 - 30 + 23",
    "correct_answer": 19,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "889 * 191",
    "correct_answer": 169799,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "49 + 80 - 88",
    "correct_answer": 41,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "267 + 207 * 34 + 104 * 971",
    "correct_answer": 108289,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "928 * 44",
    "correct_answer": 40832,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "228 % 13",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "17 - 36 + 80",
    "correct_answer": 61,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "36 * 43",
    "correct_answer": 1548,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "98 - 74",
    "correct_answer": 24,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "48 * 37",
    "correct_answer": 1776,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "8940 + 6636",
    "correct_answer": 15576,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "19 + 8 - 18 + 4 - 4 - 19 + 16 + 17 + 5 + 7 - 12 - 5 + 21 + 12 + 4 + 29 - 7 - 20 + 28 - 19 - 6 + 3 - 11 + 20 + 24 + 25 - 8",
    "correct_answer": 113,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "52 + 54 - 94",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "93 - 74",
    "correct_answer": 19,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(35 + 62) * (96 - 17)",
    "correct_answer": 7663,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "8 + 2 - 3 + 8 + 8 - 2 - 5 - 5 - 8 + 7 + 3 + 2 + 9 + 2 - 8 - 4 - 7 + 8 + 5 + 5 - 6 + 8 - 3 + 7 + 2 - 7 + 5 - 9 - 1 - 1 + 4 - 9 + 5 - 8 - 7 - 1 + 5 + 2",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "91 * 155 * 758 - 889 * 486",
    "correct_answer": 10259536,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "13 + 20 - 12 - 20 + 17 + 16 + 7 + 16 + 1 + 7 - 25 + 27 + 5 - 25 + 10 - 6 + 19 - 25 - 20 + 4 - 3",
    "correct_answer": 26,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "56 + 63",
    "correct_answer": 119,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "3440 - 3875",
    "correct_answer": -435,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "(12 + 35) * (57 - 42)",
    "correct_answer": 705,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "3308 - 6103",
    "correct_answer": -2795,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "296 - 527",
    "correct_answer": -231,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "58 * 73",
    "correct_answer": 4234,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "141 - 318",
    "correct_answer": -177,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "19 + 26 + 2 - 24 - 21 - 26 + 20 + 2 + 3 - 29 + 28 + 10 + 12 - 13 + 1 - 27 - 26 - 14 - 10 + 1 + 1",
    "correct_answer": -65,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "19 * 27",
    "correct_answer": 513,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "54 + 58 * 53 - 40 * 82",
    "correct_answer": -152,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "4834 - 4998",
    "correct_answer": -164,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "2 + 30 + 21 + 10 - 9 - 5 + 13 - 21 - 8 + 6 - 23 - 3 - 19 - 6 - 24 - 15 - 22 - 23 - 7 + 23 + 19 - 1",
    "correct_answer": -62,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "6 - 5 + 7 + 3 - 4 - 2 + 3 - 1 + 6 + 7 + 3 - 3 - 9 + 1 + 5 - 9 - 4 + 5 - 6 - 6 + 1 + 7",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "46 * 35",
    "correct_answer": 1610,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "321 + 590 - 929 - 185 - 242",
    "correct_answer": -445,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "16 * 47",
    "correct_answer": 752,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "5 - 3 - 1 - 7 - 1 - 6 - 9 + 9 + 7 + 1 + 7 + 4 + 5 + 1 + 6 + 7 + 4 + 9 + 9 + 6 + 1 + 4",
    "correct_answer": 58,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "72 + 87 * 63 - 40 * 41",
    "correct_answer": 3913,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "2706 - 5337",
    "correct_answer": -2631,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "624 + 276 - 101 * 184 + 130",
    "correct_answer": -17554,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "856 * 875 - 829 * 287 * 724",
    "correct_answer": -171507252,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "16 + 19 + 6 + 22 - 18 + 17 + 21 + 18 - 17 - 10 + 17 - 25 - 25 - 14 - 8 + 29 + 24 + 18 + 10 - 6 - 6 - 14",
    "correct_answer": 74,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(48 + 30) * (12 - 96)",
    "correct_answer": -6552,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "228 * 40",
    "correct_answer": 9120,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "5 - 20 + 27 - 10 - 17 + 23 - 18 + 13 - 29 + 22 + 16 - 10 - 26 + 4 - 12 - 18 - 7 + 26 - 11 - 4 + 6",
    "correct_answer": -40,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "806 + 171 - 910 + 92 + 17",
    "correct_answer": 176,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "882 * 75",
    "correct_answer": 66150,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "346 % 16",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "6 + 2 - 8 + 6 + 1 + 3 + 3 - 5 + 3 + 5 + 5 + 1 + 2 + 5 - 6 + 1 + 3 - 5 - 9 + 9",
    "correct_answer": 22,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "9 - 9 + 2 - 8 + 9 - 1 + 8 + 3 + 9 + 7 - 9 + 3 + 8 - 2 - 2 + 8 + 9 + 9 + 7 - 3 + 3",
    "correct_answer": 60,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "329 - 717 - 152 * 921 - 545",
    "correct_answer": -140925,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "19 - 24 - 3 - 2 - 8 - 25 + 18 + 26 - 29 + 17 + 16 + 1 + 17 + 11 + 11 + 18 + 9 + 7 + 10 + 11 + 18 + 23",
    "correct_answer": 141,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "306 * 94",
    "correct_answer": 28764,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "187 * 508",
    "correct_answer": 94996,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "6 + 1 - 9 - 6 + 3 - 9 + 5 + 6 - 6 + 3 + 3 - 3 + 4 + 1 - 7 + 2 + 1",
    "correct_answer": -5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "3645 - 5466",
    "correct_answer": -1821,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "38 + 19 * 65 - 87 * 21",
    "correct_answer": -554,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "3 - 9 + 15 - 29 + 11 - 28 + 9 + 12 - 14 - 10 + 22 - 20 - 24 - 24 + 9 + 22 + 27 - 30 + 18 - 9 - 27 + 5 + 20 + 26 + 15 - 20 - 30",
    "correct_answer": -60,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "17 - 5 - 13 + 3 + 3 - 21 - 29 - 28 - 18 - 19 - 18 - 17 - 19 + 24 - 3 + 30 - 2 - 6 + 21 + 9 + 13",
    "correct_answer": -78,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "3877 - 2956",
    "correct_answer": 921,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "2391 - 2565",
    "correct_answer": -174,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "9 + 7 + 7 - 3 - 1 + 4 - 5 + 6 + 5 + 5 + 8 + 3 - 5 - 2 + 5 - 4 - 9 - 1 - 1 - 9 + 4 + 1 - 5 - 7 + 9 + 8 - 2 + 2 + 7 - 2 - 5 - 2 - 2 - 4 + 6 + 6 - 9",
    "correct_answer": 24,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "18 * 25",
    "correct_answer": 450,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(17 + 84) * (47 - 21)",
    "correct_answer": 2626,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "726 % 5",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "1 + 9 - 1 - 9 + 9 - 3 + 9 - 5 - 3 + 7 + 9 + 2 - 6 + 8 - 6 + 4 - 3 + 4 + 8 + 5 - 2 - 9 - 9 - 2 - 7 - 3 + 6 + 1 + 7 + 1",
    "correct_answer": 22,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "890 - 291 - 549 + 547 + 722",
    "correct_answer": 1319,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "890 * 941",
    "correct_answer": 837490,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "13 + 23 - 11 + 26 + 21 + 4 + 3 - 14 - 19 + 14 + 29 + 21 - 6 - 29 - 15 - 25 + 5 - 5 + 19 + 13 - 2 - 27 - 20",
    "correct_answer": 18,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "45 + 40",
    "correct_answer": 85,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(17 + 54) * (57 - 51)",
    "correct_answer": 426,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "34 * 32",
    "correct_answer": 1088,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(38 + 18) * (77 - 58)",
    "correct_answer": 1064,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "1535 - 3152",
    "correct_answer": -1617,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "400 - 319 - 697 * 145 * 52",
    "correct_answer": -5255299,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "4228 + 8496",
    "correct_answer": 12724,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "90 + 12 * 18 - 46 * 49",
    "correct_answer": -1948,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "5 - 28 + 11 - 12 + 29 - 17 + 21 + 23 + 15 + 16 - 5 + 7 + 10 + 23 + 22 + 16 + 24 - 5 + 16 + 15 + 8 - 29 - 5 - 15 - 15 - 14 + 30",
    "correct_answer": 146,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "740 - 69 + 409 + 337 - 432",
    "correct_answer": 985,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "26 - 5 - 14 + 28 + 21 - 16 + 27 + 26 + 8 - 27 - 14 + 29 + 1 - 18 - 9 - 15 + 13 + 14 - 29 - 2 + 10 + 1 - 3 - 3 + 29 + 22",
    "correct_answer": 100,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "2 - 1 + 5 - 8 + 9 - 5 + 6 + 7 + 1 + 4 - 7 + 4 + 7 - 8 - 1 - 8 - 2 + 3 + 3 - 8 - 5 - 1 + 8 + 9 + 4 - 6 + 1 - 4 + 4 - 3 - 9",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "56 + 78",
    "correct_answer": 134,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "409 * 340 - 110 * 112 + 701",
    "correct_answer": 127441,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "47 + 56",
    "correct_answer": 103,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "71 + 92 - 42",
    "correct_answer": 121,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "57 - 70",
    "correct_answer": -13,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "507 * 617 * 723 * 872 - 465",
    "correct_answer": 197218614999,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "74 * 82",
    "correct_answer": 6068,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(55 + 22) * (89 - 46)",
    "correct_answer": 3311,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "316 * 308",
    "correct_answer": 97328,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "(56 + 76) * (36 - 43)",
    "correct_answer": -924,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "34 * 67",
    "correct_answer": 2278,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "54 + 23 - 26",
    "correct_answer": 51,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "2237 + 2525",
    "correct_answer": 4762,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "27 - 9 + 98",
    "correct_answer": 116,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "5 + 2 - 2 + 4 + 8 + 1 + 9 + 5 + 9 + 7 + 7 + 9 + 8 + 2 - 7 + 7 + 4",
    "correct_answer": 78,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "693 + 469 * 897 + 343 * 829",
    "correct_answer": 705733,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "8080 - 7481",
    "correct_answer": 599,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "802 * 39",
    "correct_answer": 31278,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "407 * 42",
    "correct_answer": 17094,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(40 + 55) * (64 - 49)",
    "correct_answer": 1425,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "472 % 19",
    "correct_answer": 16,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "187 * 713 - 856 - 828 + 213",
    "correct_answer": 131860,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "422 * 663",
    "correct_answer": 279786,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "425 + 254 + 163 + 38 - 826",
    "correct_answer": 54,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(85 + 28) * (50 - 21)",
    "correct_answer": 3277,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "792 * 56 - 187 + 74 + 290",
    "correct_answer": 44529,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "8 - 5 - 7 - 2 - 8 - 4 - 8 - 5 + 5 + 3 + 8 + 5 + 9 - 5 + 9 + 8 + 3 - 6 + 9 + 3 - 7 - 2 + 8 - 9 - 4 + 4 + 9 + 9 - 5 - 4 + 3 - 4",
    "correct_answer": 18,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "16 - 16 + 22 - 13 + 14 - 16 + 24 - 2 + 19 - 20 + 24 + 11 - 25 + 27 + 19 - 8 - 26 + 24 + 28 - 17 - 25 - 20 + 14",
    "correct_answer": 54,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "13 - 98 + 82",
    "correct_answer": -3,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "497 - 474 + 462 * 625 + 16",
    "correct_answer": 288789,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "3596 - 4327",
    "correct_answer": -731,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "955 % 7",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "16 + 25 + 15 - 5 - 19 - 4 + 14 - 24 - 1 - 28 - 6 + 6 - 23 + 7 - 16 - 15 + 5 - 28 + 2 - 24 + 10 - 3",
    "correct_answer": -96,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "23 + 52 * 77 - 10 * 79",
    "correct_answer": 3237,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "908 - 253 - 472 * 231 + 319",
    "correct_answer": -108058,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2 - 5 + 5 - 9 - 4 - 4 - 7 + 1 + 7 - 1 + 3 - 5 + 9 - 5 + 6 - 4 - 6 + 8 + 8 - 5 - 1 - 7 - 9 - 2 - 5 + 1 - 4 - 9 + 9 + 9 - 6 - 4 + 4 + 8 + 5 - 1 - 2",
    "correct_answer": -20,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "1 + 9 + 6 - 1 + 9 + 6 - 1 - 6 + 3 + 8 - 4 - 2 - 3 - 3 + 3 + 8 - 1 - 2 - 5 + 2",
    "correct_answer": 27,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "5247 + 3735",
    "correct_answer": 8982,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "162 * 678 + 10 - 690 + 282",
    "correct_answer": 109438,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1527 - 2023",
    "correct_answer": -496,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "359 % 4",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "37 + 91 * 23 - 63 * 83",
    "correct_answer": -3099,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "719 % 7",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "7275 + 3248",
    "correct_answer": 10523,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "917 * 47",
    "correct_answer": 43099,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "94 * 47",
    "correct_answer": 4418,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "5 - 9 + 3 + 6 + 1 + 3 - 9 - 9 + 7 - 4 - 4 + 6 - 8 - 8 - 6 - 6 + 7 + 2 + 1 - 1 + 4 + 4 - 6 + 7 - 3 + 1 + 2 + 9 + 5 + 6 + 1 + 5 - 5 - 6",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "177 - 189",
    "correct_answer": -12,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "13 - 4 + 11 - 21 - 23 - 6 + 12 + 4 + 16 + 16 + 6 - 1 - 5 + 24 - 18 + 11 + 10 - 18 + 24 - 24 + 22",
    "correct_answer": 49,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "23 - 15 + 85",
    "correct_answer": 93,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "339 % 10",
    "correct_answer": 9,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "8973 + 9804",
    "correct_answer": 18777,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "3 + 5 - 9 - 8 + 2 - 5 + 3 + 6 - 1 - 3 + 8 + 1 - 5 - 7 + 1 - 7 + 8 + 5 + 6 + 5 + 6 + 7 - 2 - 8 - 5 - 4 - 5 - 9 + 2 - 8 + 4 - 5 + 7 - 4 + 4 + 7 - 8 + 9 + 2",
    "correct_answer": -2,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "53 + 96 * 45 - 73 * 58",
    "correct_answer": 139,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "48 * 30",
    "correct_answer": 1440,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "93 + 50 * 53 - 34 * 49",
    "correct_answer": 1077,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "3139 + 8951",
    "correct_answer": 12090,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "9 + 5 - 1 - 3 + 6 + 7 - 1 + 2 - 5 + 4 - 5 + 7 - 2 - 8 - 8 - 3 + 2 - 3 - 8 - 9 - 2",
    "correct_answer": -16,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "18 + 86 * 71 - 54 * 37",
    "correct_answer": 4126,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "14 + 32",
    "correct_answer": 46,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "96 + 77 * 51 - 17 * 98",
    "correct_answer": 2357,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "176 + 899 * 193 - 62 - 325",
    "correct_answer": 173296,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "16 + 2 + 26 - 15 - 10 - 3 - 28 + 25 + 5 + 22 + 18 - 9 - 8 + 15 - 15 + 22 + 11 + 24 - 2 + 21 - 18",
    "correct_answer": 99,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "657 % 19",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "10 - 18 - 5 - 12 + 26 - 16 + 19 - 26 - 29 - 21 + 1 + 5 - 1 - 1 - 6 - 9 + 24 - 20 + 2 - 25 + 2 - 5 + 15 + 15",
    "correct_answer": -75,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "8 - 7 + 29 - 29 - 20 + 11 - 19 + 26 + 17 + 24 - 20 + 30 - 17 - 18 - 25 - 21 + 17 - 25 - 7 - 28 + 8 - 19 + 15",
    "correct_answer": -70,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "695 * 902",
    "correct_answer": 626890,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "776 % 12",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "89 * 39",
    "correct_answer": 3471,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "419 - 603",
    "correct_answer": -184,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "2 + 8 + 7 - 7 + 5 - 3 - 9 + 7 - 2 - 3 + 7 + 4 - 3 - 9 - 6 + 5 - 3",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "51 - 36 + 25",
    "correct_answer": 40,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "6 + 4 - 7 - 2 - 8 + 7 - 7 + 1 + 4 - 8 - 4 - 8 + 1 + 3 - 7 + 8 - 8 - 5 + 6 + 1 - 5 - 1 - 8 - 4 + 9 + 6 - 6 + 3 - 8 - 6 - 5 - 7 + 2 - 8 + 8 + 8 + 6 + 8",
    "correct_answer": -31,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(10 + 50) * (88 - 27)",
    "correct_answer": 3660,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "507 * 523 + 859 * 491 * 554",
    "correct_answer": 233925187,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "394 * 114",
    "correct_answer": 44916,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "64 + 52",
    "correct_answer": 116,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "754 * 162",
    "correct_answer": 122148,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "9 - 6 + 4 + 2 + 7 + 9 - 5 + 1 + 8 + 5 - 1 + 7 - 5 + 6 + 3 + 9 + 9 + 7 - 5 + 8 + 7",
    "correct_answer": 79,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "797 * 68",
    "correct_answer": 54196,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "6 - 3 + 3 - 7 + 9 - 8 + 9 + 8 + 5 - 5 - 5 + 4 - 2 - 3 + 4 - 1 + 7 + 8 - 2 + 4 + 4 + 1 - 5 + 9 + 5 + 4 + 6 - 2 - 7 + 7 - 3 - 4 - 1",
    "correct_answer": 45,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "554 % 12",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "79 + 99",
    "correct_answer": 178,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "49 * 76",
    "correct_answer": 3724,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "30 - 13",
    "correct_answer": 17,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "7 + 7 + 8 + 4 + 5 - 6 + 2 + 7 + 5 - 5 + 4 - 3 + 2 - 6 - 4 + 1 + 7 + 8",
    "correct_answer": 43,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "857 * 650",
    "correct_answer": 557050,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "7 + 7 + 2 + 8 + 9 + 7 - 5 + 1 + 1 + 2 + 9 - 6 + 9 + 5 - 6 - 1 - 7 - 9 + 9 - 1 + 2",
    "correct_answer": 43,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(10 + 83) * (98 - 15)",
    "correct_answer": 7719,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "631 * 199",
    "correct_answer": 125569,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "7401 + 2083",
    "correct_answer": 9484,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "28 - 26 + 8 - 28 - 12 + 16 - 13 + 22 + 16 - 15 + 15 + 8 + 14 + 5 + 3 + 11 + 4 + 8 + 2 - 1 + 11 + 12 - 6 - 13 - 17 + 23",
    "correct_answer": 75,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "93 - 93",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "92 + 44",
    "correct_answer": 136,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "47 * 47",
    "correct_answer": 2209,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "5 - 4 - 4 + 1 + 8 + 3 + 1 - 8 + 6 - 6 + 1 - 7 - 5 - 4 + 6 - 4 - 4 - 4 + 7 + 3 + 1 + 8 + 4 - 3 + 3 - 9 + 4 + 2 + 8 + 4",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "39 * 37",
    "correct_answer": 1443,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "1 - 4 - 7 - 7 + 1 - 4 + 6 + 8 - 4 - 6 + 8 - 3 - 3 + 4 - 7 - 4 - 3 + 2 - 6 - 5 + 4 + 5 + 6 - 6 - 5 - 7 - 1 + 4 - 7 + 5 + 2 - 6 - 2",
    "correct_answer": -41,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "89 - 77",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "3 + 5 + 9 - 9 + 4 + 3 - 7 - 9 - 7 - 1 - 9 + 5 + 4 - 5 - 2 - 6 - 8 - 6 + 9 + 8 + 6 + 5 + 1 - 3 - 1 + 7 - 5 - 7 + 3 - 1 + 4",
    "correct_answer": -10,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "247 * 246 - 36 * 91 - 808",
    "correct_answer": 56678,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "296 - 909 * 225 - 526 * 915",
    "correct_answer": -685519,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "78 * 97",
    "correct_answer": 7566,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(46 + 43) * (99 - 58)",
    "correct_answer": 3649,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "9 + 9 - 5 - 1 - 9 + 3 - 3 + 6 + 7 - 7 - 4 + 4 + 7 - 1 + 8 + 1 - 9 + 7 - 9 + 9 - 1 - 1",
    "correct_answer": 20,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "18 * 27",
    "correct_answer": 486,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "123 - 142",
    "correct_answer": -19,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "291 % 18",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "28 + 2 - 25 - 8 - 17 + 7 + 26 + 20 - 6 - 28 + 12 + 26 - 13 - 1 - 18 + 27 - 27 + 30 + 27 - 21 + 29 + 25 + 2 - 14",
    "correct_answer": 83,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "417 - 561",
    "correct_answer": -144,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "90 + 96 * 98 - 60 * 58",
    "correct_answer": 6018,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "11 + 42 - 78",
    "correct_answer": -25,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "265 % 13",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "4 - 15 - 1 - 14 - 12 + 17 - 21 - 11 - 28 + 28 + 6 - 6 + 6 + 9 + 1 + 13 + 23 + 19 + 28 - 27 - 28",
    "correct_answer": -9,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "30 - 19 + 27 + 15 - 8 - 13 - 2 - 3 - 5 + 10 + 2 - 20 + 2 - 8 + 5 + 19 + 4 + 20 + 12 + 10 + 20 - 6 + 2 - 23",
    "correct_answer": 71,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "27 + 47 * 92 - 39 * 10",
    "correct_answer": 3961,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "416 % 18",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "95 - 561 * 703 + 990 - 534",
    "correct_answer": -393832,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "7 + 8 + 8 - 5 - 1 + 8 + 6 + 8 + 5 - 6 - 4 + 4 - 1 - 1 - 5 + 7 - 6 + 3 - 5 + 6 - 6 + 7 - 6 - 4 - 3 - 7 - 1 + 1 - 1 + 2 - 4 - 6 + 2 - 9 - 7 + 2",
    "correct_answer": -4,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "54 + 62 - 61",
    "correct_answer": 55,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "3 - 9 - 7 + 5 + 7 - 9 + 8 - 3 + 5 - 5 + 5 + 2 + 7 - 8 + 4 - 3 - 7 - 4 + 2 + 5 + 7 + 3 - 3 + 6 + 2 + 9 + 8 + 8 - 2 + 8 - 6 + 1",
    "correct_answer": 39,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "709 * 689",
    "correct_answer": 488501,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "77 + 68 - 38",
    "correct_answer": 107,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "123 - 402 * 486 - 51 + 385",
    "correct_answer": -194915,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "691 * 76",
    "correct_answer": 52516,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "4738 - 6817",
    "correct_answer": -2079,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "(52 + 10) * (90 - 91)",
    "correct_answer": -62,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "475 * 564",
    "correct_answer": 267900,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "77 * 95",
    "correct_answer": 7315,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "912 % 14",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "7 + 84",
    "correct_answer": 91,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(72 + 98) * (62 - 35)",
    "correct_answer": 4590,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "44 * 18",
    "correct_answer": 792,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(36 + 15) * (25 - 64)",
    "correct_answer": -1989,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "2 - 1 - 23 - 9 - 9 + 13 - 10 + 12 - 12 - 1 + 29 - 28 - 13 - 5 - 15 + 2 + 7 - 23 - 20 + 24 + 3 + 6 - 26",
    "correct_answer": -97,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "896 % 15",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "7 + 1 - 1 - 2 - 7 + 3 - 3 + 9 - 8 - 3 - 8 + 4 + 9 - 6 - 1 - 6 + 8 + 4 + 2",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "10 + 77 * 53 - 41 * 68",
    "correct_answer": 1303,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "872 * 179 - 630 * 201 - 129",
    "correct_answer": 29329,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "3 + 9 - 8 + 8 - 7 - 4 + 9 - 2 - 3 + 6 + 6 - 8 + 1 - 9 + 7 + 2 + 1 + 8 + 7",
    "correct_answer": 26,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "497 * 776",
    "correct_answer": 385672,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "510 * 88",
    "correct_answer": 44880,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "412 * 560",
    "correct_answer": 230720,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "54 + 44 - 65",
    "correct_answer": 33,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "38 + 3 - 85",
    "correct_answer": -44,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "596 + 698 - 741 * 542 + 263",
    "correct_answer": -400065,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "20 - 20",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "42 + 81 - 41",
    "correct_answer": 82,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "26 + 24 - 16 + 21 - 27 - 21 + 11 + 1 - 3 + 7 - 25 + 4 + 16 + 12 + 4 - 19 - 13 + 23 + 9 - 12 + 11 + 11 - 16 - 10 - 14",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "520 + 704 - 193 * 629 + 344",
    "correct_answer": -119829,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "23 - 27 - 5 + 4 - 11 + 25 - 6 + 1 - 17 - 28 - 12 + 19 + 29 - 23 - 13 - 29 + 28 + 28 - 22 - 9 + 7 + 18 + 6 - 18",
    "correct_answer": -32,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "38 + 46 - 48",
    "correct_answer": 36,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "22 + 87 * 89 - 44 * 33",
    "correct_answer": 6313,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "(65 + 63) * (84 - 55)",
    "correct_answer": 3712,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "8 + 1 + 4 - 3 - 6 + 5 - 4 - 6 + 3 + 4 - 1 - 3 + 7 + 2 + 2 - 3 + 3 + 2",
    "correct_answer": 15,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "45 + 35 * 90 - 14 * 13",
    "correct_answer": 3013,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "478 - 523",
    "correct_answer": -45,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "4232 + 8365",
    "correct_answer": 12597,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "87 + 96",
    "correct_answer": 183,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "181 * 64",
    "correct_answer": 11584,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "90 - 94",
    "correct_answer": -4,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "56 + 62 * 39 - 82 * 42",
    "correct_answer": -970,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "75 + 72 * 88 - 92 * 15",
    "correct_answer": 5031,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "651 * 938",
    "correct_answer": 610638,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "172 - 206",
    "correct_answer": -34,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "572 % 12",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "582 - 767 + 239 + 820 - 167",
    "correct_answer": 707,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "4172 - 5829",
    "correct_answer": -1657,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "733 + 630 + 17 * 850 + 415",
    "correct_answer": 16228,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "800 * 16",
    "correct_answer": 12800,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "9 + 4 - 6 + 9 + 1 + 7 + 2 - 4 + 2 + 8 + 4 + 7 - 5 - 9 - 1 + 8 - 1 + 6 + 2 + 3 + 1 + 8 + 9 + 3 + 8 + 5 + 7 + 6 - 3 + 5 - 8 + 8 - 6 + 1 + 4 + 5 + 7 - 6 - 3",
    "correct_answer": 97,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(96 + 47) * (55 - 86)",
    "correct_answer": -4433,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "30 + 65",
    "correct_answer": 95,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "999 % 8",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "86 - 90 + 95",
    "correct_answer": 91,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "920 * 80",
    "correct_answer": 73600,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(69 + 59) * (28 - 49)",
    "correct_answer": -2688,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "27 + 24 - 2 - 10 - 3 - 8 - 21 + 2 + 22 + 21 + 3 + 16 + 24 + 22 + 2 - 30 - 16 - 16 - 26 + 15 - 28 - 11",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "28 - 84",
    "correct_answer": -56,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "4 + 1 + 4 - 2 + 3 - 8 - 1 + 9 + 8 + 4 + 1 + 2 + 3 + 3 + 1 + 2 + 6 + 8 - 5 + 1 - 3 - 5 + 7 - 2 + 3 - 6 + 3 - 9 - 1 + 9 - 2 - 6 - 6 - 4 - 5 - 5 - 2 + 8 - 8",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "38 + 41 * 54 - 76 * 24",
    "correct_answer": 428,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "165 * 43",
    "correct_answer": 7095,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "7270 + 7990",
    "correct_answer": 15260,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "88 + 93",
    "correct_answer": 181,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "719 * 92",
    "correct_answer": 66148,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "39 + 64 - 15",
    "correct_answer": 88,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "53 - 6 + 41",
    "correct_answer": 88,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "2 + 6 - 3 - 2 + 1 + 4 + 7 + 4 + 4 - 1 + 5 - 9 + 8 + 7 + 4 + 7 - 9 + 6 - 7 + 8 - 2 + 6 - 4 - 3 - 8 - 7 - 7 + 2 + 2 - 3 + 8 - 1 + 7 + 2 - 6 - 1 + 2",
    "correct_answer": 29,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "27 + 12 - 3 - 26 - 2 + 1 + 16 + 3 - 17 - 20 - 18 + 9 - 24 + 6 - 11 - 2 + 16 + 17 - 17 + 15 - 13 + 17",
    "correct_answer": -14,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "748 * 544",
    "correct_answer": 406912,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "9 - 3 + 2 + 5 - 9 - 7 - 3 - 9 + 2 + 9 + 8 - 2 - 6 + 9 + 2 - 5 - 1",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "2 - 10 - 27 + 17 + 8 - 10 - 25 - 5 + 8 + 7 + 29 + 9 + 8 + 1 + 4 - 3 - 14 - 27 + 6 + 10 - 15 + 17",
    "correct_answer": -10,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "703 - 106 - 36 * 707 - 134",
    "correct_answer": -24989,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "30 * 41",
    "correct_answer": 1230,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "6131 - 2931",
    "correct_answer": 3200,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "3258 + 7286",
    "correct_answer": 10544,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "(72 + 75) * (37 - 49)",
    "correct_answer": -1764,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "4 - 8 - 2 - 4 - 2 + 3 + 6 + 4 - 3 + 8 + 3 + 7 + 1 - 9 + 6 - 3 + 8",
    "correct_answer": 19,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "59 + 68 * 96 - 47 * 81",
    "correct_answer": 2780,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "136 + 487 + 542 - 517 - 731",
    "correct_answer": -83,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "23 - 6 - 10 - 13 + 23 + 17 + 10 - 8 - 28 - 11 - 11 - 9 + 26 + 13 + 9 + 14 + 12 + 8 - 27 - 20 - 19 + 13 + 18 - 17 - 25 + 17 + 10",
    "correct_answer": 9,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "233 * 638 - 118 - 742 + 115",
    "correct_answer": 147909,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "449 - 628",
    "correct_answer": -179,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "1021 - 3375",
    "correct_answer": -2354,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "4517 + 4066",
    "correct_answer": 8583,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "9 - 31 + 81",
    "correct_answer": 59,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "191 - 228",
    "correct_answer": -37,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "76 + 29",
    "correct_answer": 105,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "3 + 5 - 7 - 8 + 9 + 8 + 4 - 5 + 7 + 8 + 3 - 4 + 7 + 9 + 3 + 6 + 2 - 9 + 7 + 2 + 5 - 4 - 9 - 9 - 8 + 1 + 1 + 9 + 6 + 4 - 5 + 7 - 5",
    "correct_answer": 43,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "430 * 519",
    "correct_answer": 223170,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "419 * 51",
    "correct_answer": 21369,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "4 + 6 - 1 + 2 - 3 + 7 + 1 - 7 - 8 - 1 - 1 + 8 + 9 + 8 + 6 - 7 - 2 - 3 + 8 - 5 + 9 - 1 + 2 + 4 + 3 - 5 + 7 + 7 - 2 + 2 - 6 - 4",
    "correct_answer": 37,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "5489 + 2529",
    "correct_answer": 8018,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "35 - 22 + 33",
    "correct_answer": 46,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "9827 + 3758",
    "correct_answer": 13585,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "304 % 6",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "433 * 579 - 730 - 790 + 561",
    "correct_answer": 249748,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "8 + 8 + 5 - 1 - 8 - 7 - 7 + 3 - 9 - 8 - 8 - 1 - 2 + 5 - 9 + 5",
    "correct_answer": -26,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "69 + 66 * 59 - 17 * 24",
    "correct_answer": 3555,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "2020 + 8126",
    "correct_answer": 10146,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "348 * 735",
    "correct_answer": 255780,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "41 + 70",
    "correct_answer": 111,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "38 + 24 * 58 - 34 * 38",
    "correct_answer": 138,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "179 * 321",
    "correct_answer": 57459,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "96 + 43 * 37 - 91 * 69",
    "correct_answer": -4592,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "8 - 27",
    "correct_answer": -19,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "454 % 19",
    "correct_answer": 17,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "396 * 905",
    "correct_answer": 358380,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "57 * 89",
    "correct_answer": 5073,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "980 * 33 * 672 + 651 + 938",
    "correct_answer": 21734069,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "36 * 30",
    "correct_answer": 1080,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "3439 - 5163",
    "correct_answer": -1724,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "46 + 70 * 27 - 33 * 39",
    "correct_answer": 649,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "599 * 504",
    "correct_answer": 301896,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "3 + 96",
    "correct_answer": 99,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(91 + 72) * (26 - 75)",
    "correct_answer": -7987,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "22 - 25 + 28 + 19 + 21 + 27 - 26 - 17 + 10 + 22 - 5 + 16 - 5 + 16 - 30 - 13 + 7 + 27 - 22 - 10 - 16 + 1 + 22",
    "correct_answer": 69,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "943 * 28",
    "correct_answer": 26404,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "466 * 841",
    "correct_answer": 391906,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "46 + 27",
    "correct_answer": 73,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "50 * 47",
    "correct_answer": 2350,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "738 - 401 - 400 + 568 + 688",
    "correct_answer": 1193,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "7 + 11 - 15 + 16 + 11 - 27 - 4 - 13 - 12 - 30 - 11 + 1 + 26 + 23 - 15 + 5 - 19 - 24 - 17 + 21 + 3 + 19 + 6 + 11 - 24 - 11",
    "correct_answer": -62,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "86 + 95",
    "correct_answer": 181,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "26 - 5 - 15 - 1 + 25 - 20 + 21 + 23 + 14 - 14 - 25 + 10 - 23 - 19 + 21 - 29 + 13 + 22 - 16 + 14 - 29 + 12 - 11 - 15 - 23 - 29 + 19",
    "correct_answer": -54,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "43 - 32 + 17",
    "correct_answer": 28,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "26 + 19",
    "correct_answer": 45,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "15 + 14 - 26 - 10 + 8 - 22 + 29 + 13 + 20 - 17 - 15 - 8 - 20 - 15 + 25 + 4 - 21 + 6 + 1 + 10 - 21 - 18 + 6 - 10 + 24",
    "correct_answer": -28,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "46 - 45",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(45 + 23) * (16 - 39)",
    "correct_answer": -1564,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "8501 + 3826",
    "correct_answer": 12327,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "138 * 59",
    "correct_answer": 8142,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "16 + 14 + 19 - 15 + 13 - 27 - 26 - 13 + 8 - 8 - 27 - 15 - 24 + 8 + 16 - 5 + 30 + 17 + 20 + 12 + 6 - 16 - 7",
    "correct_answer": -4,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "136 + 103 - 733 - 659 * 97",
    "correct_answer": -64417,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "827 * 44",
    "correct_answer": 36388,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "253 * 434",
    "correct_answer": 109802,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "68 + 22 * 86 - 66 * 26",
    "correct_answer": 244,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "4 - 15",
    "correct_answer": -11,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "910 % 9",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "549 * 11",
    "correct_answer": 6039,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "311 - 497",
    "correct_answer": -186,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "553 * 58",
    "correct_answer": 32074,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "8 + 7 + 3 + 3 - 5 + 1 + 4 - 2 - 5 - 1 + 6 + 4 - 2 - 3 + 7 + 2 + 6",
    "correct_answer": 33,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "198 - 655 * 820 + 149 + 420",
    "correct_answer": -536333,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "254 - 510 * 74 - 668 * 521",
    "correct_answer": -385514,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "20 + 490 - 902 - 719 + 713",
    "correct_answer": -398,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "431 * 849",
    "correct_answer": 365919,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "6 - 9 - 1 - 3 + 9 + 7 + 9 + 3 - 7 - 5 + 5 - 7 + 6 + 1 - 2 + 9 - 7 + 5 - 2 - 6 + 6 + 3 + 9 - 9 - 8 + 7 + 4 - 7 + 1",
    "correct_answer": 17,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "1777 - 2529",
    "correct_answer": -752,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "474 * 62",
    "correct_answer": 29388,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "29 - 18",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "75 + 19 - 30",
    "correct_answer": 64,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "32 + 16 * 74 - 28 * 33",
    "correct_answer": 292,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "7 + 8 - 2 - 7 - 6 + 1 + 7 - 8 - 6 + 6 + 1 + 6 - 2 - 3 - 9 + 8 + 1 + 3",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "4 + 26 - 1 - 11 + 22 + 30 - 18 - 29 + 7 - 13 - 13 + 4 - 22 - 13 - 9 - 27 + 20 - 17 - 17 + 8 + 10 + 18 + 11 - 24 + 20",
    "correct_answer": -34,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "726 * 949 - 348 - 474 + 40",
    "correct_answer": 688192,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "71 + 93 - 28",
    "correct_answer": 136,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "21 - 17 - 4 - 22 - 29 - 7 + 23 - 2 - 7 - 29 + 7 - 17 - 12 + 16 + 16 - 14 + 9 - 9 + 1 - 2 - 2",
    "correct_answer": -80,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "432 * 115",
    "correct_answer": 49680,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "19 * 19",
    "correct_answer": 361,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(86 + 51) * (86 - 14)",
    "correct_answer": 9864,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "(44 + 94) * (18 - 18)",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "66 + 47 - 3",
    "correct_answer": 110,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "753 * 405",
    "correct_answer": 304965,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "1 - 3 + 1 + 2 + 1 + 3 - 5 + 2 - 5 - 3 + 1 + 5 + 1 - 6 - 7 + 8 - 5 + 6 + 6 - 7 + 4 + 2 + 5 + 1 + 9 - 2 + 9 + 4 - 7 + 2 - 5 + 2 + 7",
    "correct_answer": 27,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "44 * 47",
    "correct_answer": 2068,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "20 - 25",
    "correct_answer": -5,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "18 + 75 * 37 - 26 * 57",
    "correct_answer": 1311,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "963 * 517 * 654 + 547 - 307",
    "correct_answer": 325607874,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "95 + 22",
    "correct_answer": 117,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "18 - 1 - 28 - 17 + 5 - 18 + 7 + 23 + 4 + 17 - 15 + 26 + 26 - 21 - 14 + 13 - 13 + 16 + 17 + 21 - 6 - 28 - 19 + 11 + 7 - 22 + 20",
    "correct_answer": 29,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "70 - 5",
    "correct_answer": 65,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "8 + 4 + 2 - 3 + 7 - 6 + 2 - 7 - 6 + 9 + 7 + 2 + 6 - 7 + 6 - 8 - 5 + 7 - 6 + 6",
    "correct_answer": 18,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "555 * 56",
    "correct_answer": 31080,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "8826 - 2160",
    "correct_answer": 6666,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "717 % 16",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "13 + 22 - 6 + 13 - 30 + 23 - 5 - 11 + 5 - 25 + 20 - 9 - 2 + 17 - 15 - 16 + 6 - 20 + 27 + 13 - 26 - 12",
    "correct_answer": -18,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "266 * 869 - 399 * 872 * 227",
    "correct_answer": -78748502,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(74 + 57) * (14 - 47)",
    "correct_answer": -4323,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "89 - 32",
    "correct_answer": 57,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "360 - 472",
    "correct_answer": -112,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "957 - 286 * 237 + 697 + 785",
    "correct_answer": -65343,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "29 * 31",
    "correct_answer": 899,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "44 - 36",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "17 * 27",
    "correct_answer": 459,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "3693 + 8365",
    "correct_answer": 12058,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "(98 + 90) * (45 - 25)",
    "correct_answer": 3760,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "20 + 90 * 66 - 11 * 95",
    "correct_answer": 4915,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "8 + 14 - 23 + 18 - 30 + 5 + 22 + 1 + 30 + 18 + 3 - 1 - 13 + 14 + 15 + 1 - 21 - 8 - 25 + 17 - 29 - 12 + 16 + 15 + 19 - 12",
    "correct_answer": 42,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "31 + 50 * 10 - 36 * 77",
    "correct_answer": -2241,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "4 - 16 + 20 + 11 + 10 + 30 + 18 + 7 - 4 + 26 + 17 - 4 - 13 + 18 + 6 + 14 + 18 + 28 + 28 - 17 + 7 - 4 + 9 - 19 + 18 - 12 - 8",
    "correct_answer": 192,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "9614 + 5082",
    "correct_answer": 14696,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "30 + 9",
    "correct_answer": 39,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "7 + 4 + 5 - 1 - 5 + 7 - 6 + 1 - 4 + 6 + 3 - 1 + 8 - 7 + 5 + 9 - 1 + 2 - 9 + 9 + 5 + 3 - 1 + 6 - 1 + 5 + 4 + 6 + 9 - 6 + 2 - 4 + 2 + 8 - 2 + 4 - 2",
    "correct_answer": 70,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "60 - 57",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(87 + 69) * (26 - 58)",
    "correct_answer": -4992,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "189 % 13",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "19 + 10",
    "correct_answer": 29,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(42 + 86) * (13 - 65)",
    "correct_answer": -6656,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "729 * 31",
    "correct_answer": 22599,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "98 * 98",
    "correct_answer": 9604,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "8 - 2 + 1 - 5 - 9 + 9 - 5 + 6 + 2 + 3 + 9 - 5 - 8 - 7 - 9 - 4 + 4 - 8 + 7 - 9 + 2 - 7 + 3 - 5 + 8 + 5 - 3 + 7 - 9 - 5 - 2 - 8 - 2 + 5 - 7 + 3 + 8 - 8 - 9",
    "correct_answer": -46,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "295 * 793 * 794 - 617 * 784",
    "correct_answer": 185260662,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "605 * 37",
    "correct_answer": 22385,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "696 * 779",
    "correct_answer": 542184,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "973 * 18",
    "correct_answer": 17514,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "7819 + 6241",
    "correct_answer": 14060,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "19 - 23 + 29 - 13 - 29 - 21 + 12 - 20 - 27 - 19 + 13 + 24 + 5 - 13 - 10 + 22 - 28 - 8 + 22 - 24 - 7 - 5 + 20 - 28",
    "correct_answer": -109,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "56 * 991 - 921 - 763 + 671",
    "correct_answer": 54483,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "4733 - 5550",
    "correct_answer": -817,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "543 % 19",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "86 * 51",
    "correct_answer": 4386,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "29 - 12 - 22 - 24 + 25 - 22 - 9 + 30 - 15 - 15 + 23 + 21 + 26 + 25 + 24 + 15 + 22 - 30 - 1 + 16 + 4 - 10 - 4 - 12 + 18 - 29",
    "correct_answer": 73,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "821 - 971 - 472 * 904 - 146",
    "correct_answer": -426984,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "81 * 85",
    "correct_answer": 6885,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "54 + 69",
    "correct_answer": 123,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "2857 - 3497",
    "correct_answer": -640,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "79 * 53",
    "correct_answer": 4187,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "406 * 11",
    "correct_answer": 4466,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "57 + 11",
    "correct_answer": 68,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "773 * 261",
    "correct_answer": 201753,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "319 * 75",
    "correct_answer": 23925,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "15 - 18 + 6",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "767 * 685",
    "correct_answer": 525395,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "862 * 662",
    "correct_answer": 570644,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "628 * 78",
    "correct_answer": 48984,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "372 * 895",
    "correct_answer": 332940,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "(12 + 72) * (31 - 39)",
    "correct_answer": -672,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "510 + 12 - 570 + 79 - 437",
    "correct_answer": -406,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1681 - 8231",
    "correct_answer": -6550,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "35 + 82",
    "correct_answer": 117,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "1 - 28 + 2 + 12 + 11 + 26 + 12 - 6 + 14 - 30 + 22 - 28 - 20 - 2 - 14 - 18 - 11 - 4 + 19 - 6 - 2",
    "correct_answer": -50,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "6399 - 8212",
    "correct_answer": -1813,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "670 - 353 - 602 * 681 - 815",
    "correct_answer": -410460,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "229 - 304 - 58 - 597 + 833",
    "correct_answer": 103,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "236 - 249 + 381 - 297 * 936",
    "correct_answer": -277624,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "7 - 5 + 1 - 6 + 4 - 9 - 6 + 5 + 9 - 8 + 1 - 7 + 5 + 9 + 9 + 6 - 2 - 9 + 5 - 6 + 3 + 1 + 8 - 5 + 6 + 1 - 7 - 8 - 1",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(22 + 26) * (96 - 86)",
    "correct_answer": 480,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "87 * 70",
    "correct_answer": 6090,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "526 * 988",
    "correct_answer": 519688,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "76 + 72 - 72",
    "correct_answer": 76,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "2 - 54",
    "correct_answer": -52,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "634 + 412 - 670 + 121 - 563",
    "correct_answer": -66,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "28 - 11 - 26 + 27 - 19 - 16 - 2 - 9 - 27 + 7 - 3 + 9 - 19 - 9 - 29 + 24 + 23 - 25 - 17 + 18 + 2 + 11 + 4 + 19 - 14 - 5",
    "correct_answer": -59,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "483 % 10",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "1157 - 8939",
    "correct_answer": -7782,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "72 * 77",
    "correct_answer": 5544,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "6 - 22 + 2 - 12 + 20 + 10 - 4 - 1 + 28 - 25 + 9 - 21 - 22 - 16 - 28 + 29 + 27 + 21 + 23 + 25 + 23 - 4 - 13",
    "correct_answer": 55,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "6 - 2 + 8 + 1 + 7 - 2 - 1 - 6 - 7 - 6 + 7 - 3 - 5 - 7 + 5 + 5 + 1",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "8389 + 1878",
    "correct_answer": 10267,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "184 * 865 + 75 - 126 * 619",
    "correct_answer": 81241,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "91 - 49 + 50",
    "correct_answer": 92,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "5 - 9 + 7 - 5 - 8 + 2 + 4 + 6 + 1 + 6 + 7 - 6 + 8 - 7 - 7 + 8 - 2 + 6 + 7 + 4 - 6 + 1 + 6 + 9 - 7 + 7 - 2 - 5 - 9 - 6 - 6 - 7 + 4",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "16 - 17 + 4 - 9 + 22 - 13 - 11 + 3 - 30 - 10 - 16 - 23 - 4 + 11 - 15 + 25 - 12 - 24 - 26 + 22 - 28 - 5 + 21 + 23",
    "correct_answer": -96,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "227 - 238",
    "correct_answer": -11,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "19 * 31",
    "correct_answer": 589,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(38 + 90) * (39 - 52)",
    "correct_answer": -1664,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "87 - 69",
    "correct_answer": 18,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "356 - 564",
    "correct_answer": -208,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "233 * 880",
    "correct_answer": 205040,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "11 - 23 - 13 + 7 - 27 - 23 + 6 - 23 - 1 + 7 - 22 - 6 - 30 + 5 - 16 - 19 - 22 - 2 + 27 - 24 - 27 + 1 - 14 + 26 + 26 - 25",
    "correct_answer": -201,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "5 - 6 - 3 + 9 + 7 + 1 + 4 - 8 - 5 - 9 + 3 - 7 + 2 - 4 + 3 + 2 + 6",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "249 * 551",
    "correct_answer": 137199,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "31 * 21",
    "correct_answer": 651,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "96 * 65",
    "correct_answer": 6240,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "7 + 3 + 2 - 3 - 7 + 4 - 9 - 2 + 8 - 7 + 3 - 6 + 4 + 2 + 6 + 5 + 2 - 1 + 5 - 4 + 1 - 2 - 1 + 8 + 6 + 5 - 6 + 7 - 6 - 6 + 2 + 9",
    "correct_answer": 29,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "518 + 164 * 543 - 33 * 436",
    "correct_answer": 75182,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "68 * 41",
    "correct_answer": 2788,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "882 * 748",
    "correct_answer": 659736,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "1378 - 3671",
    "correct_answer": -2293,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "121 * 711 - 799 - 345 * 670",
    "correct_answer": -145918,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1023 - 7164",
    "correct_answer": -6141,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "200 - 294",
    "correct_answer": -94,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "373 % 5",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "164 % 17",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "38 * 921 - 616 - 257 - 753",
    "correct_answer": 33372,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2110 - 2400",
    "correct_answer": -290,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "7 + 1 - 3 - 4 + 8 - 6 - 1 - 5 + 2 + 2 + 8 - 8 - 2 + 6 - 5 - 5 + 8 + 8 - 4 + 1 + 5 + 6 + 6 + 8 - 4 - 1 - 6 + 3 - 3 - 1 + 9 - 7 + 1 - 9 - 2",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "761 * 698 + 798 - 542 * 703",
    "correct_answer": 150950,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "105 - 796 - 340 - 929 + 849",
    "correct_answer": -1111,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "6 + 4 - 3 - 6 + 7 - 1 - 6 - 3 + 7 + 9 - 9 - 7 - 9 - 7 + 6 - 3 + 3 - 9 + 3 - 3 - 1 + 2 + 3 + 4 + 9 - 7 - 5 + 7 - 7",
    "correct_answer": -16,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "126 + 642 * 133 - 239 - 274",
    "correct_answer": 84999,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1549 - 3239",
    "correct_answer": -1690,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "521 * 25",
    "correct_answer": 13025,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "17 + 61",
    "correct_answer": 78,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "793 - 336 - 994 - 320 * 773",
    "correct_answer": -247897,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "390 % 5",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "9 + 1 + 1 - 7 + 1 - 9 + 8 + 2 - 5 - 2 + 6 + 6 - 4 + 4 - 6 + 2 - 8 + 5 + 8 - 8 - 5 + 3 + 5 - 6 + 5 - 3 + 5 - 8 - 3 + 3 - 5 - 5 - 1 + 5 + 1 - 9 + 9 - 3 - 3",
    "correct_answer": -11,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "4 - 3 - 2 + 8 - 9 + 5 + 5 - 5 + 8 - 2 + 6 - 2 - 8 - 7 + 7 + 6 - 8 + 7 - 1 - 3 + 6 + 1",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "180 * 898",
    "correct_answer": 161640,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "48 + 70 - 83",
    "correct_answer": 35,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "31 * 29",
    "correct_answer": 899,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "954 * 411",
    "correct_answer": 392094,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "1 + 8 + 1 + 4 - 9 - 4 + 2 - 6 + 4 - 5 - 9 + 4 - 6 + 9 + 5 + 3 + 2 - 1",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(91 + 94) * (64 - 35)",
    "correct_answer": 5365,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "87 - 28",
    "correct_answer": 59,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "18 + 13 + 17 - 24 - 13 + 20 + 17 - 9 - 20 + 2 - 20 - 26 + 8 + 22 + 28 + 12 - 1 - 1 + 29 + 20 - 26 - 23 - 17 + 1 + 12",
    "correct_answer": 39,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "58 - 65 + 29",
    "correct_answer": 22,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "780 - 432 * 253 * 460 + 662",
    "correct_answer": -50274718,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "26 + 25 + 10 + 23 + 28 - 16 + 17 + 28 - 18 + 20 - 1 + 7 - 28 - 4 + 12 - 28 - 6 + 3 - 1 + 8 + 30 + 1 + 15 - 25",
    "correct_answer": 126,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "3 + 27 + 21 - 21 - 6 + 17 + 10 + 10 + 25 - 7 - 23 + 29 + 19 + 10 - 14 + 5 + 29 + 27 + 27 - 4 + 10 + 5",
    "correct_answer": 199,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "85 + 14",
    "correct_answer": 99,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "666 * 209 + 549 - 810 + 210",
    "correct_answer": 139143,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "578 % 7",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "(55 + 15) * (18 - 21)",
    "correct_answer": -210,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "62 + 29 - 14",
    "correct_answer": 77,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "13 + 9 + 14 - 26 - 1 - 15 + 23 + 11 - 24 - 10 + 14 - 4 + 10 - 24 + 22 - 15 + 8 - 6 - 2 - 19 - 27 + 30",
    "correct_answer": -19,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "32 + 56 - 76",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "8 + 7 - 9 + 9 + 9 - 1 + 5 + 8 + 7 - 9 - 2 - 3 - 6 - 6 - 9 - 2 + 5 + 1",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "3181 + 3340",
    "correct_answer": 6521,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "821 + 487 * 310 - 519 - 526",
    "correct_answer": 150746,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1921 - 3240",
    "correct_answer": -1319,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "459 % 17",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "82 - 36",
    "correct_answer": 46,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "927 * 123 - 198 - 311 + 686",
    "correct_answer": 114198,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(30 + 22) * (36 - 37)",
    "correct_answer": -52,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "19 + 59 * 39 - 16 * 32",
    "correct_answer": 1808,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "2 + 5 + 7 - 27 - 26 + 12 - 15 + 15 + 7 + 7 + 27 - 26 + 28 - 29 - 3 + 11 - 6 + 4 + 30 - 2 - 17 - 16 - 17 - 11 - 22 - 1 + 19",
    "correct_answer": -44,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "2 + 8 - 4 - 5 - 6 + 1 - 4 + 6 - 8 - 5 - 8 + 9 - 4 + 2 - 1 + 4 + 9 + 7 + 1 + 4 + 1 + 7 - 8 + 3 - 7 - 8 - 2 + 8 + 8 + 3 + 1 - 6 + 6",
    "correct_answer": 14,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "58 * 43",
    "correct_answer": 2494,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "8 - 3 + 8 + 1 - 8 - 1 + 8 + 7 - 1 + 9 - 8 + 3 - 4 + 7 - 8 + 9 - 6 + 1 - 7 - 2 + 1 - 5 + 9 + 6 + 9 - 3 + 5 + 3 - 7",
    "correct_answer": 31,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "569 * 819",
    "correct_answer": 466011,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "950 % 16",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "173 + 696 * 65 - 382 - 224",
    "correct_answer": 44807,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "3124 - 4073",
    "correct_answer": -949,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "653 + 975 + 40 + 765 + 860",
    "correct_answer": 3293,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "597 - 866 * 127 - 620 * 343",
    "correct_answer": -322045,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "382 * 61",
    "correct_answer": 23302,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "54 + 74 * 82 - 98 * 84",
    "correct_answer": -2110,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "6 + 4 - 5 - 9 + 8 - 2 + 2 - 7 + 9 + 9 - 6 - 9 + 8 - 7 + 1 + 4 + 4",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "536 * 93",
    "correct_answer": 49848,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "47 - 12 + 56",
    "correct_answer": 91,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "21 + 23 - 12 - 15 - 2 + 19 + 22 - 17 + 8 + 21 - 5 - 10 - 3 - 23 - 19 - 14 - 21 + 17 - 17 - 7 + 24 + 28 - 28 - 20 - 25 + 26",
    "correct_answer": -29,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "293 * 10",
    "correct_answer": 2930,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "7 - 2 - 21 + 17 - 17 + 12 - 8 - 27 - 6 + 23 + 2 - 20 - 25 - 9 + 17 + 4 + 18 + 13 - 10 - 4 + 8 + 26 + 5 - 3 - 21",
    "correct_answer": -21,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "344 % 16",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "393 % 18",
    "correct_answer": 15,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "38 + 42 - 16",
    "correct_answer": 64,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "62 + 78 * 54 - 70 * 49",
    "correct_answer": 844,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "59 - 42 + 25",
    "correct_answer": 42,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "62 - 28",
    "correct_answer": 34,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "9231 - 6269",
    "correct_answer": 2962,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "319 * 484",
    "correct_answer": 154396,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "3039 - 5707",
    "correct_answer": -2668,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "732 * 29",
    "correct_answer": 21228,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "6210 + 6878",
    "correct_answer": 13088,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "499 * 58",
    "correct_answer": 28942,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "82 + 20 * 77 - 46 * 75",
    "correct_answer": -1828,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "295 - 419",
    "correct_answer": -124,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "653 - 322 + 599 + 123 * 265",
    "correct_answer": 33525,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "699 * 42",
    "correct_answer": 29358,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "18 - 8 - 12 - 20 - 29 - 30 + 26 - 4 + 18 - 7 - 26 - 23 + 14 - 18 + 25 + 10 - 1 + 25 + 10 - 3 - 3 - 30 - 22",
    "correct_answer": -90,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "19 + 79 * 11 - 58 * 22",
    "correct_answer": -388,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "97 - 282 - 742 * 379 + 690",
    "correct_answer": -280713,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "307 * 41",
    "correct_answer": 12587,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "34 * 94",
    "correct_answer": 3196,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "35 * 48",
    "correct_answer": 1680,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "82 - 15 + 68",
    "correct_answer": 135,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "224 % 9",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "29 + 19 - 17 + 4 - 5 - 21 + 25 + 9 + 17 - 11 + 5 + 8 - 30 + 11 + 18 + 28 - 25 + 6 + 26 - 28 + 7",
    "correct_answer": 75,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "36 + 42 * 14 - 38 * 17",
    "correct_answer": -22,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "946 * 29",
    "correct_answer": 27434,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "2 - 5 + 5 + 2 + 8 + 4 + 2 + 8 - 8 + 6 - 3 + 1 + 6 + 8 + 7 + 9 - 9 + 9 - 2 + 9 + 4 - 4 + 6 + 2 + 7 + 7 - 2 + 1 + 9 + 8 - 7 + 6",
    "correct_answer": 96,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "1199 - 1506",
    "correct_answer": -307,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "978 * 360 * 277 - 473 * 261",
    "correct_answer": 97402707,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "5558 + 7046",
    "correct_answer": 12604,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "661 * 57",
    "correct_answer": 37677,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "8 + 7 + 1 + 4 + 7 - 4 - 6 - 7 + 1 - 1 + 9 - 3 + 7 - 2 + 4 - 4 - 9 - 9 + 5 - 2 + 3 - 6 + 4 + 6 - 3 + 4 + 5 - 6 + 8 - 3 + 2 + 6 - 1 + 5 + 2 - 4 + 4 + 6 - 2",
    "correct_answer": 36,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "202 - 405",
    "correct_answer": -203,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "187 + 214 - 630 - 113 - 975",
    "correct_answer": -1317,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1894 - 3007",
    "correct_answer": -1113,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "104 - 330",
    "correct_answer": -226,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "9 - 1 - 6 - 2 + 6 - 6 + 2 + 8 - 2 + 3 - 7 + 2 + 9 - 2 - 7 + 7",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "72 - 26",
    "correct_answer": 46,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "388 + 953 - 626 + 122 * 388",
    "correct_answer": 48051,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "90 - 67",
    "correct_answer": 23,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "88 + 92 * 20 - 97 * 68",
    "correct_answer": -4668,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "(59 + 95) * (12 - 65)",
    "correct_answer": -8162,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "63 - 25 + 29",
    "correct_answer": 67,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "83 + 84 * 90 - 19 * 55",
    "correct_answer": 6598,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "406 + 392 * 478 * 208 - 377",
    "correct_answer": 38974237,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "30 * 95",
    "correct_answer": 2850,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "8848 + 1999",
    "correct_answer": 10847,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "468 * 81",
    "correct_answer": 37908,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "442 - 476",
    "correct_answer": -34,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "1485 - 2316",
    "correct_answer": -831,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "524 % 4",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "950 % 17",
    "correct_answer": 15,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "73 - 28",
    "correct_answer": 45,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "24 + 27 - 23 + 8 - 7 + 1 + 13 + 14 + 11 - 2 - 27 + 13 + 16 - 2 + 22 - 26 + 4 + 8 - 1 + 15 + 2 + 10 - 16 + 3",
    "correct_answer": 87,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "8 - 7 - 8 + 4 - 2 + 6 - 8 + 7 - 2 - 5 - 5 + 9 - 5 + 2 + 8 + 8 - 7 - 2 - 8 - 7 + 7 - 2 - 2 - 2 + 4 - 7 + 1 - 8 + 9 - 7",
    "correct_answer": -21,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "6 - 5 + 8 + 7 - 3 - 1 + 8 + 3 - 7 - 9 + 1 - 2 + 8 + 8 + 3 + 6 - 3 + 2 + 8 - 7 - 3 + 1 + 4 + 8 - 8 + 2 + 3 + 1 - 6",
    "correct_answer": 33,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "27 * 36",
    "correct_answer": 972,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "729 % 5",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "90 - 33",
    "correct_answer": 57,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "479 * 81",
    "correct_answer": 38799,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "8 + 8 + 2 + 7 - 2 - 8 - 7 - 6 + 8 + 3 + 7 - 2 + 9 + 3 + 9 - 2 + 8 + 8 + 8 + 1 - 9 + 8 + 5 + 2 + 4 + 5 - 1 + 3 - 7 + 9 - 8",
    "correct_answer": 73,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "6744 + 8015",
    "correct_answer": 14759,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "289 + 149 - 274 * 684 * 190",
    "correct_answer": -35608602,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "4 + 28 - 17 + 15 + 17 + 13 + 24 - 4 - 26 - 4 - 20 - 6 - 30 - 15 - 4 - 21 + 24 + 7 - 3 + 19 + 3 - 21 - 27",
    "correct_answer": -44,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "323 * 83",
    "correct_answer": 26809,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "8 + 3 - 1 - 3 + 7 - 7 + 3 + 7 - 8 + 7 + 6 - 3 + 9 - 6 - 8 - 7 - 8 - 8 - 6 + 7 + 2 + 9 - 9 - 5 + 4 - 4 - 4 + 2 + 3 + 1 + 2 - 1 - 8 - 3 - 2 - 5 - 4 - 5",
    "correct_answer": -35,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "58 * 50",
    "correct_answer": 2900,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "1 + 30 - 15 + 4 - 8 + 23 + 30 - 25 + 16 - 16 - 12 - 9 + 13 + 15 - 15 + 16 - 11 + 10 - 10 + 4 - 30",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "784 + 394 - 16 - 664 + 434",
    "correct_answer": 932,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "54 * 73",
    "correct_answer": 3942,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "191 * 215",
    "correct_answer": 41065,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "12 + 81 * 88 - 39 * 13",
    "correct_answer": 6633,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "690 - 648 + 406 - 931 * 357",
    "correct_answer": -331919,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "727 * 389",
    "correct_answer": 282803,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "13 + 20 + 5 - 19 - 1 + 27 - 25 - 8 - 8 - 13 + 30 - 30 - 27 + 16 + 24 + 14 + 26 + 30 - 2 - 19 - 4 - 7 + 5 + 9 + 24 + 1 - 6",
    "correct_answer": 75,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "8 + 19 - 11 - 14 - 29 - 5 + 14 - 27 - 13 + 29 + 21 + 22 + 14 + 13 - 11 + 2 + 13 - 8 - 1 + 8 + 28 + 5 - 27 - 13 - 14 - 11",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "164 * 774",
    "correct_answer": 126936,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "1793 - 1752",
    "correct_answer": 41,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "2311 - 3243",
    "correct_answer": -932,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "911 % 7",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "(17 + 88) * (55 - 60)",
    "correct_answer": -525,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "39 * 22",
    "correct_answer": 858,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(33 + 79) * (90 - 62)",
    "correct_answer": 3136,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "6 + 1 + 9 - 9 - 1 + 1 - 7 - 4 + 5 - 8 + 8 - 4 - 2 + 4 + 2 - 4 + 1 - 5 - 4 - 8 - 3",
    "correct_answer": -22,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "21 * 48",
    "correct_answer": 1008,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "375 * 26",
    "correct_answer": 9750,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "150 * 475",
    "correct_answer": 71250,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "7 + 9 - 8 + 1 - 3 + 6 - 9 - 7 + 4 + 4 + 5 + 6 + 3 + 5 + 8 + 7 - 7 + 2 + 2 - 2 - 7 + 1 - 3 - 7 + 1 + 7 + 1 - 5 - 2 + 8 - 8 - 9 - 2 - 7 - 7",
    "correct_answer": -6,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "4 + 3 - 5 - 3 + 2 + 3 - 8 + 5 + 9 + 3 + 5 + 2 - 7 - 5 - 7 - 4 - 1 + 4 + 5 - 8 + 1 + 9 + 6 + 8 + 3 - 6 - 7 + 6 + 6",
    "correct_answer": 23,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "55 + 29",
    "correct_answer": 84,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "21 - 29 - 25 + 4 + 30 + 12 + 19 + 21 + 8 - 23 - 27 - 16 + 22 - 20 + 5 - 17 - 22 + 17 + 9 - 20 + 5 + 2 - 11 + 16 + 20 - 7 + 1",
    "correct_answer": -5,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "3431 - 4908",
    "correct_answer": -1477,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "331 * 87",
    "correct_answer": 28797,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "704 * 362",
    "correct_answer": 254848,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "3 + 5 + 6 - 3 - 8 + 5 - 1 + 3 - 7 + 2 - 7 + 6 - 1 + 6 + 3 + 2 - 4 - 4 - 6 + 4",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "6 + 4 + 5 + 3 - 9 - 4 + 7 + 4 + 3 + 9 + 2 + 5 + 5 + 7 + 3 + 5 + 2 - 2",
    "correct_answer": 55,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "2494 + 2559",
    "correct_answer": 5053,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "95 - 48 + 17",
    "correct_answer": 64,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "954 - 698 - 948 + 826 + 671",
    "correct_answer": 805,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "100 * 76",
    "correct_answer": 7600,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "2 + 2 - 6 - 7 + 7 + 4 - 3 + 6 - 4 - 3 - 9 + 6 + 9 - 8 + 5 - 5 + 5 + 7 - 6 - 4 - 1 + 2 - 6 + 6 - 7 + 8 - 9 + 3 + 4 + 8 - 1 + 1 - 6",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "55 + 23 * 64 - 61 * 55",
    "correct_answer": -1828,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "836 - 821 + 718 + 221 - 665",
    "correct_answer": 289,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "3162 - 7337",
    "correct_answer": -4175,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "656 * 456",
    "correct_answer": 299136,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "35 * 47",
    "correct_answer": 1645,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "851 * 172",
    "correct_answer": 146372,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "17 - 85",
    "correct_answer": -68,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "55 - 53",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "5842 - 1894",
    "correct_answer": 3948,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "775 + 607 - 475 + 800 * 905",
    "correct_answer": 724907,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "77 * 66",
    "correct_answer": 5082,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "26 - 30 - 8 - 25 + 24 - 28 + 24 + 9 + 16 + 16 + 5 + 9 - 14 - 27 + 28 + 23 + 29 + 7 + 5 + 15 + 29 - 12 - 22 - 24 + 29 + 27 + 3",
    "correct_answer": 134,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "86 - 84",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "1972 - 6747",
    "correct_answer": -4775,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "24 - 12 + 18 - 7 - 27 - 30 + 26 + 29 + 6 - 12 - 26 - 23 - 21 + 19 + 3 + 22 - 11 + 26 + 2 + 14 + 24 + 28",
    "correct_answer": 72,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "29 - 7 - 27 + 20 - 6 + 21 - 23 - 10 + 25 - 6 - 30 + 11 + 3 - 24 - 6 + 25 - 18 + 5 - 15 + 15 + 24 - 10 - 9",
    "correct_answer": -13,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "426 - 495",
    "correct_answer": -69,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "132 * 684",
    "correct_answer": 90288,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "18 - 10 + 8 + 1 - 9 + 2 - 23 - 27 - 1 + 29 - 13 + 19 - 16 + 20 - 10 + 15 - 21 + 24 - 2 + 16 - 5 + 21 - 6",
    "correct_answer": 30,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "479 % 14",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "180 * 58",
    "correct_answer": 10440,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "2 + 1 - 3 + 3 + 6 - 7 - 5 + 9 - 2 - 8 + 8 + 5 - 3 + 1 + 9 + 8 - 8 + 6 + 2 - 6 + 6 + 9 - 5 - 3 + 8 + 4 - 2 + 2 - 2 - 2 + 9 - 6 + 9 - 1 + 2 - 1",
    "correct_answer": 45,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "6 + 9 + 9 + 1 + 7 + 6 - 4 + 8 + 9 + 8 - 4 + 1 + 4 - 8 - 2 + 8 + 7 + 4 - 1 + 1 + 9 + 3 - 4 + 9 + 1 + 4 + 6 + 9 - 1 + 4 - 3 + 7",
    "correct_answer": 113,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "98 - 87",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "5 + 6 - 8 - 9 + 5 + 6 - 8 + 7 + 9 - 1 + 8 - 7 - 1 - 1 + 3 + 7 + 1 + 6 - 6 + 9 + 5",
    "correct_answer": 36,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "993 % 11",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "337 - 581",
    "correct_answer": -244,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "2025 - 2667",
    "correct_answer": -642,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "10 - 57 + 45",
    "correct_answer": -2,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "(63 + 61) * (32 - 74)",
    "correct_answer": -5208,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "893 * 789 + 529 * 485 + 685",
    "correct_answer": 961827,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "770 * 36",
    "correct_answer": 27720,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "84 + 92 * 17 - 48 * 37",
    "correct_answer": -128,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "3002 - 4400",
    "correct_answer": -1398,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "948 * 11",
    "correct_answer": 10428,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "4 + 4 + 3 - 9 + 3 + 3 - 5 - 6 - 9 - 9 - 2 - 7 - 7 - 1 + 6 + 3 - 3 - 4 + 1 - 7 - 2",
    "correct_answer": -44,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "355 * 338",
    "correct_answer": 119990,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "884 * 39",
    "correct_answer": 34476,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "96 * 76",
    "correct_answer": 7296,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "3078 - 3174",
    "correct_answer": -96,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "5 - 7 - 1 + 7 + 1 - 6 - 9 + 6 + 7 + 7 - 7 + 7 - 7 + 3 + 6 + 7 + 3 - 7 - 5 - 3 + 4 + 1 + 3 - 9 - 2 - 1 - 3 + 6 + 4 - 9 - 7 + 1 - 3",
    "correct_answer": -8,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "76 + 95 * 21 - 77 * 25",
    "correct_answer": 146,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "855 - 555 * 472 * 386 * 978",
    "correct_answer": -98891994825,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "270 - 485",
    "correct_answer": -215,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "528 % 8",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "649 - 37 + 506 * 139 - 88",
    "correct_answer": 70858,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "5 + 1 + 5 - 4 + 8 + 9 + 4 - 2 - 7 + 5 - 7 + 2 + 7 + 3 + 8 - 2 + 9 - 8 + 7 + 1 - 9 + 6 + 2 + 4 - 7 + 1 + 8 + 9 - 5 - 7 - 9 + 9 + 2 + 4 + 2 - 1",
    "correct_answer": 53,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "2526 + 8511",
    "correct_answer": 11037,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "557 - 883 - 92 - 788 + 673",
    "correct_answer": -533,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "20 + 21 * 59 - 67 * 11",
    "correct_answer": 522,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "10 - 12 - 10 + 20 - 7 + 29 - 20 - 26 - 7 + 25 + 4 - 5 + 20 - 19 + 12 + 8 + 18 + 7 + 7 - 7 + 22 - 10 + 11 + 15",
    "correct_answer": 85,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "893 * 96",
    "correct_answer": 85728,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "792 * 94",
    "correct_answer": 74448,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(45 + 24) * (37 - 56)",
    "correct_answer": -1311,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "89 + 85 * 12 - 11 * 90",
    "correct_answer": 119,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "475 * 696",
    "correct_answer": 330600,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "2380 + 5065",
    "correct_answer": 7445,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "727 * 83",
    "correct_answer": 60341,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "59 - 48 + 87",
    "correct_answer": 98,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "14 + 24 + 14 + 3 - 24 - 15 + 30 - 1 - 7 - 15 + 29 - 24 + 10 - 9 - 30 - 26 - 28 + 15 + 3 - 25 - 17 + 19 - 13 - 8 + 21 - 1 + 8",
    "correct_answer": -53,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "3920 - 4321",
    "correct_answer": -401,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "370 * 373 + 319 - 523 + 841",
    "correct_answer": 138647,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "13 - 25",
    "correct_answer": -12,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "209 - 512 * 627 + 533 * 940",
    "correct_answer": 180205,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "94 * 33",
    "correct_answer": 3102,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "380 - 621",
    "correct_answer": -241,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "48 * 16",
    "correct_answer": 768,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(59 + 60) * (76 - 88)",
    "correct_answer": -1428,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "46 - 90",
    "correct_answer": -44,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "96 + 41",
    "correct_answer": 137,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "7102 - 8511",
    "correct_answer": -1409,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "96 * 83",
    "correct_answer": 7968,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "728 * 99",
    "correct_answer": 72072,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "128 - 14 + 964 * 713 + 902",
    "correct_answer": 688348,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "7 + 4 + 9 - 3 + 5 + 6 + 3 + 3 + 7 + 1 - 1 - 2 - 5 + 4 + 2 + 3 + 9 - 2 + 3 + 5 - 7 + 6 + 5 + 7 - 5 - 7 + 3 + 9 + 4 - 1 + 6 - 8 - 8 + 4 - 9",
    "correct_answer": 57,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "86 - 43",
    "correct_answer": 43,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "43 - 71 + 98",
    "correct_answer": 70,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "333 * 578 + 29 * 601 - 349",
    "correct_answer": 209554,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "13 + 14 * 12 - 37 * 59",
    "correct_answer": -2002,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "(67 + 84) * (36 - 99)",
    "correct_answer": -9513,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "68 - 12 + 83",
    "correct_answer": 139,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "6 + 9 + 7 + 1 + 9 + 5 + 8 - 4 + 7 + 1 + 9 + 6 - 2 + 8 + 2 + 2 - 1 + 1 + 6 + 4",
    "correct_answer": 84,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(44 + 31) * (21 - 12)",
    "correct_answer": 675,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "911 * 594",
    "correct_answer": 541134,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "(29 + 65) * (37 - 69)",
    "correct_answer": -3008,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "95 * 41",
    "correct_answer": 3895,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "14 + 47 * 28 - 95 * 53",
    "correct_answer": -3705,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "813 + 373 * 798 + 283 * 883",
    "correct_answer": 548356,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "439 * 314",
    "correct_answer": 137846,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "487 * 59",
    "correct_answer": 28733,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "458 - 484",
    "correct_answer": -26,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "3949 - 5759",
    "correct_answer": -1810,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "9 - 52",
    "correct_answer": -43,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "82 + 65",
    "correct_answer": 147,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "44 - 4",
    "correct_answer": 40,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "4239 - 8265",
    "correct_answer": -4026,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "19 + 34",
    "correct_answer": 53,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "354 * 46",
    "correct_answer": 16284,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "716 - 298 + 819 - 325 * 528",
    "correct_answer": -170363,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "393 - 576",
    "correct_answer": -183,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "684 * 685",
    "correct_answer": 468540,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "5 + 2 - 1 + 9 + 5 - 4 + 8 + 9 + 8 - 2 - 3 + 6 + 6 - 6 + 5 + 7 + 1 + 2 + 8 + 9 + 2 - 9 - 8 + 8 - 8 + 4 - 4 - 3 + 1 + 3 - 4 - 3 - 7 - 2 - 4 + 3 + 3 - 6 - 4",
    "correct_answer": 36,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "17 * 23",
    "correct_answer": 391,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "3 - 8 - 1 - 6 - 4 + 2 + 7 - 4 + 1 + 2 + 6 - 1 + 7 + 5 + 9 - 2 - 6 - 3 + 6 - 4 + 6 + 6 + 1 - 8 - 1 - 7 + 9 + 9 + 8 - 1 - 4 + 9",
    "correct_answer": 36,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "814 * 77",
    "correct_answer": 62678,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "23 * 25",
    "correct_answer": 575,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "17 - 4 - 13 + 12 + 12 + 16 + 23 + 1 - 2 - 24 + 29 - 25 + 20 + 8 + 16 - 29 - 10 - 1 - 24 - 2 - 12 - 30 + 27 - 24",
    "correct_answer": -19,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "78 + 33",
    "correct_answer": 111,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "291 * 80",
    "correct_answer": 23280,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "820 % 17",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "29 - 87 + 93",
    "correct_answer": 35,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "43 * 20",
    "correct_answer": 860,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "130 + 721 - 476 * 43 * 170",
    "correct_answer": -3478709,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "8552 + 1829",
    "correct_answer": 10381,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "687 + 260 * 250 * 329 * 96",
    "correct_answer": 2052960687,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "48 + 57 * 55 - 86 * 16",
    "correct_answer": 1807,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "838 * 44",
    "correct_answer": 36872,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "998 - 864 + 999 - 47 - 67",
    "correct_answer": 1019,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(99 + 36) * (89 - 13)",
    "correct_answer": 10260,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "54 - 35 + 28",
    "correct_answer": 47,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "77 - 162 + 870 - 357 * 651",
    "correct_answer": -231622,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "489 - 568",
    "correct_answer": -79,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "175 - 698 * 635 * 718 * 619",
    "correct_answer": -196990027485,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "26 + 26 + 6 - 28 + 9 - 20 - 11 + 2 + 23 - 15 - 9 - 5 - 21 - 18 + 5 + 30 - 8 - 11 - 6 + 2 + 18",
    "correct_answer": -5,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "34 + 97",
    "correct_answer": 131,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "1 + 4 - 5 + 17 + 18 + 9 + 11 - 21 + 19 + 23 + 11 + 25 - 20 + 13 - 21 + 14 - 19 - 29 - 14 - 26 + 10",
    "correct_answer": 20,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "22 - 24 + 15 - 29 - 14 - 24 - 16 + 21 + 25 + 23 + 3 + 10 + 18 - 17 - 8 + 28 + 13 + 26 - 21 - 16 - 26 + 21 - 7 + 5 + 11 + 19 + 20",
    "correct_answer": 78,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "5 + 2 + 9 + 3 + 7 + 7 - 2 + 3 + 9 + 4 + 6 + 1 + 5 - 2 - 4 + 9 - 5 - 5 - 4 + 7 - 2 - 9 - 4 + 3 + 3 - 5 + 3 + 4 + 1 + 9 + 4 + 7 + 9 + 1 + 5 - 6 + 4 + 1 + 1",
    "correct_answer": 84,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "664 - 474 - 797 * 718 - 798",
    "correct_answer": -572854,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "118 * 485",
    "correct_answer": 57230,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "9 - 9 - 7 + 8 + 4 - 8 - 5 - 3 + 3 - 9 - 3 + 5 + 2 - 3 - 2 - 4 + 3 - 3",
    "correct_answer": -22,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "20 + 21 - 10 - 5 - 29 - 4 - 15 + 5 - 26 - 24 + 8 - 20 - 10 + 10 + 20 - 5 + 17 - 24 - 17 + 1 - 19 - 4 + 22 + 18",
    "correct_answer": -70,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "30 - 53 + 44",
    "correct_answer": 21,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "1 - 3 - 1 + 5 - 9 + 2 - 9 - 8 + 2 - 8 + 9 - 5 + 9 - 2 - 7 - 5 - 3 - 8 + 6",
    "correct_answer": -34,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "651 * 32",
    "correct_answer": 20832,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "6869 - 2037",
    "correct_answer": 4832,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "6 - 6 + 8 - 4 - 4 - 6 - 6 - 2 + 3 + 8 + 2 - 8 - 7 + 8 + 9 + 6 - 8 + 2 - 6 - 5 + 3 - 1 + 9 - 7 - 1 - 9 - 3 + 9 + 8 - 3 - 1",
    "correct_answer": -6,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "20 + 7 + 7 - 26 - 29 + 11 + 18 - 7 - 29 - 6 + 11 + 28 + 12 + 8 + 27 + 2 - 6 - 10 - 15 + 25 - 10 - 28 + 16 + 8 - 23 - 1",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "39 + 66 * 13 - 56 * 14",
    "correct_answer": 113,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "472 * 102 + 522 * 194 * 970",
    "correct_answer": 98278104,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "258 * 196",
    "correct_answer": 50568,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "1 + 11 + 24 + 9 + 21 - 23 - 19 - 8 + 8 - 17 + 30 + 15 + 12 + 8 - 11 + 8 + 4 - 13 - 28 - 10 - 11 - 5 - 4 + 4 + 15 - 24",
    "correct_answer": -3,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "68 * 69",
    "correct_answer": 4692,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "29 - 1 - 18 - 16 - 1 + 12 + 4 + 19 + 27 - 11 - 15 - 23 - 25 + 27 - 3 - 25 - 3 - 6 - 14 - 24 - 3 + 29 + 26 - 25 + 7 + 8",
    "correct_answer": -25,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "993 * 43",
    "correct_answer": 42699,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "341 + 795 * 126 - 351 * 415",
    "correct_answer": -45154,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2 - 11 - 29 - 16 + 12 + 20 - 3 + 13 - 27 - 2 + 28 - 17 + 29 - 28 - 3 + 25 - 9 + 8 - 5 + 29 - 18 - 10 + 28 - 26",
    "correct_answer": -10,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "142 * 426",
    "correct_answer": 60492,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "30 * 36",
    "correct_answer": 1080,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(87 + 90) * (87 - 97)",
    "correct_answer": -1770,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "3 - 15",
    "correct_answer": -12,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "363 - 492",
    "correct_answer": -129,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "338 * 424",
    "correct_answer": 143312,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "952 * 43",
    "correct_answer": 40936,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "59 + 41",
    "correct_answer": 100,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "8 + 1 + 2 - 6 + 5 - 9 + 4 - 1 + 3 - 5 - 7 + 3 - 6 + 3 + 8 + 8 + 4 - 6 - 6 - 8 + 9 - 6 - 3 - 4 - 4 + 4 - 8 + 6 + 2 - 3 + 2",
    "correct_answer": -10,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "134 - 169",
    "correct_answer": -35,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "3369 - 5834",
    "correct_answer": -2465,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "602 * 33",
    "correct_answer": 19866,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "460 - 715 - 759 + 853 * 157",
    "correct_answer": 132907,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "44 * 445 - 413 * 839 + 851",
    "correct_answer": -326076,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(55 + 67) * (87 - 50)",
    "correct_answer": 4514,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "421 + 642 - 466 - 104 * 66",
    "correct_answer": -6267,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "75 + 77",
    "correct_answer": 152,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "88 + 85 * 29 - 69 * 53",
    "correct_answer": -1104,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "814 * 79",
    "correct_answer": 64306,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "90 - 98 + 40",
    "correct_answer": 32,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "62 + 45 * 23 - 89 * 71",
    "correct_answer": -5222,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "66 * 40",
    "correct_answer": 2640,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "41 * 46",
    "correct_answer": 1886,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "53 * 95",
    "correct_answer": 5035,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "126 * 60",
    "correct_answer": 7560,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "184 * 587",
    "correct_answer": 108008,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "390 + 305 - 161 - 301 + 989",
    "correct_answer": 1222,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1 + 3 - 8 + 3 + 3 - 2 + 7 + 2 - 4 - 3 - 5 - 9 - 7 - 7 + 2 - 6 - 5 - 7 - 1 + 8 - 2",
    "correct_answer": -37,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "81 - 31",
    "correct_answer": 50,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "3 - 2 - 2 + 8 - 3 + 8 - 7 - 9 - 4 + 9 - 6 + 3 + 5 + 6 + 6 - 2 + 6",
    "correct_answer": 19,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(34 + 89) * (96 - 56)",
    "correct_answer": 4920,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "7 - 30 + 15 - 22 - 28 - 28 - 1 + 13 + 28 - 16 + 14 + 21 + 15 + 19 + 14 + 25 - 30 + 26 - 4 + 17 + 24 + 1 + 14 + 19 - 19",
    "correct_answer": 94,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "2 - 3 + 2 - 2 - 4 - 7 + 7 + 8 + 9 + 2 - 8 + 4 + 3 - 7 + 1 - 6 - 9 - 8 + 7 - 4 + 5 - 2 + 7 + 4 - 9 + 6 + 2 + 3 + 2 - 1 - 8 - 5 - 8 + 5 + 1 - 7",
    "correct_answer": -18,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(16 + 67) * (94 - 66)",
    "correct_answer": 2324,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "932 + 572 * 10 - 583 - 122",
    "correct_answer": 5947,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "124 * 888",
    "correct_answer": 110112,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "1 + 3 + 4 + 5 + 8 + 3 + 4 - 5 + 7 - 2 + 3 + 1 - 1 + 7 + 3 + 3 + 7 + 3 - 9 - 9 - 6",
    "correct_answer": 30,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "658 % 12",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "267 * 352 - 834 + 54 + 768",
    "correct_answer": 93972,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "4827 + 2223",
    "correct_answer": 7050,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "12 + 49",
    "correct_answer": 61,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "457 - 91 + 317 * 140 - 934",
    "correct_answer": 43812,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "413 - 504",
    "correct_answer": -91,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "104 * 43",
    "correct_answer": 4472,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "22 + 38 * 65 - 99 * 87",
    "correct_answer": -6121,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "865 * 768",
    "correct_answer": 664320,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "3 - 5 + 3 - 9 - 4 - 4 + 4 + 5 - 4 - 2 - 1 - 7 - 2 - 2 - 4 + 7 + 2",
    "correct_answer": -20,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "139 * 78",
    "correct_answer": 10842,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(59 + 38) * (74 - 33)",
    "correct_answer": 3977,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "20 + 48",
    "correct_answer": 68,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "7 + 87 - 11",
    "correct_answer": 83,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "12 + 30",
    "correct_answer": 42,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "2931 - 3286",
    "correct_answer": -355,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "2626 - 4755",
    "correct_answer": -2129,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "7 - 8 + 9 - 7 - 7 - 7 + 3 - 2 - 8 - 7 + 8 - 5 + 5 - 2 - 1 + 6 - 7 - 2 + 5 - 8 + 3 - 6 + 4 - 5 - 7 + 2 - 6 - 7 + 6 - 5 + 3",
    "correct_answer": -46,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "10 + 91",
    "correct_answer": 101,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(30 + 39) * (74 - 99)",
    "correct_answer": -1725,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "2 + 27 - 22 + 9 + 15 - 2 + 25 + 11 - 5 - 5 - 19 - 16 - 8 + 3 - 22 + 13 + 11 - 20 + 14 + 10 - 24 + 24",
    "correct_answer": 21,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "808 % 18",
    "correct_answer": 16,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "16 + 1 + 9 + 17 - 21 + 3 + 7 - 12 + 19 + 2 + 22 - 26 + 13 - 27 + 21 + 1 + 15 - 19 + 24 + 22 - 13",
    "correct_answer": 74,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "6620 + 2791",
    "correct_answer": 9411,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "13 - 65 + 99",
    "correct_answer": 47,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "360 - 506",
    "correct_answer": -146,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "1 + 4 - 6 + 2 + 6 - 1 + 1 - 2 - 5 - 1 - 8 + 3 - 7 - 7 - 5 + 8 + 9 - 9 - 7 + 4 + 2 - 9 - 4 + 4 + 4 - 3 + 7 - 9 + 1 - 1 + 8 + 2 - 7 - 1 - 3",
    "correct_answer": -29,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "27 * 31",
    "correct_answer": 837,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "87 - 31",
    "correct_answer": 56,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "5 - 6 + 5 + 7 - 5 + 5 - 3 - 4 + 4 - 3 + 9 - 7 - 7 + 5 - 3 - 2 + 1 + 7 - 8",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "335 * 50",
    "correct_answer": 16750,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(21 + 95) * (64 - 85)",
    "correct_answer": -2436,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "9 - 5 - 10 + 28 - 9 + 21 + 25 - 25 - 20 + 14 - 15 + 17 - 22 - 15 + 9 - 10 - 17 + 22 - 10 + 13 - 26 + 8 - 26 - 11",
    "correct_answer": -55,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "861 * 99",
    "correct_answer": 85239,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(62 + 45) * (53 - 18)",
    "correct_answer": 3745,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "582 - 541 - 902 - 608 - 661",
    "correct_answer": -2130,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1 + 9 + 9 - 3 + 4 - 5 - 6 + 7 - 6 + 1 + 2 + 9 - 6 + 5 + 9 + 7 - 6 + 5 - 4 - 3 - 5 - 4 - 4 + 2 + 3 + 6 - 6 + 8 + 6 + 3 - 4 + 4 + 6 + 9 + 7 - 1",
    "correct_answer": 59,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "72 + 53",
    "correct_answer": 125,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "2442 - 3235",
    "correct_answer": -793,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "838 + 556 - 954 + 591 * 105",
    "correct_answer": 62495,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2 + 24 - 22 + 9 - 3 - 12 - 1 + 8 + 6 - 23 - 7 + 7 - 27 + 26 + 3 - 4 + 19 + 14 + 3 + 30 - 24 + 1 + 14 - 7 - 11 - 28",
    "correct_answer": -3,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "7 + 1 - 9 + 3 + 7 - 5 + 7 + 1 + 8 - 5 + 8 + 7 - 7 + 8 + 9 + 7 - 8 - 6 + 2 + 1",
    "correct_answer": 36,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(86 + 94) * (24 - 57)",
    "correct_answer": -5940,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "358 * 223 - 615 - 813 - 590",
    "correct_answer": 77816,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "832 * 66",
    "correct_answer": 54912,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "7 + 5 + 6 + 28 + 30 - 18 + 26 - 17 - 29 - 2 + 7 - 8 - 1 - 18 + 17 + 16 + 4 - 4 + 27 - 5 + 21 + 17",
    "correct_answer": 109,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "60 - 75 + 71",
    "correct_answer": 56,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "442 * 456",
    "correct_answer": 201552,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "8096 + 7471",
    "correct_answer": 15567,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "(60 + 69) * (86 - 84)",
    "correct_answer": 258,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "215 * 341",
    "correct_answer": 73315,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "482 % 10",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "111 * 749",
    "correct_answer": 83139,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "760 * 874",
    "correct_answer": 664240,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "7022 + 5902",
    "correct_answer": 12924,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "801 * 482",
    "correct_answer": 386082,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "6152 - 3290",
    "correct_answer": 2862,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "636 * 799",
    "correct_answer": 508164,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "15 * 40",
    "correct_answer": 600,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "936 % 9",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "974 * 294 - 366 * 174 * 809",
    "correct_answer": -51234000,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "3962 - 4151",
    "correct_answer": -189,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "1 + 3 + 3 - 8 + 8 - 8 - 4 - 3 + 1 + 3 + 1 + 9 + 1 - 3 + 1 + 6 + 3 + 4 - 4 + 9 - 3 - 1 - 8 - 1 - 5 - 7 + 7 + 8 - 8",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "7965 + 2677",
    "correct_answer": 10642,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "381 * 108 - 603 + 853 + 23",
    "correct_answer": 41421,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "285 * 577 + 701 * 262 + 677",
    "correct_answer": 348784,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1152 - 1132",
    "correct_answer": 20,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "25 + 20 - 11 + 23 - 27 + 1 + 22 + 19 + 7 + 7 + 13 - 16 + 14 + 6 - 8 - 25 - 3 - 16 + 3 + 24 - 17 - 6 - 3 - 26 + 25",
    "correct_answer": 51,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(96 + 51) * (87 - 59)",
    "correct_answer": 4116,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "9 - 7 + 4 - 3 - 7 + 1 + 3 - 3 + 9 + 5 + 7 + 2 + 9 + 2 - 1 + 2 + 4 - 1 - 1 - 5 + 4 + 8",
    "correct_answer": 41,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "85 - 75",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "8 + 27 - 2 + 8 + 20 - 15 + 8 - 6 - 14 - 12 + 28 + 6 - 7 - 3 - 12 + 17 + 14 - 9 - 11 + 11 - 14 + 5 + 22 - 13",
    "correct_answer": 56,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(68 + 32) * (86 - 53)",
    "correct_answer": 3300,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "982 * 803 - 267 + 915 * 253",
    "correct_answer": 1019774,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "96 - 61",
    "correct_answer": 35,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "11 - 17 + 20 + 30 - 25 - 8 + 24 - 2 - 29 - 27 + 20 + 25 + 19 + 15 - 22 + 9 + 14 - 17 - 28 - 29 + 1 - 2 + 21 - 25 - 7 - 18 + 6",
    "correct_answer": -41,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "17 + 80",
    "correct_answer": 97,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "785 + 451 + 211 * 43 * 535",
    "correct_answer": 4855291,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(62 + 10) * (98 - 90)",
    "correct_answer": 576,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "(75 + 47) * (21 - 75)",
    "correct_answer": -6588,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "7590 + 2350",
    "correct_answer": 9940,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "16 + 73",
    "correct_answer": 89,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "894 * 32",
    "correct_answer": 28608,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "3788 - 6522",
    "correct_answer": -2734,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "554 % 5",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "9 - 8 - 4 + 4 + 4 + 6 - 1 - 8 - 5 + 2 + 5 + 2 - 9 + 9 - 6 - 6 - 3 + 7 - 4 - 6 - 6 - 2 - 1 - 4 + 6 - 8 + 2 + 8 + 5 - 6 + 9 - 5 + 3 + 1 - 2 + 3 - 8 + 7 + 3",
    "correct_answer": -7,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "15 + 19 * 21 - 68 * 19",
    "correct_answer": -878,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "6890 + 9796",
    "correct_answer": 16686,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "32 + 96 * 54 - 30 * 29",
    "correct_answer": 4346,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "71 + 10",
    "correct_answer": 81,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "257 - 394",
    "correct_answer": -137,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "10 + 69",
    "correct_answer": 79,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "14 + 581 + 206 + 552 - 643",
    "correct_answer": 710,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "386 + 193 - 700 + 698 - 415",
    "correct_answer": 162,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "57 + 5 - 75",
    "correct_answer": -13,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "95 + 60 * 48 - 58 * 50",
    "correct_answer": 75,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "67 + 78 * 16 - 58 * 44",
    "correct_answer": -1237,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "6 - 94",
    "correct_answer": -88,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "1323 - 2951",
    "correct_answer": -1628,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "193 % 10",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "(16 + 61) * (94 - 42)",
    "correct_answer": 4004,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "837 * 50",
    "correct_answer": 41850,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(88 + 40) * (88 - 53)",
    "correct_answer": 4480,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "63 * 41",
    "correct_answer": 2583,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "26 + 31 * 62 - 99 * 71",
    "correct_answer": -5081,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "(84 + 13) * (60 - 93)",
    "correct_answer": -3201,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "7 + 8 - 11 - 4 - 26 + 18 + 23 - 2 + 30 - 19 + 11 - 6 - 12 - 4 + 19 + 25 + 14 - 12 + 20 - 4 + 11 - 24 + 11 + 7 - 30 + 4 - 14",
    "correct_answer": 40,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "3001 - 5729",
    "correct_answer": -2728,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "3 + 9 + 4 - 3 + 6 - 9 + 1 - 1 + 9 - 7 + 1 + 5 + 4 - 2 - 7 - 3 - 5",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "7 - 75",
    "correct_answer": -68,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "3712 - 5771",
    "correct_answer": -2059,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "999 * 70",
    "correct_answer": 69930,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "89 - 61",
    "correct_answer": 28,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "591 * 504 + 387 - 604 * 994",
    "correct_answer": -302125,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "941 * 477",
    "correct_answer": 448857,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "42 - 52",
    "correct_answer": -10,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "8 - 5 - 27 - 22 - 25 - 22 + 20 + 25 + 21 + 9 + 17 - 26 + 15 - 9 + 27 - 10 - 1 + 28 + 4 + 2 - 17 - 25 + 8 + 8",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "38 + 64 * 43 - 51 * 43",
    "correct_answer": 597,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "240 - 165 - 928 + 682 * 99",
    "correct_answer": 66665,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "63 + 72",
    "correct_answer": 135,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "9 + 6 + 7 + 7 + 9 + 7 - 3 - 5 + 9 - 9 + 5 + 7 + 1 + 9 + 1 - 5 + 2 - 2 - 8 + 1 - 9 - 1 + 9 + 8 + 3 - 5 - 1 + 4 + 1 + 2 + 4 + 8 + 9 - 1",
    "correct_answer": 79,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "514 * 530 + 404 + 285 - 335",
    "correct_answer": 272774,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "553 * 460",
    "correct_answer": 254380,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "589 * 79",
    "correct_answer": 46531,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "65 + 98",
    "correct_answer": 163,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "3 + 20 - 22 + 28 + 27 - 7 + 6 + 30 - 4 + 21 + 19 - 21 - 29 - 24 - 6 - 27 + 14 + 5 - 4 - 11 + 14 + 21 + 20 - 22 + 2 + 10 + 24",
    "correct_answer": 87,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "29 - 4 + 14 - 7 - 26 - 22 + 4 - 11 + 19 + 11 + 30 - 25 - 14 + 9 - 13 + 4 + 30 + 16 - 22 - 13 + 7 - 10 + 4 + 9 + 16 - 2 - 10",
    "correct_answer": 23,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "727 * 53",
    "correct_answer": 38531,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "44 * 82",
    "correct_answer": 3608,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "65 - 14",
    "correct_answer": 51,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "382 * 698",
    "correct_answer": 266636,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "(19 + 94) * (27 - 13)",
    "correct_answer": 1582,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "56 * 64",
    "correct_answer": 3584,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "161 * 66 + 367 + 158 * 693",
    "correct_answer": 120487,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "15 - 474 * 251 * 605 * 741",
    "correct_answer": -53336639055,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "21 + 5 + 17 + 28 + 9 - 27 + 1 - 19 - 12 - 23 - 4 + 13 + 19 - 16 - 9 + 9 + 9 - 26 - 24 + 23 + 14 + 5",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "1 - 4 - 1 + 6 - 7 - 8 + 5 + 6 + 4 + 1 - 5 + 3 - 9 - 7 - 3 + 2 - 9 + 4 + 5 - 2 - 6 - 3 + 4 + 8 - 8 - 3 + 6 - 4 - 9 + 9 - 9 - 7 + 2 - 2 - 7",
    "correct_answer": -47,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "39 - 97",
    "correct_answer": -58,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "248 - 735 + 208 + 131 * 486",
    "correct_answer": 63387,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "26 - 23 + 22 - 15 + 29 - 27 - 8 - 23 + 2 - 4 + 4 - 22 - 1 + 19 + 26 - 13 - 12 + 11 - 16 + 10 + 23",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "474 * 88",
    "correct_answer": 41712,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "728 * 46",
    "correct_answer": 33488,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "191 * 869 + 18 - 483 + 968",
    "correct_answer": 166482,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "170 - 755 - 735 * 790 * 520",
    "correct_answer": -301938585,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "325 - 415",
    "correct_answer": -90,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "14 - 23 + 5 + 8 - 26 - 30 - 3 - 18 - 24 + 9 - 6 - 19 + 11 + 7 + 23 - 24 + 20 - 12 - 4 - 7 + 4 - 1 - 16 + 11 + 22",
    "correct_answer": -79,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "596 * 987",
    "correct_answer": 588252,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "93 * 78",
    "correct_answer": 7254,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "45 * 15",
    "correct_answer": 675,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "51 - 2 + 34",
    "correct_answer": 83,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "306 - 577 - 53 * 864 - 321",
    "correct_answer": -46384,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "3754 - 5781",
    "correct_answer": -2027,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "309 - 365",
    "correct_answer": -56,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "387 - 446",
    "correct_answer": -59,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "68 * 67",
    "correct_answer": 4556,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "315 * 63",
    "correct_answer": 19845,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "14 + 12 - 7 - 21 - 12 - 10 + 24 + 5 - 8 - 24 + 15 - 14 + 10 + 3 + 23 - 29 + 22 - 27 - 7 - 29 + 27 - 11 - 5 + 26 + 16 + 27",
    "correct_answer": 20,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "19 * 20",
    "correct_answer": 380,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "401 * 543 * 637 + 712 + 437",
    "correct_answer": 138703440,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "6134 - 7367",
    "correct_answer": -1233,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "68 + 28 * 15 - 66 * 48",
    "correct_answer": -2680,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "381 % 4",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "4 + 8 - 1 - 5 + 6 - 9 + 7 + 6 - 6 + 9 + 5 - 8 - 2 - 6 + 2 - 3 + 2 + 3 - 3",
    "correct_answer": 9,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "2 + 3 + 9 + 5 + 7 + 6 + 5 - 1 - 7 - 1 + 5 - 5 + 6 + 8 + 9 + 5 - 9 + 5 - 1 + 5 + 8 - 1 + 2 + 9 - 8 - 3 + 3 - 1 + 3",
    "correct_answer": 68,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "68 * 92",
    "correct_answer": 6256,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "44 * 32",
    "correct_answer": 1408,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "649 + 770 * 744 * 107 - 354",
    "correct_answer": 61298455,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "506 * 36",
    "correct_answer": 18216,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "8 + 66",
    "correct_answer": 74,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "42 - 28",
    "correct_answer": 14,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "90 + 88",
    "correct_answer": 178,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "49 * 56",
    "correct_answer": 2744,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "132 * 306",
    "correct_answer": 40392,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "9 - 99",
    "correct_answer": -90,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "181 % 13",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "67 - 49",
    "correct_answer": 18,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "623 * 669",
    "correct_answer": 416787,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "369 * 40",
    "correct_answer": 14760,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "8 - 1 - 20 + 22 - 24 - 14 + 4 - 15 + 11 - 19 - 6 - 26 + 18 - 23 + 22 - 17 - 1 - 11 + 25 + 23 + 12 - 24 - 11 - 5",
    "correct_answer": -72,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "21 - 25 - 19 + 12 + 11 + 16 + 23 - 12 + 4 - 26 - 7 + 29 - 2 + 28 - 21 - 16 + 4 - 2 + 3 + 20 + 29 - 4 - 18 - 10 + 26 - 27 - 4",
    "correct_answer": 33,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "46 * 36",
    "correct_answer": 1656,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "5 - 5 - 7 - 9 - 8 + 5 - 9 + 5 + 6 + 6 + 7 - 6 + 9 - 3 + 8 + 7 + 9 - 9 - 6 + 1 - 3 + 5 - 3 + 1 + 6 - 8 + 3 - 4 + 9",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(28 + 80) * (56 - 73)",
    "correct_answer": -1836,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "1725 - 7547",
    "correct_answer": -5822,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "97 + 55 - 93",
    "correct_answer": 59,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "31 * 96",
    "correct_answer": 2976,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "5 - 14",
    "correct_answer": -9,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "28 + 79 * 36 - 20 * 21",
    "correct_answer": 2452,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "16 + 49 * 46 - 76 * 47",
    "correct_answer": -1302,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "885 + 245 * 431 + 510 - 615",
    "correct_answer": 106375,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "676 * 71",
    "correct_answer": 47996,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "224 * 41",
    "correct_answer": 9184,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "9 - 65",
    "correct_answer": -56,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "86 * 58",
    "correct_answer": 4988,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "455 * 71",
    "correct_answer": 32305,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "8 - 1 + 2 - 6 - 2 + 6 + 8 - 5 - 6 + 4 + 3 + 6 + 8 + 7 + 8 - 3 + 7 - 1 + 6 + 3 + 1 + 3 + 3 + 1 + 3 + 4 + 7 + 9 + 4 + 8",
    "correct_answer": 95,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "50 - 49",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "213 * 198",
    "correct_answer": 42174,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "812 % 18",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "12 + 97",
    "correct_answer": 109,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "40 + 47",
    "correct_answer": 87,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "16 - 12 + 29 - 17 + 13 - 16 - 8 - 21 + 2 + 1 - 28 + 16 + 22 + 15 + 27 + 13 + 12 - 27 + 12 - 6 + 15 - 9 + 22 - 23 - 5 - 18",
    "correct_answer": 25,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "3706 - 5362",
    "correct_answer": -1656,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "47 * 40",
    "correct_answer": 1880,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "31 + 74 - 50",
    "correct_answer": 55,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "597 + 260 - 82 - 637 - 563",
    "correct_answer": -425,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "13 - 14 + 21 + 16 - 18 - 21 - 27 - 29 + 18 + 29 - 2 + 3 + 19 - 23 - 5 + 7 - 24 - 16 + 16 - 22 - 15 + 17",
    "correct_answer": -57,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "422 * 73",
    "correct_answer": 30806,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "956 % 18",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "755 - 919 - 769 - 832 + 305",
    "correct_answer": -1460,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "5 - 3 + 9 + 2 - 8 + 2 + 8 - 7 - 5 + 9 + 3 + 4 + 9 - 4 + 7 - 3 + 1 - 4 + 9 + 9 + 2 + 1 + 3 - 9 - 9 - 6 - 3 - 3 + 1",
    "correct_answer": 20,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "9 + 8 - 9 + 2 + 5 + 1 + 8 + 7 - 1 - 1 + 4 + 6 + 9 + 3 + 2 - 3 + 9 + 6 + 1 - 3 - 7",
    "correct_answer": 56,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "8 + 5 + 1 + 7 - 9 + 6 - 9 + 4 + 6 + 8 - 4 + 4 + 1 - 2 + 6 + 3 + 7 - 5 + 9 - 2 + 8 + 6 - 2 - 8 - 8 - 1 + 6 + 3 + 9 + 6 - 4 - 8 - 5 - 4 + 6 + 2 - 6 + 2",
    "correct_answer": 46,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "459 * 96",
    "correct_answer": 44064,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "601 * 638",
    "correct_answer": 383438,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "4 - 7 - 7 - 2 + 4 - 9 + 1 - 8 + 1 + 8 - 6 + 1 + 8 + 8 - 1 + 3 + 2 - 7",
    "correct_answer": -7,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "29 - 29 + 20 - 14 - 17 + 20 + 8 + 27 - 15 + 9 - 4 - 14 - 11 + 1 + 9 - 27 + 11 + 24 - 11 + 12 + 29 - 20 + 2 - 27 + 2 + 19",
    "correct_answer": 33,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "6 + 1 - 8 + 1 + 8 - 2 + 2 + 1 + 4 + 1 - 8 + 2 - 2 - 4 - 4 - 2 - 3 - 7 + 3 + 6 + 8 - 3 - 1 + 9 + 3 + 8 + 5 + 1 + 9 - 9 - 8 - 9 + 1 + 3",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "800 * 63",
    "correct_answer": 50400,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "8 - 7 - 7 - 1 + 6 - 2 + 8 - 1 + 9 + 7 + 2 + 1 - 4 + 6 + 3 - 1 + 8 + 6 + 9 + 3 + 4 - 8 + 2 + 2 - 1 + 9 - 2 + 5 - 7 - 9 - 6 + 3 - 6 + 7 + 4 - 8 - 4 + 9 - 1",
    "correct_answer": 46,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "3 + 3 - 2 - 1 - 2 - 6 - 7 - 3 - 8 + 8 + 9 + 2 - 3 - 6 - 3 + 2 + 7 + 2 + 4 - 3 + 9",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "2880 - 5294",
    "correct_answer": -2414,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "18 - 2 - 7 + 21 - 23 + 27 + 14 + 16 - 21 - 1 + 2 + 24 - 5 - 14 - 28 + 21 - 19 - 3 + 20 + 19 + 1 + 20 - 14 - 12 - 10 + 10",
    "correct_answer": 54,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "19 - 21 - 14 + 8 + 19 - 8 - 8 - 16 + 7 + 20 - 19 + 28 + 23 - 1 - 4 - 5 - 16 + 2 - 23 + 14 + 21 - 9 + 12",
    "correct_answer": 29,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "4176 - 5435",
    "correct_answer": -1259,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "(69 + 65) * (58 - 39)",
    "correct_answer": 2546,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "16 * 45",
    "correct_answer": 720,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "805 * 486",
    "correct_answer": 391230,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "26 + 25 - 22 - 26 - 15 + 28 - 25 - 26 - 9 + 11 - 6 - 30 + 5 + 5 + 18 - 26 - 25 - 27 - 22 + 26 - 19 + 4 + 17 + 15 - 18 - 2",
    "correct_answer": -118,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "4578 - 4976",
    "correct_answer": -398,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "23 + 9 - 2 - 1 + 5 - 4 + 16 + 7 - 28 - 13 - 9 + 4 + 13 - 26 - 2 + 15 - 16 + 17 - 3 + 4 + 2 + 15 + 26 - 17 + 16 + 24",
    "correct_answer": 75,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "42 + 34 * 35 - 94 * 85",
    "correct_answer": -6758,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "22 - 3 - 15 + 28 + 3 + 12 + 28 - 21 + 24 + 25 - 27 + 25 - 27 - 30 - 16 - 25 - 28 - 7 + 3 - 15 + 1 - 28 + 8 + 18 + 26 + 23",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "45 + 9",
    "correct_answer": 54,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "6277 + 5055",
    "correct_answer": 11332,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "22 + 10 * 29 - 27 * 26",
    "correct_answer": -390,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "98 + 15 * 56 - 86 * 64",
    "correct_answer": -4566,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "28 + 70",
    "correct_answer": 98,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "45 * 27",
    "correct_answer": 1215,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "5402 + 7786",
    "correct_answer": 13188,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "507 % 13",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "18 - 19 + 1 - 13 + 28 + 29 + 16 + 10 + 12 - 18 - 13 + 17 + 14 - 22 + 20 - 6 - 4 - 20 + 1 + 4 + 18 + 17 + 9 - 20",
    "correct_answer": 79,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "2 - 1 - 6 + 2 - 8 - 6 - 2 - 1 - 4 + 2 + 2 + 4 + 2 + 9 - 4 - 8",
    "correct_answer": -17,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "540 * 945",
    "correct_answer": 510300,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "34 - 27",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "52 + 35",
    "correct_answer": 87,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "8 - 4 - 3 + 6 + 6 + 5 - 2 + 6 + 6 - 2 + 2 + 8 - 7 - 4 - 2 - 1 + 8 + 5 - 4 - 1 - 6 - 2 - 1 - 4 + 9 - 2 - 1 + 7 - 3 + 1",
    "correct_answer": 28,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "29 * 15",
    "correct_answer": 435,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "25 + 22 + 22 + 10 + 19 + 3 + 16 + 6 - 4 + 16 + 2 - 6 + 20 + 29 - 4 - 16 + 13 + 1 + 23 + 21 - 15 - 28 + 27 + 27 - 10 + 17",
    "correct_answer": 236,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "418 + 271 - 255 + 101 + 882",
    "correct_answer": 1417,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "141 + 773 - 140 * 965 + 886",
    "correct_answer": -133300,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "136 * 58 + 973 - 469 * 596",
    "correct_answer": -270663,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "293 * 62",
    "correct_answer": 18166,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(43 + 26) * (55 - 94)",
    "correct_answer": -2691,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "86 - 14",
    "correct_answer": 72,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "41 * 20",
    "correct_answer": 820,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "969 * 716",
    "correct_answer": 693804,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "689 * 22",
    "correct_answer": 15158,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "933 % 8",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "22 + 11 - 15 - 26 - 1 - 17 - 6 - 14 + 15 - 8 - 17 - 14 - 20 + 2 + 18 - 1 - 13 - 22 + 27 + 11 - 11",
    "correct_answer": -79,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "91 * 83",
    "correct_answer": 7553,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "220 - 344",
    "correct_answer": -124,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "902 * 81",
    "correct_answer": 73062,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "926 * 98",
    "correct_answer": 90748,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "1528 - 8368",
    "correct_answer": -6840,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "123 - 235",
    "correct_answer": -112,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "254 * 11",
    "correct_answer": 2794,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(24 + 65) * (57 - 37)",
    "correct_answer": 1780,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "261 - 275",
    "correct_answer": -14,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "30 - 17 + 13 - 8 - 4 + 20 - 8 - 30 - 13 + 5 - 28 - 10 - 9 + 7 - 4 - 25 - 19 - 1 - 2 - 21 + 4 + 23 + 16 + 30",
    "correct_answer": -51,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "2 - 18 - 9 + 27 + 28 + 5 - 1 - 18 - 23 + 15 + 9 - 15 - 20 - 17 - 18 - 6 + 9 + 23 + 1 - 19 - 3 - 9 - 27 - 19 + 1 + 26",
    "correct_answer": -76,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "4951 + 5366",
    "correct_answer": 10317,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "425 - 199 - 651 * 730 * 11",
    "correct_answer": -5227304,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "130 - 379",
    "correct_answer": -249,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "50 + 27 * 75 - 75 * 78",
    "correct_answer": -3775,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "771 - 251 + 233 + 119 - 229",
    "correct_answer": 643,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "10 + 21 - 7 + 1 - 21 + 26 - 28 - 9 - 13 + 22 + 29 + 22 + 27 + 19 + 8 - 9 - 18 + 5 + 29 - 8 + 7 - 16 - 2 + 22",
    "correct_answer": 117,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "972 * 775",
    "correct_answer": 753300,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "73 + 85 - 52",
    "correct_answer": 106,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "512 * 685 * 711 - 595 * 497",
    "correct_answer": 249066205,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "845 * 973",
    "correct_answer": 822185,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "993 + 694 * 710 * 562 * 329",
    "correct_answer": 91106641513,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "5 - 1 - 11 + 28 - 5 + 21 + 10 + 10 + 23 + 16 + 12 - 29 + 7 + 2 - 11 + 18 + 21 - 20 + 8 + 24 - 6 - 6 - 9 - 10 - 18 - 2",
    "correct_answer": 77,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "42 * 85",
    "correct_answer": 3570,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "8 - 6 - 6 - 3 - 2 + 1 + 2 - 8 - 2 + 5 - 4 - 8 + 8 - 6 + 9 - 5 - 2 + 4 + 3 - 7 + 2 - 4 + 4 - 6 + 9 - 2 - 8 + 2 - 6 - 1 - 3 + 8 + 1 - 3",
    "correct_answer": -26,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "72 + 49 * 62 - 16 * 20",
    "correct_answer": 2790,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "209 * 597",
    "correct_answer": 124773,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "338 * 21",
    "correct_answer": 7098,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "143 + 451 + 624 - 853 * 754",
    "correct_answer": -641944,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "83 + 30 * 51 - 46 * 60",
    "correct_answer": -1147,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "282 - 433",
    "correct_answer": -151,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "3661 - 3890",
    "correct_answer": -229,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "33 - 11",
    "correct_answer": 22,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "29 + 43 - 22",
    "correct_answer": 50,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "11 - 16 + 14 + 14 + 12 + 16 + 17 + 27 + 7 + 29 - 19 + 1 + 20 - 10 + 16 - 21 + 12 - 17 + 5 - 1 + 27 - 13 + 17 + 17",
    "correct_answer": 165,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "343 % 12",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "4022 - 4053",
    "correct_answer": -31,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "131 % 7",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "25 + 12 - 14 + 5 + 1 - 5 - 10 + 19 - 4 + 13 + 4 - 19 - 8 + 22 - 27 - 22 - 8 - 1 + 26 + 6 - 1 - 7",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "56 - 75",
    "correct_answer": -19,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "176 - 407 * 301 * 780 + 167",
    "correct_answer": -95555117,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "228 * 599",
    "correct_answer": 136572,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "1 - 7 + 9 + 6 + 2 + 7 - 6 + 1 - 4 - 5 - 1 + 2 + 4 + 5 - 7 - 4 - 5 + 2 - 9 + 5 - 1 + 7 + 4 - 5 + 2 - 1 - 2 - 1 - 3 + 1 - 9 - 7 + 2 - 9 - 2 + 1 + 3 + 4 + 6",
    "correct_answer": -14,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "67 * 56",
    "correct_answer": 3752,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "10 + 89",
    "correct_answer": 99,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "122 - 234",
    "correct_answer": -112,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "383 - 632",
    "correct_answer": -249,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "8 + 8 - 9 - 5 + 4 + 3 - 4 + 1 + 7 + 9 + 4 - 7 - 3 - 7 + 1 + 3",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "386 * 60",
    "correct_answer": 23160,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "14 + 7 - 16 - 16 - 23 + 5 + 5 + 28 - 22 + 5 - 26 + 7 + 22 + 30 - 9 + 7 - 15 + 4 + 22 - 19 + 18 - 24",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "5 + 8 - 2 + 2 + 3 + 6 - 4 - 7 - 6 - 7 - 2 + 1 + 5 - 9 + 4 - 3 - 7 + 7 + 4 - 6 + 1 - 6 + 8 + 9 + 1 - 5 + 8 + 9 - 6 - 7 - 2 + 2 - 7 + 6 + 6 - 2",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "3 - 28 + 19 - 1 - 25 - 1 + 28 - 8 + 12 - 10 + 2 + 14 + 26 - 10 + 18 - 5 + 4 - 28 + 21 + 26 + 11 + 14 + 3 - 17 + 2 - 11 - 28",
    "correct_answer": 31,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "92 - 90",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "71 + 38",
    "correct_answer": 109,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "787 * 523",
    "correct_answer": 411601,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "89 - 39",
    "correct_answer": 50,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "908 * 348",
    "correct_answer": 315984,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "140 * 506 + 478 * 731 * 893",
    "correct_answer": 312101114,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "862 * 52",
    "correct_answer": 44824,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "8 + 6 - 2 - 3 + 1 + 9 - 3 + 8 - 8 + 6 - 5 + 3 - 5 - 5 + 6 + 2 - 1 - 2 + 7 + 6 - 5 - 5 - 7 - 3 + 6 - 8 + 1 + 7 - 4 + 7 - 7 - 5 + 1 + 5",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "451 * 810",
    "correct_answer": 365310,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "3 + 2 - 8 - 2 + 5 + 6 - 7 - 2 + 9 + 9 - 4 - 4 + 6 - 3 + 9 + 9 - 4 + 9 + 3 - 3",
    "correct_answer": 33,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(27 + 58) * (39 - 35)",
    "correct_answer": 340,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "38 + 96 * 30 - 46 * 62",
    "correct_answer": 66,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "691 * 54",
    "correct_answer": 37314,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "42 + 40 * 20 - 70 * 81",
    "correct_answer": -4828,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "7 - 22 - 21 - 16 + 25 + 14 + 19 + 30 + 26 - 6 + 3 + 30 + 5 - 28 - 6 - 8 + 28 - 30 - 9 - 12 + 3",
    "correct_answer": 32,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "13 - 57 + 22",
    "correct_answer": -22,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "458 * 731",
    "correct_answer": 334798,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "333 - 381",
    "correct_answer": -48,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "694 * 22",
    "correct_answer": 15268,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "545 * 21",
    "correct_answer": 11445,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "24 - 19 - 2 - 24 - 30 - 25 + 15 - 16 - 18 + 24 + 11 + 6 - 11 - 14 + 26 - 3 - 26 + 25 + 28 - 28 + 19 - 20 - 19 + 11 - 7 - 16 + 22",
    "correct_answer": -67,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "180 % 16",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "884 * 65",
    "correct_answer": 57460,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "3 + 7 + 7 + 3 - 2 + 9 + 1 - 9 + 9 - 9 - 9 - 2 - 4 + 2 + 3 - 8 + 2 - 4 - 2 + 1 + 2 - 6 + 3 + 1 - 1 - 9 - 5 + 8 - 8 - 9 - 6 + 9 - 2 + 1 + 4 - 4 + 9 + 6",
    "correct_answer": -9,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "815 * 784",
    "correct_answer": 638960,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "22 + 78",
    "correct_answer": 100,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(47 + 81) * (35 - 16)",
    "correct_answer": 2432,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "9 - 5 - 29 - 16 + 25 - 15 - 9 - 15 + 2 - 4 + 6 - 4 - 17 + 14 - 8 + 7 - 19 - 23 - 18 + 6 - 25 - 15",
    "correct_answer": -153,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(43 + 58) * (88 - 73)",
    "correct_answer": 1515,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "393 - 540",
    "correct_answer": -147,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "2 - 2 + 1 + 6 + 7 + 8 - 5 + 9 - 2 + 1 + 9 - 4 - 5 - 7 - 1 - 9",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "646 - 222 * 717 * 98 + 504",
    "correct_answer": -15597902,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "377 + 691 - 862 + 534 - 511",
    "correct_answer": 229,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "3623 + 6422",
    "correct_answer": 10045,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "138 * 571",
    "correct_answer": 78798,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "(94 + 13) * (97 - 61)",
    "correct_answer": 3852,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "65 + 68",
    "correct_answer": 133,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "888 * 332",
    "correct_answer": 294816,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "77 + 8 - 1",
    "correct_answer": 84,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "828 % 19",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "98 * 66",
    "correct_answer": 6468,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(36 + 46) * (97 - 93)",
    "correct_answer": 328,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "10 + 11 + 11 - 4 - 1 + 30 - 9 - 5 - 1 - 28 + 6 - 9 - 19 + 15 - 14 - 1 + 19 + 20 - 15 + 16 - 13 + 12",
    "correct_answer": 31,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "11 + 11 - 2 - 7 - 16 + 23 + 21 - 13 + 7 + 13 + 9 - 9 + 9 + 12 - 27 + 24 - 5 - 14 + 23 - 21 + 17 - 23 + 21 - 14 - 18 - 3 + 17",
    "correct_answer": 46,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "303 * 469",
    "correct_answer": 142107,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "294 - 400",
    "correct_answer": -106,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "217 + 353 * 42 + 592 + 297",
    "correct_answer": 15932,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "52 - 43",
    "correct_answer": 9,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "58 * 75",
    "correct_answer": 4350,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "1440 + 8563",
    "correct_answer": 10003,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "4 - 19 - 5 + 3 + 21 - 28 + 7 + 11 - 14 - 12 - 22 - 16 - 7 + 29 - 13 - 18 + 11 + 7 - 1 - 23 + 20 + 9 - 16 + 3",
    "correct_answer": -69,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "5 + 9 + 4 - 4 - 2 - 3 - 3 - 2 + 3 + 1 + 4 - 1 + 1 - 3 - 2 + 3",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(33 + 34) * (24 - 36)",
    "correct_answer": -804,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "51 * 30",
    "correct_answer": 1530,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "31 + 76 - 42",
    "correct_answer": 65,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "30 + 10 - 18 + 4 + 8 - 3 - 17 - 2 - 15 - 13 + 16 + 19 + 23 + 25 + 28 + 2 - 17 - 11 + 9 + 12 + 8 - 7 - 1",
    "correct_answer": 90,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "315 * 58",
    "correct_answer": 18270,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(97 + 71) * (90 - 34)",
    "correct_answer": 9408,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "9 - 7 - 7 + 6 + 1 + 8 - 4 + 6 - 6 - 5 - 7 - 2 + 6 - 8 + 5 + 6 - 4 - 1 + 7 - 3 + 2 + 4 + 5 - 3 - 6 - 6 - 3 - 5 - 3 + 1 + 9",
    "correct_answer": -5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "574 * 90",
    "correct_answer": 51660,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "68 + 67 - 79",
    "correct_answer": 56,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "14 - 16 - 18 - 15 - 29 - 16 + 28 - 25 - 3 - 8 - 22 + 10 + 20 + 16 + 17 + 6 + 15 + 25 - 7 + 18 + 28 + 4",
    "correct_answer": 42,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "42 * 62",
    "correct_answer": 2604,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "142 % 13",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "892 * 814",
    "correct_answer": 726088,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "936 * 544",
    "correct_answer": 509184,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "518 * 42",
    "correct_answer": 21756,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "918 - 262 + 424 * 632 - 854",
    "correct_answer": 267770,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "23 + 32 * 85 - 19 * 78",
    "correct_answer": 1261,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "862 * 360",
    "correct_answer": 310320,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "614 * 928 + 927 - 913 - 102",
    "correct_answer": 569704,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "688 * 45",
    "correct_answer": 30960,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "61 + 75 * 42 - 84 * 73",
    "correct_answer": -2921,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "327 * 542",
    "correct_answer": 177234,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "828 * 588 - 938 * 356 * 125",
    "correct_answer": -41254136,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1562 - 2109",
    "correct_answer": -547,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "297 * 638",
    "correct_answer": 189486,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "5933 + 5397",
    "correct_answer": 11330,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "2 + 8 + 9 - 4 - 5 + 5 + 6 - 3 - 2 - 4 + 9 - 1 - 2 - 5 + 1 + 5 + 1 - 9 - 6 + 1 - 2 + 1 - 2 - 2 - 8 - 5 + 2 + 9 + 6 - 5",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "489 - 649",
    "correct_answer": -160,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "72 + 75 * 81 - 22 * 63",
    "correct_answer": 4761,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "502 - 589 - 899 * 653 * 497",
    "correct_answer": -291762446,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "81 * 32",
    "correct_answer": 2592,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "8 - 11 + 2 - 21 + 7 + 27 - 23 - 29 + 14 - 6 + 22 - 25 + 5 + 7 - 1 + 2 - 24 + 2 + 12 + 5 - 17 - 12",
    "correct_answer": -56,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "755 * 91",
    "correct_answer": 68705,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(43 + 14) * (49 - 12)",
    "correct_answer": 2109,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "4705 + 9510",
    "correct_answer": 14215,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "709 + 988 * 109 - 662 - 989",
    "correct_answer": 106750,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "685 * 863",
    "correct_answer": 591155,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "326 * 256",
    "correct_answer": 83456,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "43 + 28 * 56 - 46 * 87",
    "correct_answer": -2391,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "1732 + 2885",
    "correct_answer": 4617,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "905 % 19",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "57 - 10",
    "correct_answer": 47,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "56 - 23",
    "correct_answer": 33,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(70 + 36) * (43 - 86)",
    "correct_answer": -4558,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "7 - 4 + 5 - 7 - 7 + 5 - 2 - 5 + 8 + 2 - 4 - 3 - 2 + 4 + 1 - 4 - 2 - 3 - 5 - 1 - 2",
    "correct_answer": -19,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "73 - 6",
    "correct_answer": 67,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "861 * 525",
    "correct_answer": 452025,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "686 * 747 - 842 - 373 + 609",
    "correct_answer": 511836,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "993 + 217 - 647 - 22 - 519",
    "correct_answer": 22,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2354 - 3119",
    "correct_answer": -765,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "34 + 91 * 68 - 56 * 55",
    "correct_answer": 3142,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "106 * 79",
    "correct_answer": 8374,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "923 * 40",
    "correct_answer": 36920,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "170 * 643",
    "correct_answer": 109310,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "87 + 57 * 33 - 21 * 22",
    "correct_answer": 1506,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "482 % 11",
    "correct_answer": 9,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "204 - 301",
    "correct_answer": -97,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "793 * 99",
    "correct_answer": 78507,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "835 - 755 - 756 * 152 + 622",
    "correct_answer": -114210,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "392 % 14",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "18 * 636 + 423 - 882 - 73",
    "correct_answer": 10916,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "9450 + 1752",
    "correct_answer": 11202,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "69 + 18 - 50",
    "correct_answer": 37,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "1064 - 1191",
    "correct_answer": -127,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "366 * 56",
    "correct_answer": 20496,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "87 * 92",
    "correct_answer": 8004,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "6 - 8 + 8 - 5 - 2 - 7 + 4 + 6 + 1 - 2 - 9 + 5 + 5 + 7 - 6 - 3 + 7 - 3 + 9",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "8167 + 4909",
    "correct_answer": 13076,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "26 + 7 + 18 - 20 + 21 - 2 - 17 + 8 - 9 - 4 - 11 - 24 + 30 - 21 + 27 + 9 + 18 - 16 - 25 + 24 + 8 - 12",
    "correct_answer": 35,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "98 + 44",
    "correct_answer": 142,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "8 - 6 - 3 - 8 + 7 + 7 - 5 - 6 + 8 - 9 - 3 + 6 - 3 - 9 - 3 - 3 - 4 + 7 - 7 - 9 + 9 + 1 - 9 - 3 + 6 - 6 - 6 + 7 + 7 - 6 + 2 + 8 - 4 - 9",
    "correct_answer": -38,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "3919 - 5650",
    "correct_answer": -1731,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "379 + 417 - 743 - 388 + 391",
    "correct_answer": 56,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "11 - 16 - 23 - 7 + 23 - 1 - 4 - 25 - 8 - 30 + 2 - 4 - 1 + 15 + 4 + 11 + 18 + 28 - 30 - 3 - 21",
    "correct_answer": -61,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "3 - 6 - 7 - 1 - 5 - 8 - 7 + 3 + 2 + 4 - 2 - 3 - 7 - 6 - 7 + 5 - 6 + 6 + 9 + 7",
    "correct_answer": -26,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "238 % 5",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "812 % 7",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "56 - 95",
    "correct_answer": -39,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "2871 - 6700",
    "correct_answer": -3829,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "7 - 8 - 5 - 8 - 3 + 6 + 2 + 3 - 6 - 4 + 7 + 4 - 4 - 8 - 6 - 6 + 7 + 1 - 3 + 4 - 2 - 4 - 2 + 1 + 4 - 8 + 5 - 5 + 4",
    "correct_answer": -27,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(51 + 30) * (74 - 76)",
    "correct_answer": -162,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "652 * 39",
    "correct_answer": 25428,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "5 - 3 + 4 - 3 + 3 - 5 + 6 - 8 + 9 + 3 + 1 - 4 + 9 + 1 + 5 + 4 + 2 + 9 + 5 - 5 + 1 + 5 - 1 - 3 - 4 - 8 - 6 - 9 + 7 + 8",
    "correct_answer": 28,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "12 - 10 + 14 + 14 - 24 + 17 + 8 + 10 - 1 - 22 - 28 + 17 + 3 - 4 + 7 + 14 - 30 - 16 + 7 + 4 - 4 - 9 + 20 + 19 - 25",
    "correct_answer": -7,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "507 % 18",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "473 % 10",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "4777 - 6719",
    "correct_answer": -1942,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "44 + 21 - 48",
    "correct_answer": 17,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "494 * 294",
    "correct_answer": 145236,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "76 + 71",
    "correct_answer": 147,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "257 - 307",
    "correct_answer": -50,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "9083 + 4201",
    "correct_answer": 13284,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "363 * 78",
    "correct_answer": 28314,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "3838 - 3733",
    "correct_answer": 105,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "23 * 185 - 498 - 718 * 899",
    "correct_answer": -641725,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "273 + 175 + 293 - 401 + 350",
    "correct_answer": 690,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "11 - 71",
    "correct_answer": -60,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "8 + 5 + 3 - 2 - 5 - 7 - 2 - 3 - 7 - 2 + 7 + 5 - 2 + 9 + 4 + 7 - 1 - 1 - 8 - 9 - 6 - 1 - 7 + 5 + 9 - 5 - 1 - 3 + 8 + 4",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "27 * 18",
    "correct_answer": 486,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "92 + 59 * 34 - 50 * 19",
    "correct_answer": 1148,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "3 + 23 + 22 - 26 - 8 + 23 - 2 - 19 - 11 - 17 + 6 + 18 + 18 - 3 - 9 + 6 + 23 + 4 - 6 - 12 - 10 + 1 + 2 + 22 + 4 - 3 + 17",
    "correct_answer": 66,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(50 + 56) * (85 - 56)",
    "correct_answer": 3074,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "6090 - 6362",
    "correct_answer": -272,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "31 * 44",
    "correct_answer": 1364,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "295 - 160 + 120 - 266 + 519",
    "correct_answer": 508,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "667 * 264",
    "correct_answer": 176088,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "18 * 26",
    "correct_answer": 468,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "49 * 40",
    "correct_answer": 1960,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "292 * 51",
    "correct_answer": 14892,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "381 - 624",
    "correct_answer": -243,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "11 - 2 - 20 + 6 - 13 - 20 - 22 - 5 - 6 + 11 + 18 + 10 - 2 + 26 - 21 - 25 + 30 - 22 - 30 + 5 - 16 + 9 - 30",
    "correct_answer": -108,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "150 * 78",
    "correct_answer": 11700,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "771 * 603",
    "correct_answer": 464913,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "523 * 80",
    "correct_answer": 41840,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "460 - 417 - 802 + 482 - 442",
    "correct_answer": -719,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "43 * 36",
    "correct_answer": 1548,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "342 % 18",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "17 + 3 - 9 + 10 - 24 - 18 - 6 + 7 + 27 - 30 - 21 - 1 - 14 + 4 - 13 - 8 - 30 + 20 + 29 + 26 - 17 + 20 - 13 - 1 - 3 + 15",
    "correct_answer": -30,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "726 - 347 + 598 * 537 - 972",
    "correct_answer": 320533,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "361 - 485",
    "correct_answer": -124,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "4 - 10 + 4 - 15 + 22 + 25 + 18 - 14 - 26 + 11 + 19 - 30 - 16 + 13 - 15 - 25 - 11 + 1 - 25 + 19 - 20 - 12 + 11 - 13 + 21 + 6 - 28",
    "correct_answer": -86,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "7 - 1 + 5 - 1 - 1 - 8 + 8 - 8 - 9 + 1 - 3 - 3 + 3 + 2 + 1 + 9 - 4 + 1 - 6",
    "correct_answer": -7,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "3955 - 5175",
    "correct_answer": -1220,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "3711 + 1848",
    "correct_answer": 5559,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "671 * 907",
    "correct_answer": 608597,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "9 - 4 + 5 + 1 + 7 + 5 - 6 + 8 - 3 + 7 - 7 - 9 + 4 + 3 + 6 - 8 - 8 - 2 + 7 - 1 - 3 + 2 + 4 - 9 + 7 - 4 + 1 + 6 + 5 - 2 + 8 + 6 + 9 + 6 + 3",
    "correct_answer": 53,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "548 * 795 - 194 + 952 - 262",
    "correct_answer": 436156,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "889 + 37 * 502 * 158 - 257",
    "correct_answer": 2935324,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "630 * 11",
    "correct_answer": 6930,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "661 * 594",
    "correct_answer": 392634,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "3 + 26 - 4 - 16 + 24 - 27 + 2 - 1 - 29 - 28 - 17 + 17 - 23 - 5 - 28 + 12 + 25 - 18 + 9 - 21 - 24 - 21 + 1",
    "correct_answer": -143,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "60 * 74",
    "correct_answer": 4440,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "33 - 601 + 664 + 338 - 207",
    "correct_answer": 227,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "7 - 9 + 1 - 5 - 8 - 9 + 5 + 7 - 1 - 8 + 8 + 6 + 3 + 1 + 2 - 9",
    "correct_answer": -9,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "195 * 61",
    "correct_answer": 11895,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "2129 - 8620",
    "correct_answer": -6491,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "(97 + 95) * (56 - 89)",
    "correct_answer": -6336,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "9 - 6 - 7 - 9 + 3 + 8 + 1 - 6 - 2 + 7 + 5 + 6 + 1 + 3 - 3 + 5 + 3 - 4 + 5 - 8 - 6 + 8 + 1 - 3 + 2 + 1 - 7 + 7 + 5 - 9 - 1 + 8 + 6 + 9 + 2 + 9 + 1 + 9 + 8",
    "correct_answer": 61,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "4 - 1 - 9 - 9 - 1 - 1 + 6 + 7 + 9 + 6 - 1 + 4 - 7 + 6 + 4 - 1 - 4 - 7 + 4 + 6 + 2 - 7 - 6 + 4 - 4 - 1 - 9 - 2 - 8 - 8 - 2 + 1 - 2",
    "correct_answer": -27,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "635 * 774",
    "correct_answer": 491490,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "399 * 988",
    "correct_answer": 394212,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "385 - 546",
    "correct_answer": -161,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "15 + 20",
    "correct_answer": 35,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "6 - 21 + 7 - 24 - 13 - 3 + 21 - 19 + 2 + 11 - 4 + 24 + 9 + 12 + 16 + 21 - 22 - 30 - 2 - 24 - 18",
    "correct_answer": -51,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "3403 - 4483",
    "correct_answer": -1080,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "9515 - 7767",
    "correct_answer": 1748,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "8 + 4 + 4 - 8 + 8 - 3 + 2 + 9 + 3 + 2 + 1 - 6 + 5 - 1 + 6 + 1 - 1 - 9 + 8 + 8 + 9 + 5 + 7 - 4 + 5 - 4 + 1 + 2 + 6 - 5 - 4 - 8 + 5 + 7 + 5 + 7",
    "correct_answer": 75,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "320 * 42",
    "correct_answer": 13440,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "247 - 275",
    "correct_answer": -28,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "21 + 16 + 6 + 29 - 3 + 16 + 22 + 14 - 19 + 12 - 5 - 22 - 9 - 8 + 22 + 9 - 29 + 23 + 20 + 1 + 6 + 24 - 27",
    "correct_answer": 119,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "26 * 39",
    "correct_answer": 1014,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "9348 + 4090",
    "correct_answer": 13438,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "642 % 14",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "4 + 6 + 6 - 4 + 3 + 2 + 1 + 8 - 8 + 5 + 3 - 5 - 3 - 9 - 5 - 6 - 9 - 3 + 1 + 9 + 1",
    "correct_answer": -3,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "635 * 950 - 888 - 353 + 283",
    "correct_answer": 602292,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "668 * 65",
    "correct_answer": 43420,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "951 % 6",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "3 - 2 + 6 + 9 + 2 - 5 - 6 + 6 - 4 - 5 - 2 + 3 + 3 + 9 + 6 - 7 + 7 - 9 + 7 - 4 - 8 - 2 - 4 - 8 + 8 + 6 + 1 + 4 + 6 - 6 - 7 - 1 + 8",
    "correct_answer": 14,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "4 + 12",
    "correct_answer": 16,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "68 + 33",
    "correct_answer": 101,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "28 + 12 + 14 - 5 - 13 + 13 + 25 - 26 - 30 - 26 - 16 + 12 + 18 - 21 - 4 + 29 + 21 - 3 - 25 - 4 - 2 - 6",
    "correct_answer": -9,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "76 + 55",
    "correct_answer": 131,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "262 * 90",
    "correct_answer": 23580,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "8 - 3 + 8 + 7 + 8 - 1 + 4 - 7 - 9 + 6 + 5 - 5 + 4 + 2 + 8 - 1 + 7 + 7 - 2 - 6 + 2 + 5 + 1 - 6 - 4 - 4 + 2 + 8 + 3 + 1 - 9 + 6 + 4",
    "correct_answer": 49,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "100 * 894",
    "correct_answer": 89400,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "84 + 20 - 10",
    "correct_answer": 94,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "177 - 64 - 379 - 661 - 59",
    "correct_answer": -986,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "3686 - 4836",
    "correct_answer": -1150,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "896 + 41 * 452 - 614 - 650",
    "correct_answer": 18164,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "600 * 333 - 75 * 924 - 437",
    "correct_answer": 130063,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "124 + 628 * 941 + 766 - 684",
    "correct_answer": 591154,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "30 + 16",
    "correct_answer": 46,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "165 * 781 + 441 - 151 - 433",
    "correct_answer": 128722,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "25 + 22 - 3 - 21 - 21 + 14 - 8 - 1 - 15 + 2 - 2 - 11 + 2 - 5 - 1 + 28 - 30 - 10 + 20 - 11 - 21 + 24 + 30 - 26",
    "correct_answer": -19,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "90 + 11 * 44 - 16 * 82",
    "correct_answer": -738,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "105 * 533 * 329 * 358 + 173",
    "correct_answer": 6591669803,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "452 * 46",
    "correct_answer": 20792,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(94 + 43) * (84 - 15)",
    "correct_answer": 9453,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "72 * 34",
    "correct_answer": 2448,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "676 * 658",
    "correct_answer": 444808,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "148 * 60",
    "correct_answer": 8880,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "214 - 437",
    "correct_answer": -223,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "319 % 12",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "6 + 9 - 1 + 5 + 1 - 1 + 9 + 8 + 1 + 4 - 4 + 8 - 8 + 6 - 6 + 1 + 1 + 3 + 6 - 1 + 1 + 6 - 3 + 2 + 6 + 2 - 8 - 4 - 8 + 6 + 2 - 4 + 1 + 3 - 3",
    "correct_answer": 46,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "466 * 790",
    "correct_answer": 368140,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "4 + 2 + 5 - 8 - 8 - 4 - 7 - 6 + 7 + 3 - 2 - 9 + 3 - 4 - 9 - 7 + 2 - 2 - 4 + 3 - 5 - 7 + 7 - 6 + 2 + 8 - 1 + 3 - 2 - 4 + 6 + 9",
    "correct_answer": -31,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "636 * 352",
    "correct_answer": 223872,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "90 * 60",
    "correct_answer": 5400,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "872 * 651 + 205 - 318 - 161",
    "correct_answer": 567398,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "62 - 1",
    "correct_answer": 61,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "3 + 17 - 7 + 30 + 25 + 19 + 17 - 10 + 1 + 1 + 9 + 21 - 13 - 16 + 9 - 24 - 7 + 18 + 7 - 30 + 21 + 29 - 21 + 26 + 18 - 12",
    "correct_answer": 131,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "25 - 19 - 11 + 16 + 5 + 27 + 21 + 30 + 11 - 11 + 12 + 15 - 13 - 18 + 10 + 11 + 19 - 9 + 30 - 10 - 5 + 4 + 7 + 8 - 25",
    "correct_answer": 130,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "21 - 21 - 10 - 6 + 21 - 2 + 22 + 15 + 24 + 24 + 24 + 4 - 10 + 17 - 12 - 20 + 5 - 4 + 10 - 1 + 9 + 27 + 22 + 15",
    "correct_answer": 174,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "2 - 73 + 88",
    "correct_answer": 17,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "(97 + 24) * (91 - 99)",
    "correct_answer": -968,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "(85 + 82) * (99 - 60)",
    "correct_answer": 6513,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "720 * 22",
    "correct_answer": 15840,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "458 * 85",
    "correct_answer": 38930,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "724 + 613 * 460 + 990 - 195",
    "correct_answer": 283499,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "7 + 78 - 96",
    "correct_answer": -11,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "32 * 48",
    "correct_answer": 1536,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "888 * 41",
    "correct_answer": 36408,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "24 + 10 * 58 - 69 * 65",
    "correct_answer": -3881,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "45 * 45",
    "correct_answer": 2025,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "958 * 101 * 677 - 918 * 436",
    "correct_answer": 65104918,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1138 + 3688",
    "correct_answer": 4826,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "445 - 858 + 93 - 73 + 919",
    "correct_answer": 526,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2463 + 2678",
    "correct_answer": 5141,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "636 % 14",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "4089 - 6150",
    "correct_answer": -2061,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "81 + 57 - 98",
    "correct_answer": 40,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "1229 - 3937",
    "correct_answer": -2708,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "6 + 5 + 8 + 8 - 2 + 8 + 6 - 6 - 1 + 3 + 7 + 6 - 1 - 6 - 9 + 4",
    "correct_answer": 36,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "41 + 58 * 19 - 38 * 97",
    "correct_answer": -2543,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "6 - 8 + 7 + 5 + 3 - 9 - 5 + 7 + 4 - 3 + 9 + 8 + 4 + 3 - 3 + 4 + 6 - 3 + 8 - 9 - 1 + 2 - 1 + 1 + 2 + 6 - 3 - 5 - 6 - 6 + 8 + 3 - 2 - 3 + 3 - 2 + 7 - 9",
    "correct_answer": 28,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "25 + 13",
    "correct_answer": 38,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "2 + 1 + 8 + 2 + 1 - 3 + 1 + 8 - 6 + 2 + 9 - 3 + 2 + 5 - 3 - 6 - 1 + 6",
    "correct_answer": 25,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "153 * 984",
    "correct_answer": 150552,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "7 + 7 + 7 - 4 + 6 + 3 + 5 + 6 + 4 - 6 - 6 - 7 + 7 + 8 + 7 - 5 - 5 + 2 - 7 + 6 - 7 + 7 - 9 + 2 - 1 - 3 - 7 - 3 - 4 - 1 + 4",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "31 * 49",
    "correct_answer": 1519,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "81 - 78 + 31",
    "correct_answer": 34,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "971 % 6",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "4 - 16 + 13 + 13 - 29 - 14 + 22 - 17 + 9 + 7 + 22 - 14 + 12 - 5 + 20 - 11 - 23 + 18 + 15 - 22 - 24 + 18 + 19 - 23 - 6 + 19",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "7434 - 9019",
    "correct_answer": -1585,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "664 * 257",
    "correct_answer": 170648,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "8 + 6 + 8 + 4 + 7 - 4 + 4 + 5 + 5 - 7 + 4 + 9 + 3 + 6 + 7 + 1 - 4 + 8 + 6 + 7 - 7 + 7 + 7 - 6 - 9 - 9 - 8 - 5 - 6 - 5 - 5 + 6 - 6 - 8 - 5 - 1",
    "correct_answer": 23,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "496 * 294",
    "correct_answer": 145824,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "6 - 94 + 85",
    "correct_answer": -3,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "31 + 21",
    "correct_answer": 52,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "54 - 76 + 96",
    "correct_answer": 74,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "2280 - 3687",
    "correct_answer": -1407,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "551 * 232 - 206 * 185 * 14",
    "correct_answer": -405708,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "754 % 17",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "56 + 32 * 14 - 66 * 59",
    "correct_answer": -3390,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "(56 + 75) * (60 - 94)",
    "correct_answer": -4454,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "5 - 1 + 6 + 9 + 9 + 2 + 3 + 6 + 3 - 5 - 2 + 8 - 8 - 3 - 9 + 9 - 6 - 6 + 7 - 1 + 3 + 2 + 8 - 4 + 4 - 3 - 7 - 7 - 1 + 2 + 2 - 6 - 1 + 6 + 8 + 9",
    "correct_answer": 41,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "782 * 323",
    "correct_answer": 252586,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "22 - 40",
    "correct_answer": -18,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "368 % 11",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "195 * 71",
    "correct_answer": 13845,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "109 * 143",
    "correct_answer": 15587,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "444 + 629 - 601 * 877 * 252",
    "correct_answer": -132822331,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "468 * 563",
    "correct_answer": 263484,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "33 - 93 + 85",
    "correct_answer": 25,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "14 - 4 + 29 + 19 + 26 - 20 - 6 + 23 + 27 - 3 + 2 - 7 + 27 + 21 + 19 + 14 - 16 + 17 - 29 - 26 + 16 + 7 + 27 + 20",
    "correct_answer": 197,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "816 * 907 + 676 + 561 * 923",
    "correct_answer": 1258591,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2 + 7 + 8 + 6 + 8 - 9 + 1 - 7 - 1 - 2 + 7 - 8 - 6 + 3 + 9 - 2 + 5 + 6 - 6 + 5 - 7 - 2 - 2 - 9 + 9 + 8 + 2 - 9 + 7 + 2 + 1 - 2 + 1 + 5 + 4",
    "correct_answer": 34,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "8 + 15 + 12 + 2 + 6 - 24 + 13 + 26 - 2 + 24 - 14 - 2 - 29 + 30 - 22 - 30 - 9 + 5 - 13 - 19 + 3 + 29 + 26 + 26",
    "correct_answer": 61,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "306 % 4",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "9907 - 1319",
    "correct_answer": 8588,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "470 - 626",
    "correct_answer": -156,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "36 - 24",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "6 + 2 - 4 + 6 + 6 - 4 + 8 + 9 + 2 + 3 + 1 - 7 + 2 + 9 + 3 + 4 + 2 - 1 + 7 - 5 - 8 + 2 - 4 - 2 - 9 + 4 - 5 - 1 - 8 - 4 + 6 - 9 + 5 - 6 - 8 + 3 - 2 - 1 + 4",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "4290 + 8848",
    "correct_answer": 13138,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "873 + 412 - 95 * 907 - 314",
    "correct_answer": -85194,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "102 - 190",
    "correct_answer": -88,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "(36 + 41) * (91 - 81)",
    "correct_answer": 770,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "2392 + 2791",
    "correct_answer": 5183,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "892 * 60",
    "correct_answer": 53520,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "23 + 16 - 24 + 28 + 26 - 28 + 15 - 17 - 16 - 16 + 30 - 2 - 1 + 13 - 20 - 28 + 11 - 27 - 4 + 16 + 3 + 5 + 10 + 9 + 23 + 15 + 19",
    "correct_answer": 79,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "7 + 1 - 7 + 5 - 9 + 9 + 4 - 7 - 2 - 8 - 6 - 5 + 8 - 7 - 7 + 2 - 5 + 2 - 9 - 1 + 3",
    "correct_answer": -32,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "633 * 67",
    "correct_answer": 42411,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "28 - 7 - 4 - 26 - 15 - 2 - 18 - 19 - 18 - 15 + 20 + 25 - 2 - 21 + 15 - 14 - 3 + 20 - 21 - 18 - 7 + 16 + 3 + 9 + 29",
    "correct_answer": -45,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "10 + 27 - 30 - 17 - 23 + 9 + 25 - 11 - 15 - 14 + 5 - 20 - 17 - 27 + 11 - 11 - 22 - 5 - 11 - 13 + 6 + 19 + 15 - 5 - 16",
    "correct_answer": -130,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "756 % 11",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "79 + 84",
    "correct_answer": 163,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "71 + 58",
    "correct_answer": 129,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "98 + 44 * 85 - 98 * 20",
    "correct_answer": 1878,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "27 - 26 - 26 + 10 + 21 + 14 + 9 + 28 + 8 + 2 - 13 - 8 + 14 + 25 - 17 - 12 + 10 + 10 - 18 - 15 + 5 - 29 + 3 + 21 - 17",
    "correct_answer": 26,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "901 + 455 - 305 * 401 * 333",
    "correct_answer": -40726209,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "90 * 75",
    "correct_answer": 6750,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "5 + 3 + 3 + 4 - 5 - 2 + 3 + 6 - 6 - 9 + 5 + 1 - 5 - 6 - 7 + 3 + 1 + 8 + 9 + 5 - 1 - 1 + 4 - 6 + 6 + 5 - 7 + 4 - 1 - 1 + 4",
    "correct_answer": 22,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "18 - 7 - 10 + 5 - 10 + 11 + 16 + 17 - 8 - 3 + 28 - 9 - 21 + 13 + 22 + 25 + 24 - 9 + 7 - 9 + 16 - 27",
    "correct_answer": 89,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "40 + 84 * 70 - 92 * 40",
    "correct_answer": 2240,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "154 - 245",
    "correct_answer": -91,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "5 - 9 - 5 + 8 - 7 - 9 + 3 - 2 - 6 + 2 - 5 - 5 + 4 - 6 + 4 + 5 + 6 + 7 - 7 - 4 - 3 + 5 - 6 + 9 - 8 + 3 - 5 - 4 + 6 + 8 + 7 - 5 - 8 + 3",
    "correct_answer": -19,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "94 + 76 * 93 - 95 * 73",
    "correct_answer": 227,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "79 * 83",
    "correct_answer": 6557,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "785 + 435 - 723 + 576 + 459",
    "correct_answer": 1532,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "225 * 601 - 872 * 65 + 280",
    "correct_answer": 78825,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "26 - 14 - 26 + 24 + 20 - 6 - 4 - 7 - 28 + 25 - 14 + 8 + 6 - 2 - 3 - 22 + 7 + 10 + 12 - 3 + 25",
    "correct_answer": 34,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "26 * 35",
    "correct_answer": 910,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "372 - 469",
    "correct_answer": -97,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "740 * 796 + 791 * 877 - 712",
    "correct_answer": 1282035,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1 - 3 + 2 + 3 + 2 + 4 + 4 - 6 - 9 - 7 + 2 - 3 - 4 + 6 - 7 - 4 - 4",
    "correct_answer": -23,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "1646 - 3412",
    "correct_answer": -1766,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "46 * 28",
    "correct_answer": 1288,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "8 + 48 - 37",
    "correct_answer": 19,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "469 - 599",
    "correct_answer": -130,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "2 - 27 + 16 - 3 - 13 + 2 + 9 + 28 + 18 - 9 + 15 + 29 + 2 - 25 - 5 - 18 - 10 + 13 - 7 - 18 + 23 + 16",
    "correct_answer": 38,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "61 - 62",
    "correct_answer": -1,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(69 + 62) * (41 - 75)",
    "correct_answer": -4454,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "40 * 17",
    "correct_answer": 680,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "193 + 276 - 525 - 962 - 908",
    "correct_answer": -1926,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "3946 + 1427",
    "correct_answer": 5373,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "(83 + 28) * (28 - 52)",
    "correct_answer": -2664,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "16 + 6 - 21 - 26 - 27 - 9 + 24 - 6 - 3 + 20 - 22 + 22 - 4 - 6 - 11 - 23 + 9 + 19 - 19 - 3 - 13 + 7 - 2 - 7 + 5 + 26",
    "correct_answer": -48,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(73 + 16) * (75 - 29)",
    "correct_answer": 4094,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "86 + 40 - 6",
    "correct_answer": 120,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "861 % 17",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "26 * 18",
    "correct_answer": 468,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "713 * 981",
    "correct_answer": 699453,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "(13 + 59) * (71 - 38)",
    "correct_answer": 2376,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "(54 + 34) * (87 - 44)",
    "correct_answer": 3784,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "75 + 18 * 34 - 96 * 32",
    "correct_answer": -2385,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "291 % 5",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "14 + 2 + 8 - 2 + 10 - 15 - 6 + 17 - 6 - 24 - 5 + 30 - 24 - 9 + 19 - 29 - 4 + 23 - 26 - 14 - 9 - 24 - 17",
    "correct_answer": -91,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "997 * 79",
    "correct_answer": 78763,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "452 * 12",
    "correct_answer": 5424,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "813 * 732",
    "correct_answer": 595116,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "177 * 80",
    "correct_answer": 14160,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "157 * 889",
    "correct_answer": 139573,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "3616 - 4924",
    "correct_answer": -1308,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "96 * 48",
    "correct_answer": 4608,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "4813 + 3615",
    "correct_answer": 8428,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "5 - 5 - 4 - 1 + 4 - 8 - 1 - 7 - 8 + 1 - 2 - 8 + 9 - 6 + 9 + 6",
    "correct_answer": -16,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "4 - 7 - 6 - 3 + 5 + 5 - 1 - 5 - 3 + 5 + 7 + 6 + 7 + 3 - 1 - 7 - 1 - 4 - 4 - 6 - 7 - 5 + 2 + 8 - 8 + 4 - 4 - 8 - 9",
    "correct_answer": -33,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "123 - 882 - 479 - 185 - 235",
    "correct_answer": -1658,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "783 % 14",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "628 + 598 + 530 * 425 + 825",
    "correct_answer": 227301,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "69 + 22 * 28 - 72 * 74",
    "correct_answer": -4643,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "8529 + 1266",
    "correct_answer": 9795,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "659 * 635",
    "correct_answer": 418465,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "20 + 25 - 21 - 29 - 18 - 11 - 23 - 16 + 1 + 20 - 21 + 12 + 29 - 15 + 11 - 9 + 27 + 14 + 10 - 18 + 2",
    "correct_answer": -10,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "57 - 39",
    "correct_answer": 18,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "672 * 19",
    "correct_answer": 12768,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "640 - 601 + 210 - 707 * 316",
    "correct_answer": -223163,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "831 * 622 + 776 - 15 * 526",
    "correct_answer": 509768,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "9044 + 4971",
    "correct_answer": 14015,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "3 - 5 - 9 - 2 - 7 - 5 + 9 + 8 + 5 + 7 - 4 + 7 + 8 + 3 + 3 - 8 - 3 + 1",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "3 + 3 + 5 - 6 - 4 - 7 + 3 - 6 + 9 + 7 + 4 - 2 - 7 - 2 - 2 + 2 + 1 - 5 - 8 - 1 - 7 + 3 - 9 - 9 + 7 - 4 - 1 - 9 - 4 - 9 - 1",
    "correct_answer": -56,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "494 * 66",
    "correct_answer": 32604,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "39 * 75",
    "correct_answer": 2925,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(30 + 19) * (55 - 42)",
    "correct_answer": 637,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "6680 + 9568",
    "correct_answer": 16248,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "35 - 828 * 936 + 167 - 358",
    "correct_answer": -775164,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "95 + 84 * 45 - 86 * 66",
    "correct_answer": -1801,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "31 * 71",
    "correct_answer": 2201,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "438 - 555",
    "correct_answer": -117,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "1780 - 2091",
    "correct_answer": -311,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "8 - 1 - 2 - 4 - 6 + 4 + 8 - 7 - 9 - 1 - 8 - 8 + 9 + 3 - 5 + 5 + 9 - 7",
    "correct_answer": -12,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "43 * 67",
    "correct_answer": 2881,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(51 + 44) * (82 - 14)",
    "correct_answer": 6460,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "198 * 67",
    "correct_answer": 13266,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "50 + 74",
    "correct_answer": 124,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "638 % 16",
    "correct_answer": 14,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "8812 + 2276",
    "correct_answer": 11088,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "5 + 7 + 6 + 3 + 3 + 2 + 4 - 1 + 4 + 7 - 2 + 3 + 2 + 5 - 1 + 8 + 2 - 5 - 1 + 1 - 9 - 7 - 5 - 8 + 7 - 6 - 4 + 7 - 1 - 6 + 1 - 7 + 3 - 2 - 5",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "17 + 12 - 38",
    "correct_answer": -9,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "7290 + 9281",
    "correct_answer": 16571,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "533 % 6",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "40 * 80",
    "correct_answer": 3200,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "18 + 20",
    "correct_answer": 38,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "3 + 2 - 3 - 6 - 9 - 8 + 9 + 4 - 4 + 8 + 7 - 1 - 8 - 2 - 2 - 6 + 9 - 9 + 5 - 8",
    "correct_answer": -19,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "878 * 517 * 602 * 758 + 307",
    "correct_answer": 207133696923,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "14 - 56",
    "correct_answer": -42,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "63 * 83",
    "correct_answer": 5229,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "6 - 1 + 7 + 4 + 5 - 5 + 9 - 8 - 9 - 6 + 2 - 1 + 6 - 4 + 8 - 3 + 5 - 2 + 4 - 5 - 7 - 1 + 4 + 6 + 2 - 2 + 3 - 7 - 2 + 4 - 5 - 9 - 3",
    "correct_answer": -5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "4263 - 7181",
    "correct_answer": -2918,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "2382 - 3536",
    "correct_answer": -1154,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "8 - 52",
    "correct_answer": -44,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "9 + 44",
    "correct_answer": 53,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "15 + 4 - 20 - 16 - 2 + 21 + 5 + 4 - 5 + 27 - 24 + 5 - 23 + 30 + 8 + 7 - 26 + 8 - 4 + 29 - 14",
    "correct_answer": 29,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "4 - 9 - 6 - 6 + 9 - 9 - 5 - 6 - 2 + 7 - 9 + 3 - 6 + 3 + 5 + 9 + 7 - 2 + 4 - 8 - 2",
    "correct_answer": -19,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "614 * 814",
    "correct_answer": 499796,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "167 * 305 + 138 + 21 + 673",
    "correct_answer": 51767,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "540 - 298 - 807 - 431 + 953",
    "correct_answer": -43,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "361 * 274",
    "correct_answer": 98914,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "62 + 68 * 85 - 17 * 80",
    "correct_answer": 4482,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "939 * 197",
    "correct_answer": 184983,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "281 * 70",
    "correct_answer": 19670,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "979 * 20",
    "correct_answer": 19580,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "464 * 259",
    "correct_answer": 120176,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "289 * 119",
    "correct_answer": 34391,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "667 % 6",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "4907 - 6357",
    "correct_answer": -1450,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "409 * 752 + 767 * 542 + 300",
    "correct_answer": 723582,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "8 + 1 + 4 + 9 - 6 - 1 + 9 + 2 - 1 + 7 + 9 - 9 + 1 - 5 - 3 + 8 + 4 - 7 + 4 + 2 + 4 + 2 - 7 - 5 - 9 + 5 + 3 - 7 + 3",
    "correct_answer": 25,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "94 + 7",
    "correct_answer": 101,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "7 + 1 - 6 + 2 + 6 - 6 + 1 - 4 + 2 + 2 + 1 - 8 + 6 + 5 + 4 + 6 + 5 - 7 + 6 - 6 - 8 - 6 - 2 - 2 - 9 + 9 - 5 - 7 + 7 - 2 - 4 + 8 + 9 - 9 - 6",
    "correct_answer": -10,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "72 * 90",
    "correct_answer": 6480,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "496 + 152 - 578 - 873 - 870",
    "correct_answer": -1673,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "611 - 751 * 785 * 470 - 837",
    "correct_answer": -277081676,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "24 + 13 - 10 - 22 + 3 - 5 - 22 - 9 + 3 - 25 - 7 + 15 - 6 + 15 + 11 - 7 + 14 - 8 + 27 - 25 - 13",
    "correct_answer": -34,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "7 + 25 + 16 - 9 - 19 - 12 + 24 + 6 + 10 + 6 + 27 + 17 + 12 - 2 + 5 - 28 - 28 + 18 + 4 - 14 - 6 - 2 + 25 + 16 + 23 + 9",
    "correct_answer": 130,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "957 + 560 + 171 * 506 + 128",
    "correct_answer": 88171,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "24 - 30 - 20 - 28 + 27 - 24 + 26 + 14 - 1 - 9 - 4 + 26 - 8 + 2 - 26 + 24 - 24 - 10 - 7 - 18 - 3 - 8 + 14 + 28",
    "correct_answer": -35,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "18 + 60",
    "correct_answer": 78,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "39 + 62 * 74 - 30 * 30",
    "correct_answer": 3727,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "798 * 20 * 835 + 976 - 96",
    "correct_answer": 13327480,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "30 + 47",
    "correct_answer": 77,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "513 * 83",
    "correct_answer": 42579,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(40 + 83) * (19 - 13)",
    "correct_answer": 738,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "301 - 363 - 325 * 905 + 99",
    "correct_answer": -294088,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "11 + 7 - 28 - 12 + 12 + 18 + 2 + 21 - 14 - 10 - 7 - 14 - 5 + 23 - 19 - 7 + 21 + 2 + 19 - 9 + 2 - 9 - 22",
    "correct_answer": -18,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "4 - 1 + 8 - 7 - 8 + 4 + 1 + 8 - 4 - 3 - 5 + 5 - 6 + 3 - 3 + 6 - 7 - 7 + 8",
    "correct_answer": -4,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(51 + 11) * (87 - 15)",
    "correct_answer": 4464,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "5 + 1 + 1 - 4 - 1 + 4 - 5 + 7 + 8 + 9 + 7 + 8 + 3 + 8 - 2 + 4 - 1 - 8 - 9 - 2 + 1 - 8 - 1 - 7 + 4 - 7 + 1 + 5 + 7 - 4 - 3 + 4 + 8 + 8 + 6 - 1",
    "correct_answer": 46,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "79 + 53 - 36",
    "correct_answer": 96,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "84 - 20 + 64",
    "correct_answer": 128,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "852 * 22",
    "correct_answer": 18744,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "84 * 82 - 755 - 805 - 29",
    "correct_answer": 5299,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "674 * 65",
    "correct_answer": 43810,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "82 * 43",
    "correct_answer": 3526,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "214 - 434 * 267 - 537 * 697",
    "correct_answer": -489953,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "258 * 560",
    "correct_answer": 144480,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "432 - 958 - 744 + 907 + 854",
    "correct_answer": 491,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "835 * 172",
    "correct_answer": 143620,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "7 + 25 - 8 - 20 - 5 - 25 + 15 + 11 - 11 - 24 + 28 + 13 + 18 + 27 + 26 + 9 + 15 + 13 - 22 + 25 - 23 - 19 - 24 - 16 + 24 + 29 - 21",
    "correct_answer": 67,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "3 - 7 + 4 - 7 - 2 + 9 - 6 + 2 - 9 - 9 - 9 - 1 - 4 - 1 - 6 - 2 - 9",
    "correct_answer": -54,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "884 * 663",
    "correct_answer": 586092,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "681 * 965 + 949 + 335 * 580",
    "correct_answer": 852414,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "849 * 502",
    "correct_answer": 426198,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "629 * 88",
    "correct_answer": 55352,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "2 + 2 + 2 + 5 + 3 - 8 + 4 - 8 + 7 + 2 + 7 - 6 - 8 + 3 - 3 + 1 - 6 - 8 + 9 - 9 + 2 - 1 + 9 + 3 + 6 + 4 + 3 + 3 + 8 + 2 - 9 - 8 + 8 - 7 + 5 - 5 - 2 + 5",
    "correct_answer": 17,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "129 * 516 * 971 - 365 - 724",
    "correct_answer": 64632555,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "296 * 201",
    "correct_answer": 59496,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "17 + 17 + 15 - 20 + 29 + 25 + 25 + 26 - 26 + 21 - 9 - 19 - 8 - 8 + 19 + 8 - 2 - 6 - 27 + 4 - 11 + 26",
    "correct_answer": 96,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "663 * 511",
    "correct_answer": 338793,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "173 * 79",
    "correct_answer": 13667,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "7743 + 1971",
    "correct_answer": 9714,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "579 * 920",
    "correct_answer": 532680,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "48 + 14 - 87",
    "correct_answer": -25,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "71 * 44",
    "correct_answer": 3124,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "474 * 33",
    "correct_answer": 15642,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "22 - 22 - 15 + 22 + 22 - 11 - 27 - 28 + 17 - 23 + 14 + 1 + 11 + 5 + 13 + 9 - 10 - 26 + 22 + 1 - 30 + 4 - 13 + 29 - 10 - 25 - 2",
    "correct_answer": -50,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "764 * 65",
    "correct_answer": 49660,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "360 * 71",
    "correct_answer": 25560,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "284 * 83",
    "correct_answer": 23572,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "91 + 22 * 23 - 40 * 44",
    "correct_answer": -1163,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "(61 + 83) * (97 - 71)",
    "correct_answer": 3744,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "70 + 60 - 53",
    "correct_answer": 77,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "137 - 158",
    "correct_answer": -21,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "93 - 22",
    "correct_answer": 71,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "11 + 28 * 89 - 57 * 88",
    "correct_answer": -2513,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "2315 - 3584",
    "correct_answer": -1269,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "910 * 209",
    "correct_answer": 190190,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "87 + 87 - 76",
    "correct_answer": 98,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "633 * 95",
    "correct_answer": 60135,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "7 + 24 + 10 + 14 - 3 - 28 - 2 - 6 + 17 + 17 + 13 + 3 + 5 - 15 + 20 + 29 + 25 + 7 + 3 - 11 - 16 - 5 + 1 - 17",
    "correct_answer": 92,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "7 + 5 + 6 + 3 - 8 - 9 - 8 + 3 + 1 - 3 + 8 + 7 - 6 - 5 + 3 + 9",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "26 * 20",
    "correct_answer": 520,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "9 - 7 + 30 - 6 - 2 + 14 - 9 + 12 - 29 - 26 + 6 - 2 + 5 - 22 - 15 + 15 - 28 + 5 - 8 + 3 - 19 + 22 - 26 - 14 + 21",
    "correct_answer": -71,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "916 - 102 * 975 + 872 + 251",
    "correct_answer": -97411,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "53 + 4",
    "correct_answer": 57,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "9 - 30 - 23 - 27 + 4 - 6 + 12 - 29 + 2 - 8 - 8 + 9 + 24 - 12 - 26 + 10 - 27 - 7 - 5 + 3 + 7 - 3 + 9 + 21 + 4 + 21 - 1",
    "correct_answer": -77,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "3 - 7 + 7 - 2 + 2 + 3 + 6 + 4 + 7 + 3 - 3 + 5 + 6 + 1 + 3 - 1 + 3 + 1 - 7 - 8 - 5",
    "correct_answer": 21,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "8 + 6 - 6 - 7 + 9 + 9 + 3 - 5 + 3 - 2 + 4 + 5 + 5 + 7 + 6 + 8 - 3 + 2 + 4 + 8 - 9",
    "correct_answer": 55,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "1 - 3 + 1 + 3 + 9 + 6 - 3 - 9 + 7 - 6 + 9 - 8 + 5 + 3 + 6 - 5 - 6 - 7 - 6 + 5 + 3 - 2 - 7 + 1 - 1 + 1 + 5 - 4 + 4 + 4 - 2 + 6 + 1 + 8 - 4 - 7 - 3",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "36 - 97",
    "correct_answer": -61,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "15 + 22 + 17 + 19 - 29 - 2 + 14 + 23 - 7 + 9 + 12 - 28 + 18 - 7 - 17 + 26 + 24 + 11 + 25 - 19 - 11 - 12 + 2 - 12",
    "correct_answer": 93,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "945 * 806",
    "correct_answer": 761670,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "(36 + 99) * (12 - 33)",
    "correct_answer": -2835,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "15 - 21 - 17 - 26 - 17 - 29 + 15 + 8 - 26 - 9 - 26 - 3 - 8 - 6 - 16 - 16 - 16 - 8 + 21 + 3 - 8 - 17 - 15 + 13 + 26",
    "correct_answer": -183,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "396 * 24",
    "correct_answer": 9504,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "235 + 74 - 446 * 840 - 704",
    "correct_answer": -375035,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "3110 - 4553",
    "correct_answer": -1443,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "9 - 5 - 7 - 7 + 9 - 3 + 1 + 6 - 3 + 2 - 8 + 5 - 1 - 9 - 7 + 3 - 4 - 4 + 3 - 4 + 2 - 2 + 9 - 7 - 3 - 4 - 9 - 1 - 9 + 3 - 1 + 1 - 3 + 1 + 9 + 7 - 1",
    "correct_answer": -32,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "38 + 29 * 77 - 85 * 44",
    "correct_answer": -1469,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "75 + 71",
    "correct_answer": 146,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "62 - 38 + 96",
    "correct_answer": 120,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "(11 + 32) * (84 - 96)",
    "correct_answer": -516,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "8570 + 4798",
    "correct_answer": 13368,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "636 * 20",
    "correct_answer": 12720,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "455 * 924",
    "correct_answer": 420420,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "629 * 78",
    "correct_answer": 49062,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "40 * 69",
    "correct_answer": 2760,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "2609 - 4875",
    "correct_answer": -2266,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "246 - 260",
    "correct_answer": -14,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "638 * 716 * 876 * 739 + 729",
    "correct_answer": 295721054841,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "187 - 218",
    "correct_answer": -31,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "31 - 35",
    "correct_answer": -4,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "299 - 934 - 637 - 539 + 456",
    "correct_answer": -1355,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "24 + 99 * 41 - 52 * 15",
    "correct_answer": 3303,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "26 - 21 + 30 - 29 - 3 - 14 - 9 + 3 + 16 + 12 - 15 - 14 + 5 + 18 + 4 + 1 - 3 + 3 + 6 + 11 + 19 - 2 + 10 - 26 - 29",
    "correct_answer": -1,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "39 + 37",
    "correct_answer": 76,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "66 + 85 * 11 - 45 * 55",
    "correct_answer": -1474,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "907 * 38",
    "correct_answer": 34466,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "26 * 48",
    "correct_answer": 1248,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "47 * 15",
    "correct_answer": 705,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "491 * 91",
    "correct_answer": 44681,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(66 + 63) * (85 - 90)",
    "correct_answer": -645,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "283 - 853 + 671 * 272 + 625",
    "correct_answer": 182567,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "16 - 7 - 16 - 12 - 20 - 6 + 26 - 1 + 29 + 27 + 7 + 16 + 1 + 25 + 10 - 23 - 10 - 7 + 5 - 26 - 27 + 3 + 18 + 1",
    "correct_answer": 29,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "457 % 3",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "281 * 85",
    "correct_answer": 23885,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(57 + 60) * (54 - 60)",
    "correct_answer": -702,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "6 - 7 - 2 + 4 - 2 - 3 + 2 + 2 - 7 - 1 - 3 + 9 + 1 - 9 - 2 + 7 - 2 - 4 + 7 + 9 - 7 - 6 - 7 + 7 + 1 - 7 - 2 + 7 + 1 - 5 + 5 + 1 + 7 - 4 - 4 + 7",
    "correct_answer": -1,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "24 + 9",
    "correct_answer": 33,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "98 + 63 - 70",
    "correct_answer": 91,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "7010 - 9880",
    "correct_answer": -2870,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "88 + 98 * 72 - 88 * 63",
    "correct_answer": 1600,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "99 + 138 + 24 + 124 + 722",
    "correct_answer": 1107,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1 - 1 + 2 - 9 + 3 + 2 + 9 + 9 + 3 - 5 + 3 - 9 + 5 + 8 + 8 - 3 - 1 - 7 + 3 + 8 - 3 - 7 + 7 + 8 - 5 - 1 - 6 - 8 + 2 + 6 - 9 + 1 + 3 - 3 + 2 + 6 + 4 - 1 - 4",
    "correct_answer": 21,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "23 + 25 + 30 - 30 - 26 + 3 + 20 - 20 - 12 + 25 + 17 - 7 + 18 - 10 - 25 - 5 - 1 - 26 + 8 + 2 - 20 + 27 + 21 - 15 - 15",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "3404 - 4094",
    "correct_answer": -690,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "92 * 75",
    "correct_answer": 6900,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "407 % 8",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "84 - 11 + 43",
    "correct_answer": 116,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "1 + 1 + 1 + 2 - 5 + 6 - 2 + 4 - 5 - 5 - 2 + 5 + 4 - 6 + 9 + 4 - 9 - 6 - 8 + 9 + 4 + 3 + 6 - 8 + 8 + 2 + 9 - 2 - 8 - 9 + 5 + 1 + 2 + 7 - 5 + 5 - 2 + 9 + 8",
    "correct_answer": 33,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "391 - 614",
    "correct_answer": -223,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "43 + 42 - 86",
    "correct_answer": -1,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "369 * 654",
    "correct_answer": 241326,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "359 * 592",
    "correct_answer": 212528,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "4401 + 8404",
    "correct_answer": 12805,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "9428 + 2560",
    "correct_answer": 11988,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "579 * 381",
    "correct_answer": 220599,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "4 - 7 + 6 - 7 - 5 + 2 + 5 + 4 - 1 + 8 + 2 + 4 + 9 - 1 + 8 + 3 - 7 + 1 - 7 + 7 - 1",
    "correct_answer": 27,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "311 - 397",
    "correct_answer": -86,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "29 - 23 + 20 + 28 + 13 + 28 + 1 + 8 - 24 - 24 - 12 - 22 + 16 - 25 - 13 + 16 + 7 - 10 + 28 + 10 - 30 + 10 - 13 + 12 - 17",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "124 + 393 + 806 + 945 * 464",
    "correct_answer": 439803,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "228 * 686 - 970 * 284 * 555",
    "correct_answer": -152734992,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "448 * 24",
    "correct_answer": 10752,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "28 * 41",
    "correct_answer": 1148,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "6 + 1 + 3 + 3 + 6 + 3 - 7 + 6 - 6 - 8 + 5 - 3 - 9 + 3 + 3 - 7 - 1 - 9 + 5 + 9 - 9 + 3 - 1 - 1 - 4 + 9 + 5 - 5 - 5",
    "correct_answer": -5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "376 + 206 * 845 - 650 * 837",
    "correct_answer": -369604,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "336 * 489",
    "correct_answer": 164304,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "11 - 83",
    "correct_answer": -72,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "38 * 35",
    "correct_answer": 1330,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "38 * 23",
    "correct_answer": 874,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "3 + 6 + 2 + 2 + 9 + 1 + 6 + 8 - 6 + 6 + 1 + 4 + 2 + 2 + 9 - 2 + 4 + 2 + 9",
    "correct_answer": 68,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "25 * 39",
    "correct_answer": 975,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "370 - 560",
    "correct_answer": -190,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "25 - 28",
    "correct_answer": -3,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "38 * 17",
    "correct_answer": 646,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "55 - 96",
    "correct_answer": -41,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "248 - 317",
    "correct_answer": -69,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "75 - 4",
    "correct_answer": 71,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "93 * 51",
    "correct_answer": 4743,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "1 + 67",
    "correct_answer": 68,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "1990 + 7520",
    "correct_answer": 9510,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "122 * 33",
    "correct_answer": 4026,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "680 * 291",
    "correct_answer": 197880,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "576 * 770",
    "correct_answer": 443520,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "432 * 965",
    "correct_answer": 416880,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "4 - 6 - 8 + 2 - 6 + 1 + 8 - 2 - 7 - 6 + 3 + 9 + 5 - 2 - 8 + 7 - 9 - 6 - 7 - 9 - 9 - 6 - 3 - 1 - 3 + 7 - 7 - 3 - 6 + 2 + 8 - 9 + 3 - 4 - 7 - 1 - 5",
    "correct_answer": -81,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "63 * 68",
    "correct_answer": 4284,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "856 % 19",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "7 + 6 - 6 + 6 + 3 + 7 + 1 + 9 - 9 - 7 + 3 + 1 + 7 + 5 + 3 - 5 + 5 - 9 - 8 + 1 + 4 - 7 + 7 - 4 - 8 + 2 + 4 - 1 - 5 + 5 + 4 + 7 - 1 - 6 - 9 + 9 - 5",
    "correct_answer": 16,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "137 - 323",
    "correct_answer": -186,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "96 + 37 * 33 - 47 * 28",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "26 - 28 + 5 - 2 + 21 - 14 + 15 + 15 - 21 + 4 + 10 - 8 - 16 - 16 - 16 + 26 + 24 + 24 - 9 + 16 + 15 - 19 - 16 - 11",
    "correct_answer": 25,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(95 + 34) * (82 - 31)",
    "correct_answer": 6579,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "4178 - 4509",
    "correct_answer": -331,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "140 * 596",
    "correct_answer": 83440,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "806 * 942",
    "correct_answer": 759252,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "69 - 91 + 30",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "835 % 7",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "582 * 123",
    "correct_answer": 71586,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "7408 + 8586",
    "correct_answer": 15994,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "(51 + 52) * (14 - 57)",
    "correct_answer": -4429,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "37 * 49",
    "correct_answer": 1813,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "222 * 20",
    "correct_answer": 4440,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "2376 - 5240",
    "correct_answer": -2864,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "5 - 1 + 4 + 4 - 1 + 7 - 9 + 5 - 9 + 9 + 3 - 6 - 1 + 8 - 9 - 6 - 3 - 9 + 5 + 2 - 2 - 7 - 4 - 9 + 4 - 9 - 4 + 8 + 4 - 4",
    "correct_answer": -25,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "7363 + 6813",
    "correct_answer": 14176,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "899 * 46",
    "correct_answer": 41354,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "45 * 50",
    "correct_answer": 2250,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "904 * 72",
    "correct_answer": 65088,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "336 * 644",
    "correct_answer": 216384,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "761 * 938 + 142 + 893 * 830",
    "correct_answer": 1455150,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "455 * 45",
    "correct_answer": 20475,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "426 + 982 - 145 + 312 + 673",
    "correct_answer": 2248,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "91 * 33",
    "correct_answer": 3003,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "480 * 69",
    "correct_answer": 33120,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "15 - 38",
    "correct_answer": -23,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "382 * 97",
    "correct_answer": 37054,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "5456 - 9582",
    "correct_answer": -4126,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "19 + 18 + 22 + 28 + 1 + 1 + 11 + 15 - 18 - 28 + 21 + 26 + 2 - 1 + 3 + 28 - 29 + 19 + 6 - 28 - 13 + 6 - 12",
    "correct_answer": 97,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "435 - 645",
    "correct_answer": -210,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "59 - 37",
    "correct_answer": 22,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "6 + 2 - 2 + 8 + 2 - 6 + 8 + 6 + 3 - 1 + 8 + 7 - 5 - 7 - 6 - 7 + 8 + 6",
    "correct_answer": 30,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "281 - 359",
    "correct_answer": -78,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "67 + 76 * 92 - 65 * 71",
    "correct_answer": 2444,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "8483 + 1130",
    "correct_answer": 9613,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "46 + 91 * 91 - 53 * 95",
    "correct_answer": 3292,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "4 + 7 + 2 - 3 + 4 - 7 - 6 - 9 - 3 - 1 - 3 - 8 + 6 - 6 - 6 - 4 + 3 + 8 - 4 + 3 - 6 - 4 + 4 + 7 + 9 + 1 - 2 - 9 + 1 - 7",
    "correct_answer": -29,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "552 * 738",
    "correct_answer": 407376,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "(56 + 23) * (98 - 80)",
    "correct_answer": 1422,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "261 * 21",
    "correct_answer": 5481,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "30 + 21 * 77 - 87 * 45",
    "correct_answer": -2268,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "(71 + 27) * (76 - 58)",
    "correct_answer": 1764,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "941 * 922",
    "correct_answer": 867602,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "82 + 74 * 94 - 32 * 70",
    "correct_answer": 4798,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "24 - 5 + 26 - 18 - 28 + 11 - 15 + 18 + 13 - 24 + 2 - 9 + 2 + 26 + 5 - 12 + 19 - 27 + 17 + 23 - 22 + 29 + 17",
    "correct_answer": 72,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "51 + 72 - 47",
    "correct_answer": 76,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "9 + 9 + 3 - 3 - 9 + 7 - 1 - 6 + 5 - 9 - 3 - 3 - 9 - 8 + 6 + 4 - 4 - 3 - 9 + 8 + 3 - 3 - 4 + 7 + 5 - 8 - 8 + 3 - 9 + 6 + 3",
    "correct_answer": -21,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "560 % 17",
    "correct_answer": 16,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "855 * 46",
    "correct_answer": 39330,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "99 - 80 + 79",
    "correct_answer": 98,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "838 + 973 - 202 + 99 + 410",
    "correct_answer": 2118,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "111 - 197",
    "correct_answer": -86,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "35 * 58",
    "correct_answer": 2030,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "89 + 35 - 4",
    "correct_answer": 120,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "97 * 54",
    "correct_answer": 5238,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "765 - 344 + 721 + 790 * 666",
    "correct_answer": 527282,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "789 * 53",
    "correct_answer": 41817,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "234 * 83",
    "correct_answer": 19422,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(23 + 63) * (28 - 69)",
    "correct_answer": -3526,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "997 % 7",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "851 * 179",
    "correct_answer": 152329,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "87 - 97 + 93",
    "correct_answer": 83,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "21 + 27 - 28 - 28 + 14 - 19 - 22 - 17 - 30 + 1 - 22 - 9 + 22 + 15 - 20 + 6 + 22 - 1 + 20 + 23 + 23 - 13 - 5 + 17 - 12",
    "correct_answer": -15,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "27 * 35",
    "correct_answer": 945,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "994 * 943 + 472 - 11 * 994",
    "correct_answer": 926880,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "109 * 99",
    "correct_answer": 10791,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "402 * 939",
    "correct_answer": 377478,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "4203 + 8501",
    "correct_answer": 12704,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "77 - 899 - 127 + 183 - 561",
    "correct_answer": -1327,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(67 + 81) * (32 - 54)",
    "correct_answer": -3256,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "(36 + 64) * (13 - 82)",
    "correct_answer": -6900,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "287 - 492",
    "correct_answer": -205,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "7 + 5 + 9 - 5 - 6 + 8 + 2 + 4 + 8 - 6 - 6 - 3 + 8 - 8 - 2 - 2 - 5 - 7 + 3 - 6 - 2 + 8 + 6 + 7 + 6 - 6 + 7 - 2 + 8 + 7 - 1 - 1 + 4 - 9 - 1 - 7 + 1 - 6",
    "correct_answer": 17,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "1 + 1 - 4 - 7 - 1 + 1 - 7 - 7 + 9 + 8 + 6 + 6 + 1 - 2 + 4 - 9 - 1 - 4 + 2 + 8 + 1 - 4 - 3 - 8 + 2 + 9 - 6 + 4 - 5 + 9 + 4 + 5",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "672 * 401",
    "correct_answer": 269472,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "3 + 3 + 4 + 8 + 5 + 2 - 4 + 7 - 7 - 9 - 1 - 6 - 3 + 5 + 1 - 2 + 8 + 5 + 5",
    "correct_answer": 24,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "240 % 4",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "25 * 31",
    "correct_answer": 775,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "3214 - 4672",
    "correct_answer": -1458,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "10 + 41 - 74",
    "correct_answer": -23,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "2036 + 3739",
    "correct_answer": 5775,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "839 + 10 + 686 * 473 - 308",
    "correct_answer": 325019,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(94 + 51) * (96 - 73)",
    "correct_answer": 3335,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "924 * 21",
    "correct_answer": 19404,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "565 * 361 + 569 + 985 + 450",
    "correct_answer": 205969,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1 + 37 - 93",
    "correct_answer": -55,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "16 - 7 - 30 + 28 - 8 + 7 + 10 + 23 + 29 + 19 - 13 + 14 + 14 - 10 - 20 - 16 + 6 + 17 - 6 + 15 - 5 - 16 - 21 + 15 - 22 - 4",
    "correct_answer": 35,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "82 + 63",
    "correct_answer": 145,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "428 - 577",
    "correct_answer": -149,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "84 + 51 * 13 - 85 * 26",
    "correct_answer": -1463,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "63 + 98 * 56 - 72 * 49",
    "correct_answer": 2023,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "35 - 71 + 17",
    "correct_answer": -19,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "4 - 7 + 8 + 7 + 8 + 3 + 2 - 3 + 4 + 4 - 5 - 5 - 3 - 1 - 9 - 7 - 5 + 3 - 2 + 1 - 2 + 4 - 9 + 4 + 3 - 7 + 7 - 5 - 2 + 2 - 4 - 2",
    "correct_answer": -14,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "817 * 57",
    "correct_answer": 46569,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "668 * 71",
    "correct_answer": 47428,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "94 + 17 * 37 - 64 * 73",
    "correct_answer": -3949,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "84 + 85 * 42 - 55 * 44",
    "correct_answer": 1234,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "167 % 12",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "4940 - 5520",
    "correct_answer": -580,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "402 - 470 - 883 - 463 + 46",
    "correct_answer": -1368,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "682 * 322",
    "correct_answer": 219604,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "7 - 7 - 6 + 5 - 6 + 4 + 6 + 3 - 4 + 3 - 9 + 9 - 4 - 9 + 4 + 1 + 8 + 7 + 3 - 8 - 1 - 8 + 3 + 6 - 5 - 1 + 8 - 3 - 4 - 5 + 5 - 9 - 3 - 6 - 1 - 6 - 2 + 9",
    "correct_answer": -16,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "144 % 16",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "39 * 90",
    "correct_answer": 3510,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "9 - 21 + 27 - 22 - 17 + 19 + 19 - 1 - 20 - 12 + 20 - 6 - 22 + 26 - 15 + 23 + 5 + 14 + 3 - 16 - 8 + 4 - 20",
    "correct_answer": -11,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "31 + 308 + 74 + 902 * 864",
    "correct_answer": 779741,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "33 * 23",
    "correct_answer": 759,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "614 % 19",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "392 * 34",
    "correct_answer": 13328,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "24 - 28 + 44",
    "correct_answer": 40,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "(17 + 87) * (83 - 69)",
    "correct_answer": 1456,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "44 * 83",
    "correct_answer": 3652,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "6 + 6 + 5 + 1 + 7 - 8 + 9 + 9 - 7 - 9 - 6 + 8 - 6 - 2 - 9 + 9 - 9 - 2 - 8 - 4 - 7 + 8 - 3 + 2 + 6 - 7 - 7 - 1 + 7 + 4 + 3 - 4 - 6 - 4 - 6 + 3",
    "correct_answer": -22,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "12 - 9 - 11 - 11 - 5 + 12 - 19 - 4 - 3 - 7 - 20 - 30 - 12 + 23 + 11 - 30 + 19 - 21 + 23 + 22 - 11 - 13 - 30 + 29",
    "correct_answer": -85,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "5 + 4 - 5 - 5 - 7 - 4 - 4 + 5 + 8 - 5 + 5 + 9 + 4 + 6 - 3 - 8 - 4 - 9",
    "correct_answer": -8,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "2 - 28 - 9 + 13 - 11 + 12 - 27 + 6 - 10 - 28 + 25 - 13 - 22 + 25 - 25 - 11 + 29 + 24 - 16 + 4 + 10 + 13 + 12 - 3",
    "correct_answer": -28,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "819 * 690",
    "correct_answer": 565110,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "43 + 99",
    "correct_answer": 142,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "723 * 346",
    "correct_answer": 250158,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "34 - 7 + 17",
    "correct_answer": 44,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "(71 + 99) * (47 - 50)",
    "correct_answer": -510,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "593 * 24",
    "correct_answer": 14232,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "1 + 2 - 4 - 6 - 5 - 4 + 1 + 2 + 2 - 7 + 1 + 1 + 2 + 5 + 6 + 7 + 4 + 9 - 7 + 6 + 3 + 2 - 1 + 4 - 1 + 1 + 3 - 7 - 4 - 2 - 8 + 8 + 8 - 5 + 3 - 8",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "43 * 58",
    "correct_answer": 2494,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "504 * 41",
    "correct_answer": 20664,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "55 + 15",
    "correct_answer": 70,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "80 + 44 * 67 - 91 * 21",
    "correct_answer": 1117,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "60 - 90 + 39",
    "correct_answer": 9,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "36 + 20",
    "correct_answer": 56,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "9 - 6 - 7 - 4 - 3 - 7 + 2 - 2 + 4 - 4 - 8 + 7 + 1 + 6 + 2 - 4 - 8",
    "correct_answer": -22,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "770 * 10",
    "correct_answer": 7700,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "34 - 75 + 49",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "7 + 27 - 15 + 28 + 4 - 20 - 7 - 3 - 17 + 2 - 22 - 22 + 20 + 17 + 14 + 1 + 16 + 6 - 18 + 3 + 25 - 17 + 12 - 8 - 19",
    "correct_answer": 14,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "924 - 304 - 193 * 938 + 670",
    "correct_answer": -179744,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "498 * 97",
    "correct_answer": 48306,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(16 + 48) * (98 - 60)",
    "correct_answer": 2432,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "398 + 444 + 536 + 427 - 789",
    "correct_answer": 1016,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "38 + 88 * 37 - 72 * 72",
    "correct_answer": -1890,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "518 * 542 - 657 + 514 * 914",
    "correct_answer": 749895,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "12 + 16 + 12 - 20 - 2 - 18 - 29 + 10 + 5 - 11 + 21 - 30 - 18 + 20 - 28 - 8 + 14 - 2 + 21 - 11 - 3 - 3 - 26 - 23 + 3 - 16",
    "correct_answer": -114,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "892 - 43 + 96 + 619 - 867",
    "correct_answer": 697,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(54 + 89) * (19 - 43)",
    "correct_answer": -3432,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "683 * 740",
    "correct_answer": 505420,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "29 + 14 + 19 - 27 + 17 - 2 - 18 + 22 - 28 + 25 - 14 + 6 - 18 - 14 - 22 - 2 - 16 - 12 - 19 + 15 - 24 + 10 + 26 - 11 + 16 + 12 + 10",
    "correct_answer": -6,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "489 - 109 * 327 * 669 - 794",
    "correct_answer": -23845472,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "40 - 71 + 2",
    "correct_answer": -29,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "353 * 14",
    "correct_answer": 4942,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "144 % 15",
    "correct_answer": 9,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "492 - 30 + 609 - 216 - 593",
    "correct_answer": 262,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(89 + 55) * (15 - 79)",
    "correct_answer": -9216,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "499 - 456 * 874 + 809 + 563",
    "correct_answer": -396673,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "6 + 7 - 7 + 3 + 6 - 7 + 6 - 5 + 3 - 5 + 1 - 4 - 9 - 9 - 6 - 7 - 1 + 3 - 2 - 4",
    "correct_answer": -31,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "5 - 8 - 3 + 1 + 4 - 5 - 1 + 4 - 6 + 9 + 1 + 5 - 8 - 7 + 5 + 8 - 5 - 6 - 6 + 7 - 8 + 5 + 9 + 2 + 5 + 3 + 6 - 1 + 5 + 6 - 7",
    "correct_answer": 19,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "196 - 445",
    "correct_answer": -249,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "473 + 517 * 95 + 781 * 719",
    "correct_answer": 611127,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "61 - 65 + 20",
    "correct_answer": 16,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "77 - 191 * 897 * 511 - 342",
    "correct_answer": -87548362,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "730 * 853",
    "correct_answer": 622690,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "2828 - 5376",
    "correct_answer": -2548,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "64 + 203 + 65 + 197 - 491",
    "correct_answer": 38,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(47 + 79) * (95 - 16)",
    "correct_answer": 9954,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "1 + 21 - 21 - 16 - 17 - 29 + 20 + 3 - 6 + 8 - 29 + 6 + 20 + 6 - 19 + 22 - 25 + 9 - 4 + 19 - 18 - 16 + 10 + 21",
    "correct_answer": -34,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "11 - 26 - 1 - 18 + 28 + 3 - 30 - 11 + 24 + 6 - 22 + 16 + 25 - 3 - 17 + 4 + 12 - 22 + 6 - 13 + 5 + 5 - 30 - 8 - 3 - 11 - 30",
    "correct_answer": -100,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "14 + 3 - 13 + 24 + 24 - 6 + 29 - 10 + 19 + 21 - 15 - 20 + 7 - 30 + 29 - 29 + 9 - 1 - 13 - 18 - 11 + 28 + 28 + 30 - 14",
    "correct_answer": 85,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "88 + 42",
    "correct_answer": 130,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(89 + 88) * (32 - 25)",
    "correct_answer": 1239,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "57 + 22 * 17 - 81 * 76",
    "correct_answer": -5725,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "870 - 532 + 56 * 766 + 586",
    "correct_answer": 43820,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "666 * 906 + 815 + 543 - 472",
    "correct_answer": 604282,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "39 + 2",
    "correct_answer": 41,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(40 + 79) * (81 - 40)",
    "correct_answer": 4879,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "21 - 60",
    "correct_answer": -39,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "91 + 28",
    "correct_answer": 119,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "25 * 41",
    "correct_answer": 1025,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "458 + 762 + 153 + 207 * 747",
    "correct_answer": 156002,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "42 * 27",
    "correct_answer": 1134,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "336 - 518",
    "correct_answer": -182,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "(38 + 37) * (76 - 33)",
    "correct_answer": 3225,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "2262 + 9128",
    "correct_answer": 11390,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "709 * 757",
    "correct_answer": 536713,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "610 * 64",
    "correct_answer": 39040,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "109 - 851 - 190 - 988 * 81",
    "correct_answer": -80960,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "26 + 20 + 15 + 12 + 20 - 3 - 27 + 9 + 18 - 7 - 21 - 21 + 29 + 18 + 4 + 26 + 15 - 22 - 19 + 13 - 10 - 11 - 1 - 28 + 29",
    "correct_answer": 84,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "3316 + 9369",
    "correct_answer": 12685,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "5 - 6 + 8 - 9 + 1 - 7 + 3 + 1 + 7 + 2 - 7 - 5 - 9 - 8 + 9 - 6 - 7 + 5",
    "correct_answer": -23,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "18 - 19 - 16 + 24 + 10 - 26 + 5 + 6 - 27 - 4 + 11 - 20 + 16 - 29 - 1 - 17 + 12 - 3 + 22 + 9 + 6",
    "correct_answer": -23,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "6005 + 4836",
    "correct_answer": 10841,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "3 + 9 - 5 - 7 - 2 + 2 - 1 + 7 + 9 + 8 - 1 + 7 - 8 + 2 - 8 - 6 + 8 + 7 - 6 + 9",
    "correct_answer": 27,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "301 - 440",
    "correct_answer": -139,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "(43 + 78) * (62 - 40)",
    "correct_answer": 2662,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "(88 + 18) * (65 - 85)",
    "correct_answer": -2120,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "51 + 95 * 30 - 36 * 35",
    "correct_answer": 1641,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "635 + 952 - 727 * 466 * 220",
    "correct_answer": -74530453,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "11 + 12 - 56",
    "correct_answer": -33,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "3161 - 5945",
    "correct_answer": -2784,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "756 * 429",
    "correct_answer": 324324,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "(41 + 18) * (25 - 20)",
    "correct_answer": 295,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "19 * 48",
    "correct_answer": 912,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "505 % 19",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "159 - 343",
    "correct_answer": -184,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "1 + 5 - 5 + 6 - 2 - 3 - 9 - 2 + 5 + 9 + 8 - 3 + 3 - 9 + 4 - 4 - 8 - 9 - 1 + 4 - 2 + 2 + 8 - 4 - 7 + 1 - 6 - 6 - 6 - 5",
    "correct_answer": -35,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "18 * 21",
    "correct_answer": 378,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "39 * 59",
    "correct_answer": 2301,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "771 * 76",
    "correct_answer": 58596,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "19 + 1 + 4 + 11 + 5 - 3 + 2 - 30 + 25 - 6 - 6 + 26 + 21 + 4 - 2 + 29 - 9 - 5 - 2 - 20 - 25 - 20 - 17",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "558 * 506",
    "correct_answer": 282348,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "12 + 12 - 24 - 7 - 28 + 30 + 3 - 4 - 11 - 29 - 10 - 16 + 6 - 21 - 6 + 13 + 17 - 29 + 3 + 20 - 4 - 9 + 21",
    "correct_answer": -61,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(13 + 79) * (17 - 29)",
    "correct_answer": -1104,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "92 - 38 + 66",
    "correct_answer": 120,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "3 + 3 + 4 + 6 - 1 - 1 - 5 + 7 - 6 - 1 - 7 - 3 + 7 + 9 - 7 + 8 - 8 + 8 + 6 - 4 + 7 + 4 - 3 + 8 + 2 - 8 + 6 - 9 + 3 + 1 + 3 + 3 + 4 + 3 + 4 + 7",
    "correct_answer": 53,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "746 % 8",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "9 - 3 + 4 + 2 + 2 + 2 + 9 - 9 - 3 - 8 - 7 - 5 - 5 + 8 - 8 + 3 - 4 + 3 - 3 + 9 - 2 + 5 + 3 - 3 + 3 + 6 + 7 + 6 - 1 - 4",
    "correct_answer": 16,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "25 * 33",
    "correct_answer": 825,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "4 - 7 + 2 + 8 - 1 - 5 - 3 - 4 - 9 + 6 - 2 + 2 + 4 + 3 + 4 + 6 + 3 + 5 - 1 + 4 - 2 + 8 - 9 + 7 + 8 + 1 + 2 - 3 - 3 - 4 - 7 - 6 + 7 + 2 - 2 - 1 - 2 - 2",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "36 - 86",
    "correct_answer": -50,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "30 * 97",
    "correct_answer": 2910,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "9 - 1 + 1 + 1 + 5 - 6 + 7 - 3 + 8 - 6 - 7 + 2 - 4 - 8 - 6 + 8 - 5 + 2 - 4 - 4 - 2 + 1 + 4 + 7 + 2 + 9 - 6 - 5 - 3 - 2 - 4 - 7 + 9 + 7",
    "correct_answer": -1,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "442 + 32 + 180 * 766 - 465",
    "correct_answer": 137889,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "388 + 837 * 277 - 251 * 195",
    "correct_answer": 183292,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "45 + 22 * 73 - 15 * 25",
    "correct_answer": 1276,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "6 - 32",
    "correct_answer": -26,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "311 * 39",
    "correct_answer": 12129,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "4 + 2 + 7 + 7 + 8 + 7 + 9 + 8 + 4 + 9 - 4 + 5 - 5 - 2 - 4 + 9 - 9 + 5 - 8 + 4 - 1 - 8 + 2 + 1 + 2 + 2 - 9 + 5 + 4 + 5 - 3 - 5 + 1 - 9 - 2 - 7",
    "correct_answer": 34,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "99 * 90",
    "correct_answer": 8910,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "1 + 3 + 2 - 9 + 2 - 7 - 7 - 5 - 9 + 5 - 7 - 9 + 3 - 7 + 1 + 5 + 5 + 4 - 9",
    "correct_answer": -38,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "639 * 31",
    "correct_answer": 19809,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "1 - 50",
    "correct_answer": -49,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "84 * 81",
    "correct_answer": 6804,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "108 - 212",
    "correct_answer": -104,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "51 + 92",
    "correct_answer": 143,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "197 * 18",
    "correct_answer": 3546,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "45 + 29",
    "correct_answer": 74,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "359 * 49",
    "correct_answer": 17591,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "75 * 69",
    "correct_answer": 5175,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "772 * 354",
    "correct_answer": 273288,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "4 + 8 - 1 + 7 + 8 + 4 + 2 + 8 + 9 - 5 + 7 + 5 + 5 + 2 - 4 - 9 + 4 + 1 + 2 - 1 + 3 + 2 + 6 + 3 - 1 - 9 - 4 + 6 - 1 - 6 - 5 + 6 + 1",
    "correct_answer": 57,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "603 * 71",
    "correct_answer": 42813,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "41 * 17",
    "correct_answer": 697,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "2 + 5 - 3 - 8 + 5 - 8 - 2 - 4 - 8 + 6 - 5 - 4 - 4 + 2 + 8 - 2 + 7 + 5 + 3 - 5 - 2 - 2 + 4 - 7 - 7 + 3 - 7 + 6 + 6 - 8 + 2 + 6 - 2 - 8 + 5 + 6 + 5",
    "correct_answer": -10,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "129 * 14",
    "correct_answer": 1806,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "53 * 72",
    "correct_answer": 3816,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "15 + 10 * 73 - 17 * 12",
    "correct_answer": 541,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "1411 - 4301",
    "correct_answer": -2890,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "112 * 96",
    "correct_answer": 10752,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "7 - 6 - 4 + 5 + 7 + 2 - 8 - 2 - 3 - 9 - 9 - 9 - 1 - 8 + 3 + 2",
    "correct_answer": -33,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "416 - 501",
    "correct_answer": -85,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "311 - 427",
    "correct_answer": -116,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "47 * 25",
    "correct_answer": 1175,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "945 % 3",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "271 - 353",
    "correct_answer": -82,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "2468 + 6798",
    "correct_answer": 9266,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "367 * 78",
    "correct_answer": 28626,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "79 + 29 - 83",
    "correct_answer": 25,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "333 - 487",
    "correct_answer": -154,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "952 * 181",
    "correct_answer": 172312,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "(30 + 54) * (23 - 69)",
    "correct_answer": -3864,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "1 + 25 + 16 - 1 + 4 + 29 + 29 - 10 + 17 - 2 + 5 + 13 - 27 - 15 - 5 - 14 - 30 + 8 - 12 - 2 + 11 + 19 + 11 - 13",
    "correct_answer": 57,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "2 - 2 - 3 + 6 - 3 - 6 - 3 - 6 - 4 - 1 + 8 - 6 - 2 + 7 + 5 + 6 + 9 + 7 - 9 - 1 + 6 - 2 + 2 + 6 - 3 + 5 - 5 + 3 + 2 - 5 + 3 + 4 - 6",
    "correct_answer": 14,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "875 * 53",
    "correct_answer": 46375,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "5984 + 1660",
    "correct_answer": 7644,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "748 - 770 - 941 - 18 * 931",
    "correct_answer": -17721,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "95 - 6 + 58",
    "correct_answer": 147,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "(38 + 19) * (70 - 91)",
    "correct_answer": -1197,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "286 * 27",
    "correct_answer": 7722,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "26 + 17 + 10 - 16 + 3 + 14 - 17 - 11 + 28 - 1 + 25 - 20 + 30 - 28 + 28 + 20 + 22 + 8 - 20 + 2 - 22 - 26 - 19 - 6 + 29 - 3 - 12",
    "correct_answer": 61,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "88 + 17 * 77 - 63 * 80",
    "correct_answer": -3643,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "865 * 85",
    "correct_answer": 73525,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "3 - 4 + 9 - 8 + 2 + 1 + 4 + 9 + 8 - 2 + 8 + 5 + 2 + 7 + 5 + 7 + 5 + 8 - 6",
    "correct_answer": 63,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "49 * 27",
    "correct_answer": 1323,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "3230 - 2785",
    "correct_answer": 445,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "52 + 529 * 181 + 130 - 942",
    "correct_answer": 94989,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(52 + 45) * (57 - 81)",
    "correct_answer": -2328,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "69 - 16",
    "correct_answer": 53,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "86 - 71",
    "correct_answer": 15,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "11 - 28 + 30 + 26 + 18 + 16 - 17 - 11 - 18 - 9 + 2 + 19 + 14 - 18 + 12 - 29 + 22 + 1 + 18 - 12 + 26 - 3 + 10",
    "correct_answer": 80,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "72 * 87",
    "correct_answer": 6264,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "8009 + 4314",
    "correct_answer": 12323,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "45 * 32",
    "correct_answer": 1440,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "3 + 8 + 5 - 8 - 4 - 9 + 1 + 6 + 2 + 2 + 5 + 1 - 5 - 2 - 7 - 4 - 5 - 9 - 4 + 1 + 8 + 7 + 3 - 1 - 3 + 5 + 4 - 7 + 5 + 6 + 4",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "28 - 20 - 10 - 30 - 19 - 2 + 4 - 20 + 29 + 26 - 4 - 16 + 5 + 19 + 30 + 16 - 11 - 30 + 1 - 13 + 5 + 13 - 24 - 11 - 23 + 24",
    "correct_answer": -33,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "843 * 431",
    "correct_answer": 363333,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "7461 + 2226",
    "correct_answer": 9687,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "5 + 8 + 2 - 5 + 6 + 2 - 1 + 3 - 6 - 9 - 4 - 4 - 2 - 3 + 2 + 4 - 8 - 2 + 6 - 8 - 4 + 3 + 4 - 5 - 9 + 6 - 2 + 2 - 9 - 9 - 3 + 3",
    "correct_answer": -37,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "312 - 439 * 917 * 727 - 904",
    "correct_answer": -292663893,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "7 + 23 - 24 + 30 - 1 + 19 - 1 + 10 - 29 + 3 + 3 + 15 - 22 + 22 + 3 - 26 + 12 + 7 - 12 - 18 - 2 + 14 - 25 - 15 + 21 + 9",
    "correct_answer": 23,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "933 * 22",
    "correct_answer": 20526,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "382 * 666",
    "correct_answer": 254412,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "215 - 383 + 161 * 164 - 711",
    "correct_answer": 25525,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "218 - 442",
    "correct_answer": -224,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "4 + 1 - 2 + 6 - 6 + 7 - 6 - 5 + 3 + 2 + 7 + 6 + 1 + 1 + 1 + 5 + 4 + 7 - 7 + 5 + 9 - 2 - 1 + 7 - 1 + 2 + 9 + 8 + 4 + 2 + 3 - 3 + 3 + 3 + 9 - 6 + 9 + 5",
    "correct_answer": 94,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "969 * 90",
    "correct_answer": 87210,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "75 + 27 * 23 - 26 * 44",
    "correct_answer": -448,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "5 - 5 + 7 - 4 - 5 + 4 - 3 + 1 + 2 + 8 + 2 - 6 - 4 + 7 - 9 - 5 - 4 + 1 + 7 + 2",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "1720 - 1968",
    "correct_answer": -248,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "81 + 83 - 6",
    "correct_answer": 158,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "826 * 10",
    "correct_answer": 8260,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "18 * 29",
    "correct_answer": 522,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "897 * 23",
    "correct_answer": 20631,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "32 - 68 + 53",
    "correct_answer": 17,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "811 - 155 + 563 + 810 - 560",
    "correct_answer": 1469,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2 - 6 + 28 + 9 + 11 - 27 - 27 + 3 + 27 + 26 - 10 + 2 - 29 + 24 + 30 + 23 - 19 - 20 + 2 - 16 + 20 - 26 - 26 - 16",
    "correct_answer": -15,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "667 % 3",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "411 % 8",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "22 * 16",
    "correct_answer": 352,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "965 - 766 + 165 + 119 + 199",
    "correct_answer": 682,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "32 - 91 + 57",
    "correct_answer": -2,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "4 - 1 + 7 - 4 + 9 + 3 - 2 - 3 + 4 - 7 - 6 + 2 + 8 + 2 + 8 - 3 - 9 + 4 + 4 - 9 + 6 - 7 + 3 + 7 + 3 + 7 - 9 + 9 + 4 + 7 - 7 + 6 - 9 - 9 + 1 - 4 + 9 + 6 + 8",
    "correct_answer": 42,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "22 - 10 + 24 + 21 + 25 + 16 - 21 - 18 - 19 - 15 + 2 + 18 - 1 - 4 - 21 - 21 - 16 - 27 + 8 + 9 - 12 - 8 - 25 + 2 - 22 - 17",
    "correct_answer": -110,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "1 + 5 + 5 + 9 + 2 + 4 + 9 + 3 - 2 + 7 + 2 + 5 + 5 - 8 + 9 - 5 + 3 - 6 - 1 - 7 - 4 + 1 - 1 + 4 + 6 + 8 + 6 + 7 + 4 - 5 - 2 - 9 - 6 + 3 - 8 - 8 - 6 + 5 + 6",
    "correct_answer": 41,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "103 - 218",
    "correct_answer": -115,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "796 % 19",
    "correct_answer": 17,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "2133 - 7703",
    "correct_answer": -5570,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "327 * 57",
    "correct_answer": 18639,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "27 - 2 + 7 + 26 - 30 + 15 + 6 - 18 - 9 + 30 - 24 - 16 - 6 + 2 - 16 - 29 - 22 + 7 + 4 + 3 - 2 + 6 + 7 + 12",
    "correct_answer": -22,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "7237 + 3777",
    "correct_answer": 11014,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "1 + 8 + 8 + 7 + 5 - 8 + 7 + 9 + 8 + 8 - 6 + 5 - 2 - 4 - 9 + 2 + 4 + 8 + 6 - 9 - 2 - 5 + 9 + 5 - 3 - 9 + 1 + 3 + 1 - 3 + 1 - 5 + 1 + 9 - 9 + 6 + 4 - 9",
    "correct_answer": 43,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "75 - 52",
    "correct_answer": 23,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "869 * 918 + 464 * 836 - 631",
    "correct_answer": 1185015,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "28 - 5 + 24 - 23 + 18 - 28 + 3 - 14 - 7 + 25 + 10 + 27 - 9 - 11 - 22 + 14 + 9 + 5 + 27 - 21 - 29 + 5 + 26",
    "correct_answer": 52,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "2 + 1 + 1 + 1 + 2 + 8 + 8 - 6 - 6 + 5 - 9 + 5 + 8 - 5 + 8 - 5 + 4 + 4 + 9 + 4 + 4 - 2 - 4 - 9 + 3 + 1 - 9 - 3 + 9 + 3 + 8 - 5 + 7 + 2 + 2 + 5",
    "correct_answer": 51,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "615 * 25",
    "correct_answer": 15375,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "71 + 17",
    "correct_answer": 88,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "1 - 30 + 11 - 28 + 23 - 19 + 26 - 12 - 26 + 30 + 12 - 9 - 16 - 16 - 10 - 19 + 9 - 2 - 14 + 26 - 2 - 1 + 19",
    "correct_answer": -47,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "31 - 47 + 13",
    "correct_answer": -3,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "49 - 83 + 43",
    "correct_answer": 9,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "8 + 7 - 6 + 1 + 6 - 5 - 4 + 5 - 7 + 8 - 7 - 3 - 1 - 5 + 1 + 4 + 2 - 6 + 8 - 1 + 2 - 6 + 8 - 4 + 5 - 2 - 5 + 8 - 6 - 8 + 6 + 2 - 5 + 8 - 7 + 6",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "26 * 25",
    "correct_answer": 650,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "452 % 7",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "65 + 34",
    "correct_answer": 99,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "68 * 60",
    "correct_answer": 4080,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "51 * 57",
    "correct_answer": 2907,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "639 * 144",
    "correct_answer": 92016,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "9 - 8 + 2 - 2 + 4 + 2 - 4 - 5 - 4 - 2 - 1 + 5 - 9 + 4 - 7 - 6 + 2 - 4 + 1 - 7 + 1 - 5 + 7 + 2 + 1 + 7 + 2 - 7 - 5 - 2 - 4 - 1 + 9 - 7 - 5 + 8 + 1 - 9 + 7",
    "correct_answer": -30,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(89 + 43) * (56 - 85)",
    "correct_answer": -3828,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "(18 + 17) * (29 - 86)",
    "correct_answer": -1995,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "25 + 21 - 30 - 13 - 15 - 24 + 12 - 11 - 18 - 13 - 1 - 25 - 9 + 17 - 22 - 10 + 4 + 2 + 2 - 11 - 9 - 21 + 11 - 8 - 15",
    "correct_answer": -161,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "42 * 66",
    "correct_answer": 2772,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "69 - 49 + 41",
    "correct_answer": 61,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "13 + 21 - 23 - 26 - 13 - 24 + 17 - 18 + 7 - 26 - 21 + 6 - 29 + 27 + 21 - 28 + 7 - 5 - 1 - 11 + 10",
    "correct_answer": -96,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "8 - 9 - 4 + 9 - 6 + 5 - 7 - 1 + 8 + 7 - 6 + 9 + 5 - 8 + 5 + 5 - 8 - 4 - 9 + 6 - 1 + 7",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(42 + 88) * (73 - 54)",
    "correct_answer": 2470,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "357 - 603",
    "correct_answer": -246,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "3317 - 3807",
    "correct_answer": -490,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "835 - 435 * 925 - 628 + 648",
    "correct_answer": -401520,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "7870 + 4678",
    "correct_answer": 12548,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "894 * 68",
    "correct_answer": 60792,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "37 - 85 + 52",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "3141 - 4879",
    "correct_answer": -1738,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "2646 + 3293",
    "correct_answer": 5939,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "61 + 143 * 492 + 61 + 402",
    "correct_answer": 70880,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "32 * 35",
    "correct_answer": 1120,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "49 + 26 * 96 - 23 * 67",
    "correct_answer": 1004,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "921 * 71",
    "correct_answer": 65391,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "7 - 28 - 2 + 24 + 12 + 26 + 28 - 14 + 15 + 3 + 18 - 11 + 18 - 18 + 26 + 27 - 16 - 8 + 19 - 4 + 24 + 10 - 8 - 4 + 8",
    "correct_answer": 152,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "69 * 80",
    "correct_answer": 5520,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "12 + 16 + 26 - 28 + 28 + 23 - 24 + 23 + 15 - 8 - 30 - 20 + 29 + 11 - 13 - 29 + 25 - 14 - 5 - 29 - 18 + 30",
    "correct_answer": 20,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(49 + 25) * (52 - 25)",
    "correct_answer": 1998,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "838 % 17",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "509 - 419 * 535 * 752 * 967",
    "correct_answer": -163009200851,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "3 + 2 - 1 + 9 + 2 - 6 + 4 + 3 + 5 - 4 + 1 + 8 + 7 + 4 + 8 + 4 - 7 + 2",
    "correct_answer": 44,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "59 + 83 - 4",
    "correct_answer": 138,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "26 * 501 + 322 - 730 * 888",
    "correct_answer": -634892,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "641 - 702 - 794 + 338 * 38",
    "correct_answer": 11989,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "40 * 49",
    "correct_answer": 1960,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "29 * 17",
    "correct_answer": 493,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "52 + 31 * 28 - 47 * 31",
    "correct_answer": -537,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "(19 + 95) * (92 - 10)",
    "correct_answer": 9348,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "(10 + 32) * (84 - 98)",
    "correct_answer": -588,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "584 * 11",
    "correct_answer": 6424,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "71 + 19 * 92 - 92 * 82",
    "correct_answer": -5725,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "7 + 4 + 1 - 6 + 5 + 4 - 5 - 6 + 3 - 6 - 3 + 7 - 1 - 2 - 5 + 2",
    "correct_answer": -1,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "60 - 86",
    "correct_answer": -26,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "128 % 13",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "280 * 63",
    "correct_answer": 17640,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "985 * 427 + 183 - 639 + 195",
    "correct_answer": 420334,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "17 - 3 + 3 - 24 - 23 + 21 - 10 - 15 - 19 - 15 + 12 + 15 + 23 + 21 + 21 - 11 - 16 - 28 + 4 - 26 - 9 - 11 - 20 + 21 - 24",
    "correct_answer": -96,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "204 - 298",
    "correct_answer": -94,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "39 * 38",
    "correct_answer": 1482,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "68 + 15 - 96",
    "correct_answer": -13,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "81 * 70",
    "correct_answer": 5670,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "271 * 913",
    "correct_answer": 247423,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "844 * 11",
    "correct_answer": 9284,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "2 + 5 - 8 - 7 + 7 + 4 + 3 - 6 + 2 - 2 + 1 + 7 - 2 - 3 + 1 + 1 - 6 - 6",
    "correct_answer": -7,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "9 + 2 + 5 + 1 - 7 + 4 + 4 + 1 + 1 - 4 + 2 - 2 - 3 + 1 - 2 - 6 - 4 + 9 + 7 + 4 + 6 - 7 + 1 + 8 - 5 + 6 + 4 - 8 - 2 + 3 - 2 - 7 + 3 - 6 + 8 - 1 + 8 + 4 + 1",
    "correct_answer": 36,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "476 % 19",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "5341 + 2964",
    "correct_answer": 8305,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "751 * 715 * 966 - 304 - 633",
    "correct_answer": 518707253,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "18 + 23 - 22 + 30 + 30 - 27 + 7 + 12 - 26 - 23 + 15 - 18 - 7 + 1 - 16 + 30 + 23 + 9 + 30 - 12 + 26 - 2 + 4 + 29 - 14 - 28 - 15",
    "correct_answer": 77,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "4 + 1 + 5 - 7 + 6 + 2 - 3 + 2 - 3 - 3 - 6 + 2 + 8 + 9 - 4 - 7 + 2 + 8 + 2 - 1 + 3 + 3 + 8 + 3 + 2 + 7 - 3 + 1 + 1",
    "correct_answer": 42,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "1 + 8 + 5 - 8 - 7 + 3 - 2 - 4 - 4 + 7 + 3 + 3 + 9 - 9 + 1 - 1 - 9 - 9 + 4 - 6 + 4 - 6 - 9 + 3 - 7 - 6 + 8 - 5 + 6 + 6 - 1 - 9 + 8",
    "correct_answer": -23,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "146 + 671 - 633 + 14 + 698",
    "correct_answer": 896,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "428 * 452",
    "correct_answer": 193456,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "339 + 359 * 480 + 346 * 945",
    "correct_answer": 499629,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "700 * 13",
    "correct_answer": 9100,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "981 + 746 - 198 + 869 + 754",
    "correct_answer": 3152,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "164 % 6",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "359 + 399 - 448 - 375 + 369",
    "correct_answer": 304,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "980 - 479 + 169 * 766 - 529",
    "correct_answer": 129426,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "320 + 250 + 580 - 28 - 912",
    "correct_answer": 210,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "82 + 15",
    "correct_answer": 97,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "716 % 8",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "2 + 6 + 2 + 5 - 9 + 7 - 5 - 7 - 6 + 1 + 7 - 8 + 2 + 7 + 9 - 1 - 5 + 3 - 7 + 7 + 1 + 6 - 8 + 5 - 2 - 8 + 4 + 3 + 5 + 4 - 6 - 7 + 1 - 9 - 5",
    "correct_answer": -6,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "71 + 19 - 50",
    "correct_answer": 40,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "327 * 83",
    "correct_answer": 27141,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "84 + 90 - 85",
    "correct_answer": 89,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "(82 + 76) * (88 - 53)",
    "correct_answer": 5530,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "14 + 24 + 19 - 16 + 25 - 19 + 23 + 8 + 26 + 26 - 30 + 21 + 22 - 25 - 18 + 17 + 16 + 9 + 21 - 12 + 25",
    "correct_answer": 176,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "8 - 7 - 7 - 5 - 2 + 7 + 6 + 2 - 1 - 5 - 5 + 9 + 1 + 6 + 3 + 2 + 6 + 6 - 6 + 6 - 6",
    "correct_answer": 18,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "1717 - 3528",
    "correct_answer": -1811,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "4329 + 3545",
    "correct_answer": 7874,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "30 - 26 - 25 - 30 - 27 - 24 - 13 - 28 - 16 - 2 + 5 - 17 + 28 - 19 - 10 - 29 + 30 - 3 + 12 - 10 + 17 - 19 - 5 - 12",
    "correct_answer": -193,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "282 * 70",
    "correct_answer": 19740,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "580 + 749 - 94 + 515 - 404",
    "correct_answer": 1346,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "4714 - 6360",
    "correct_answer": -1646,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "611 * 193",
    "correct_answer": 117923,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "5 + 9 + 1 - 2 - 2 - 6 + 1 - 6 + 7 - 6 - 9 + 5 + 4 + 6 + 9 + 1 - 2 - 5 + 7 + 3 - 7 + 2",
    "correct_answer": 15,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "470 % 15",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "805 * 11",
    "correct_answer": 8855,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "33 * 93",
    "correct_answer": 3069,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "706 % 7",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "28 - 20 - 21 + 7 - 12 - 20 + 25 - 6 + 5 + 27 + 20 - 2 - 29 + 14 - 5 - 26 + 4 - 19 + 19 - 7 + 8 + 7 - 8",
    "correct_answer": -11,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "6 + 5 + 9 - 2 + 6 + 5 - 5 - 2 - 6 - 9 + 5 + 5 + 6 - 7 + 6 - 6 + 4 + 6 - 2 - 9 - 3 + 8 + 6 - 8 + 8 + 3 + 2 + 9 - 5 + 4 - 8 + 1 - 5 - 6 - 5 - 5 + 7 - 5",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "923 * 213",
    "correct_answer": 196599,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "3830 + 8717",
    "correct_answer": 12547,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "7 - 20 + 25 - 3 + 4 + 1 + 13 - 16 + 25 - 3 - 7 - 23 - 29 - 26 - 7 - 3 - 29 + 16 + 4 + 12 + 1 - 3 + 8 - 22 - 2",
    "correct_answer": -77,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "31 * 97",
    "correct_answer": 3007,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "80 + 20",
    "correct_answer": 100,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "20 + 58 - 69",
    "correct_answer": 9,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "938 * 950 + 56 * 728 + 143",
    "correct_answer": 932011,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "8 - 7 - 8 - 5 + 6 + 7 - 4 + 9 - 7 - 7 + 3 - 5 + 9 + 3 - 6 - 1 - 5 - 3 + 8 + 8 + 3 + 3 + 2 + 4 + 4 - 9 + 6 + 3 - 8 - 7 - 8 - 8 + 2 - 6 + 3 - 6",
    "correct_answer": -19,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "710 * 116",
    "correct_answer": 82360,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "2 + 9 - 7 + 3 - 2 - 7 - 3 - 2 - 5 - 4 - 9 - 7 - 6 + 7 + 4 - 2 + 9 - 6 - 6 + 5 + 4 + 2 + 4 - 2 + 2 - 5 + 8 - 6 - 5 - 2 + 3 + 7 - 9 + 7 + 3",
    "correct_answer": -16,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "2 + 1 + 8 + 6 + 2 - 9 + 4 + 3 - 2 + 1 + 3 + 9 + 7 - 9 + 4 + 4",
    "correct_answer": 34,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "51 * 44",
    "correct_answer": 2244,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "4135 - 4697",
    "correct_answer": -562,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "70 + 490 - 940 + 54 * 318",
    "correct_answer": 16792,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "9 + 2 + 4 - 8 - 6 + 6 - 4 + 9 + 5 + 8 - 7 - 7 + 2 - 5 - 7 + 5 - 2 - 7 - 1 - 5",
    "correct_answer": -9,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "95 * 50",
    "correct_answer": 4750,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "422 - 491",
    "correct_answer": -69,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "44 + 24",
    "correct_answer": 68,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "578 * 79",
    "correct_answer": 45662,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "72 - 98",
    "correct_answer": -26,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "17 + 24 + 8 + 16 - 1 + 11 - 24 + 3 - 11 + 24 - 22 + 8 - 23 + 3 - 29 + 8 - 25 - 9 + 21 - 23 - 28",
    "correct_answer": -52,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "650 - 273 + 921 * 976 - 981",
    "correct_answer": 898292,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "609 * 884",
    "correct_answer": 538356,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "(69 + 11) * (34 - 96)",
    "correct_answer": -4960,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "4218 - 6466",
    "correct_answer": -2248,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "60 + 15 * 98 - 92 * 34",
    "correct_answer": -1598,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "41 * 25",
    "correct_answer": 1025,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "98 * 886 - 143 * 682 + 589",
    "correct_answer": -10109,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "143 * 71",
    "correct_answer": 10153,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "29 - 22 - 19 + 25 + 3 - 18 + 1 + 20 + 24 - 22 - 13 - 7 - 1 + 8 - 7 - 2 - 13 - 21 + 14 - 26 + 12",
    "correct_answer": -35,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "34 - 44 + 80",
    "correct_answer": 70,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "45 * 39",
    "correct_answer": 1755,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "85 + 19 - 45",
    "correct_answer": 59,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "428 - 515",
    "correct_answer": -87,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "333 - 764 + 792 * 579 - 661",
    "correct_answer": 457476,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "760 * 904 - 327 + 156 * 851",
    "correct_answer": 819469,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "5066 + 6828",
    "correct_answer": 11894,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "21 + 16 * 29 - 58 * 29",
    "correct_answer": -1197,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "923 * 76",
    "correct_answer": 70148,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "442 - 683",
    "correct_answer": -241,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "816 + 585 - 999 * 777 + 378",
    "correct_answer": -774444,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(30 + 49) * (12 - 94)",
    "correct_answer": -6478,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "2 - 18 + 16 - 7 + 1 + 21 - 30 + 13 + 15 + 13 + 7 + 4 + 22 + 15 + 18 + 28 + 22 + 15 + 1 - 11 - 19 - 12 + 9 + 1 + 19 - 22",
    "correct_answer": 123,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "5 - 5 + 4 + 8 + 6 + 3 + 7 - 7 + 8 + 7 - 2 - 5 - 3 + 3 + 8 + 5 + 8",
    "correct_answer": 50,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "3803 - 5051",
    "correct_answer": -1248,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "988 * 951",
    "correct_answer": 939588,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "58 - 14 + 44",
    "correct_answer": 88,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "36 * 31",
    "correct_answer": 1116,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "720 * 35",
    "correct_answer": 25200,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "42 - 24",
    "correct_answer": 18,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "11 - 51 + 40",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "11 + 29 + 7 + 15 - 13 - 14 - 2 + 7 + 3 + 19 - 23 + 23 - 4 + 11 + 1 + 16 + 24 + 27 + 9 - 8 + 16",
    "correct_answer": 154,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "15 + 60 - 10",
    "correct_answer": 65,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "11 - 12 + 13 - 17 + 19 + 17 - 18 + 29 - 20 - 10 + 19 - 2 - 23 + 16 + 27 + 30 + 15 - 13 - 1 - 1 - 9 - 29",
    "correct_answer": 41,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(59 + 82) * (96 - 95)",
    "correct_answer": 141,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "36 + 6",
    "correct_answer": 42,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "29 - 24 + 7 + 25 + 28 - 1 - 5 - 29 - 13 + 4 + 14 + 29 - 22 - 27 - 16 - 11 + 4 - 23 + 28 + 19 + 10 + 17",
    "correct_answer": 43,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "601 * 294",
    "correct_answer": 176694,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "1 + 8 + 3 + 5 - 7 - 9 + 4 - 3 - 6 - 5 + 9 - 8 + 1 + 2 + 9 + 5 - 3 + 1 + 3 - 8 - 3 - 6 - 1 + 4 + 1 + 9 - 5 + 7 - 2 + 1",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "300 * 674",
    "correct_answer": 202200,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "79 * 60",
    "correct_answer": 4740,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "21 * 36",
    "correct_answer": 756,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "969 % 17",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "47 * 34",
    "correct_answer": 1598,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "766 % 9",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "78 - 56 + 13",
    "correct_answer": 35,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "3996 - 6455",
    "correct_answer": -2459,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "(96 + 51) * (20 - 26)",
    "correct_answer": -882,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "6 - 8 + 8 + 4 + 6 - 6 - 6 - 4 - 7 + 2 - 8 - 2 - 5 - 3 + 9 - 8 - 5 - 9 + 8 - 8 - 8 + 4 - 3 + 2 + 1 - 6 + 5 - 5 - 2 - 9 + 8 - 6",
    "correct_answer": -55,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "297 * 121",
    "correct_answer": 35937,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "206 * 43",
    "correct_answer": 8858,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "213 - 279",
    "correct_answer": -66,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "4 - 8 - 3 + 5 - 4 - 7 + 7 + 4 + 2 + 8 - 7 + 7 + 5 + 8 + 9 + 1 - 7 + 4 - 2 + 7 + 7 + 6 + 5 - 5 - 7 - 8 - 4 + 2 + 1 + 6 + 1 - 8",
    "correct_answer": 29,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "804 * 50",
    "correct_answer": 40200,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "33 * 16",
    "correct_answer": 528,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "998 * 772 - 753 * 320 * 842",
    "correct_answer": -202117864,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "330 - 535",
    "correct_answer": -205,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "321 - 591 + 466 * 876 + 522",
    "correct_answer": 408468,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "18 * 24",
    "correct_answer": 432,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "254 + 562 - 674 * 765 * 902",
    "correct_answer": -465079404,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2110 - 4512",
    "correct_answer": -2402,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "50 * 94",
    "correct_answer": 4700,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "3 + 2 + 8 + 1 - 6 - 5 - 7 + 4 + 4 + 9 - 3 + 8 + 7 - 9 + 4 - 2 + 1 - 3 - 6",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "11 - 27 + 29 + 4 + 11 - 9 + 3 - 26 - 18 - 22 - 1 + 4 + 28 - 29 + 3 + 12 - 27 + 4 + 1 - 16 + 21",
    "correct_answer": -44,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "863 + 630 + 790 * 526 - 481",
    "correct_answer": 416552,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "711 % 15",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "239 + 740 - 205 * 304 - 516",
    "correct_answer": -61857,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1 + 7 + 1 - 3 - 2 - 2 - 4 - 3 - 3 + 9 - 9 + 6 + 3 - 6 + 7 + 7 - 2 + 8 + 1 - 5 + 2 + 8 + 5 - 5 + 6 - 3 + 8 - 8 - 8 - 3 + 8",
    "correct_answer": 21,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "16 + 12 + 15 - 8 + 23 - 21 - 11 - 21 - 1 + 1 - 12 - 9 + 23 - 16 - 14 - 18 - 17 + 4 + 18 + 4 - 15",
    "correct_answer": -47,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "95 - 57",
    "correct_answer": 38,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "16 + 7 + 5 - 12 - 19 - 17 + 7 - 15 - 17 + 18 + 26 + 9 - 24 + 23 - 30 - 1 + 2 + 18 - 8 - 3 + 29 + 1 - 9 + 10",
    "correct_answer": 16,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "9 + 2 + 2 - 1 + 5 + 7 + 9 - 5 + 8 + 9 - 3 + 8 + 3 - 7 + 3 - 1 - 6 - 9 + 9 + 9 - 7 + 2 - 3 - 1 + 8 + 7 - 1 + 1 + 3 - 3 + 3 + 4 - 9 - 7 - 8 - 4",
    "correct_answer": 36,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "4209 - 6154",
    "correct_answer": -1945,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "4 - 10 + 16 - 13 - 29 + 1 - 29 + 29 + 17 + 25 - 10 + 13 + 18 + 14 + 15 - 9 - 2 - 7 + 27 - 3 + 19",
    "correct_answer": 86,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "51 * 38",
    "correct_answer": 1938,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "491 + 247 * 157 - 274 + 411",
    "correct_answer": 39407,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "4764 - 5038",
    "correct_answer": -274,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "(91 + 23) * (89 - 93)",
    "correct_answer": -456,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "28 + 8 - 1 - 15 + 26 + 12 - 5 - 6 - 25 + 13 + 1 - 29 - 30 + 26 + 14 + 23 + 1 - 29 + 3 - 27 + 11 - 5",
    "correct_answer": -6,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "450 - 563",
    "correct_answer": -113,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "673 * 582 * 78 + 736 - 151",
    "correct_answer": 30552093,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "638 * 64",
    "correct_answer": 40832,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "1 - 4 + 5 + 3 + 7 + 3 + 4 + 4 - 5 - 9 + 4 + 8 + 9 - 5 + 9 - 6 + 3 + 9 - 3 + 6 + 5",
    "correct_answer": 48,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(10 + 49) * (31 - 64)",
    "correct_answer": -1947,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "44 * 17",
    "correct_answer": 748,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "40 * 65",
    "correct_answer": 2600,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "711 * 644",
    "correct_answer": 457884,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "883 - 797 * 967 * 754 * 71",
    "correct_answer": -41258599383,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "4 - 6 + 5 + 2 - 8 + 8 + 7 - 1 - 5 - 8 + 2 - 8 + 8 + 3 + 3 - 4 - 8 - 8 + 4 + 6 - 9 + 9 + 3 + 2 + 6 - 1 + 3 + 1 + 9 + 8 - 9 + 8 - 4 - 6 + 6 + 9 - 1",
    "correct_answer": 30,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "611 * 27",
    "correct_answer": 16497,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "35 * 67",
    "correct_answer": 2345,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "18 - 25 - 15 - 7 - 3 + 1 - 1 + 2 + 13 + 29 + 13 - 5 + 7 - 24 - 14 + 27 + 14 + 16 + 14 + 19 - 10 - 26 - 23 - 28 + 7 - 23 + 7",
    "correct_answer": -17,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "53 + 95 * 70 - 83 * 31",
    "correct_answer": 4130,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "649 * 817 - 677 - 724 * 918",
    "correct_answer": -135076,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "46 + 30 * 36 - 66 * 30",
    "correct_answer": -854,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "3 - 26 - 15 + 12 + 17 - 12 + 21 - 3 - 17 - 21 + 9 + 2 - 24 - 27 - 25 - 6 + 10 + 15 - 13 + 14 - 10 - 18 - 26 + 4",
    "correct_answer": -136,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "267 - 495",
    "correct_answer": -228,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "49 * 33",
    "correct_answer": 1617,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "4 - 16 + 22 - 27 + 6 - 14 + 2 - 11 + 18 + 9 - 9 - 16 - 23 - 6 + 1 + 8 + 7 + 12 - 24 - 3 - 12",
    "correct_answer": -72,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "17 + 12 + 25 + 27 - 11 + 16 + 26 - 18 - 3 - 15 - 10 + 16 - 21 - 2 + 25 + 20 + 17 + 3 - 9 + 11 - 6 - 11 + 2 - 30 - 24 + 13 + 23",
    "correct_answer": 93,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "32 * 73",
    "correct_answer": 2336,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "616 * 192",
    "correct_answer": 118272,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "765 * 93",
    "correct_answer": 71145,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "419 * 73",
    "correct_answer": 30587,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "19 + 30 - 2 + 24 - 22 - 29 + 6 + 25 + 2 - 13 + 24 + 1 + 21 - 20 - 15 - 10 + 8 + 25 - 19 - 12 - 17 - 30 - 23",
    "correct_answer": -27,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "4 + 3 + 8 - 4 - 8 + 1 + 9 + 4 - 6 + 6 - 6 + 3 - 3 + 8 + 1 + 6 + 9 + 8 - 3 - 4 + 3 - 6 - 8 + 1 - 3 - 1 + 3 + 6 + 7",
    "correct_answer": 38,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "74 - 29 + 55",
    "correct_answer": 100,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "98 + 98 - 84",
    "correct_answer": 112,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "220 * 76",
    "correct_answer": 16720,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "477 * 624 * 329 - 871 * 241",
    "correct_answer": 97716281,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "867 - 483 * 24 * 448 + 903",
    "correct_answer": -5191446,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "916 - 407 * 284 - 624 - 102",
    "correct_answer": -115398,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(87 + 64) * (93 - 37)",
    "correct_answer": 8456,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "85 - 55 + 63",
    "correct_answer": 93,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "32 - 96",
    "correct_answer": -64,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "25 - 69",
    "correct_answer": -44,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "11 + 65 - 83",
    "correct_answer": -7,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "379 % 6",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "9209 + 7806",
    "correct_answer": 17015,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "345 * 538 - 207 + 475 * 160",
    "correct_answer": 261403,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1 - 6 + 1 + 1 + 4 + 1 - 3 - 2 + 7 - 1 + 2 - 4 - 2 - 1 - 4 + 3 - 1 + 6 - 4",
    "correct_answer": -2,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "80 - 11",
    "correct_answer": 69,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "2669 + 3290",
    "correct_answer": 5959,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "6 + 9 + 8 - 7 + 7 + 2 + 6 - 9 + 3 + 3 - 3 - 8 + 9 + 5 - 3 - 2 + 4 + 5 + 7 + 1 + 1 - 5 + 1 + 3 - 4 + 4 + 8 + 4 - 7 - 9 + 2 - 3 - 3 + 2 - 2 - 4 - 7",
    "correct_answer": 24,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "15 * 20",
    "correct_answer": 300,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "29 * 23",
    "correct_answer": 667,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "4974 - 8600",
    "correct_answer": -3626,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "6 - 22 + 1 - 16 - 7 + 21 + 22 + 22 - 5 - 24 - 5 - 23 - 14 + 27 - 19 + 2 - 2 - 13 + 18 + 15 - 5 + 11 - 10 + 26 - 17 + 6",
    "correct_answer": -5,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "156 - 272",
    "correct_answer": -116,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "162 - 240",
    "correct_answer": -78,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "377 * 154",
    "correct_answer": 58058,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "765 + 432 + 394 - 85 - 609",
    "correct_answer": 897,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "566 + 836 - 632 + 253 * 612",
    "correct_answer": 155606,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "351 + 488 * 115 * 794 - 773",
    "correct_answer": 44558858,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "555 * 27",
    "correct_answer": 14985,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "437 + 481 + 129 + 955 - 501",
    "correct_answer": 1501,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "22 - 20 - 23 - 6 - 4 - 17 + 30 + 13 - 4 - 4 + 28 + 3 + 9 - 24 + 4 - 10 - 12 - 14 + 7 + 30 + 15 - 30 - 29 + 3 - 22 - 13 - 10",
    "correct_answer": -78,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "90 * 36",
    "correct_answer": 3240,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(59 + 84) * (24 - 52)",
    "correct_answer": -4004,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "497 - 229 - 89 * 703 * 422",
    "correct_answer": -26403006,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(40 + 83) * (91 - 21)",
    "correct_answer": 8610,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "20 - 25 + 8 + 15 + 30 - 14 + 15 - 10 - 8 + 11 + 3 + 12 + 29 + 22 + 1 - 24 - 17 - 12 + 15 + 29 + 27 + 16",
    "correct_answer": 143,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "11 - 13 + 21 - 10 + 13 + 22 + 7 + 19 - 28 - 18 - 6 - 13 + 30 + 13 - 3 + 7 - 1 + 13 - 4 - 6 + 29 + 17 + 8 - 23 + 10",
    "correct_answer": 95,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(33 + 76) * (60 - 41)",
    "correct_answer": 2071,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "775 - 703 + 245 + 343 + 110",
    "correct_answer": 770,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "206 * 270",
    "correct_answer": 55620,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "5 - 25 - 16 + 30 + 12 - 14 + 17 - 12 - 24 - 4 - 12 - 22 - 3 - 14 + 2 + 14 - 13 + 14 - 11 + 11 - 23 + 4 + 8 - 19 + 14 + 6 - 9",
    "correct_answer": -84,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "391 % 5",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "25 * 25",
    "correct_answer": 625,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "823 * 548",
    "correct_answer": 451004,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "7660 + 2978",
    "correct_answer": 10638,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "816 + 748 + 425 * 226 * 693",
    "correct_answer": 66564214,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "7 - 26 - 4 + 30 - 11 - 24 - 10 + 20 - 4 + 21 - 29 + 1 + 16 + 18 + 29 - 28 + 2 + 20 + 22 + 28 + 10 + 6 + 6",
    "correct_answer": 100,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "786 * 447 - 76 + 492 * 134",
    "correct_answer": 417194,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "7899 + 5911",
    "correct_answer": 13810,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "2916 + 3999",
    "correct_answer": 6915,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "157 * 44",
    "correct_answer": 6908,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "421 + 613 + 513 - 358 - 194",
    "correct_answer": 995,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2685 + 2889",
    "correct_answer": 5574,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "801 * 689",
    "correct_answer": 551889,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "27 * 27",
    "correct_answer": 729,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "50 + 99",
    "correct_answer": 149,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "94 + 17 * 46 - 72 * 42",
    "correct_answer": -2148,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "42 * 20",
    "correct_answer": 840,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "8 + 13 - 1 - 29 + 20 - 10 - 24 - 10 - 2 + 22 + 11 + 20 - 20 + 30 + 16 + 28 + 20 + 14 - 1 + 22 - 21 + 27 - 29 + 10 - 14 - 28",
    "correct_answer": 72,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "39 + 71 * 20 - 89 * 93",
    "correct_answer": -6818,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "7 + 5 + 1 - 9 + 1 + 2 + 7 - 3 - 7 - 5 + 9 - 1 + 1 + 9 - 6 - 3 - 8 + 2 + 9 - 2 - 7 - 3 + 7 - 1 + 9 + 1 + 2 - 3 + 7 + 5 + 4",
    "correct_answer": 30,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "868 * 364",
    "correct_answer": 315952,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "6 - 9 + 3 - 3 + 5 + 6 - 3 + 5 - 6 + 7 + 5 - 8 - 9 + 4 + 1 - 2 + 4 - 5 - 4 + 5 - 1 - 4 + 5 + 1 - 4 + 6 - 7 - 8 - 3 - 8 - 5 + 4 - 2 - 1 - 1 + 1 - 7 + 3",
    "correct_answer": -29,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "625 % 7",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "4 - 4 - 3 + 9 + 2 + 1 - 8 - 5 + 5 + 9 - 9 - 6 + 9 + 9 - 6 + 8 + 3 + 9 + 8 + 3 - 4 - 6 - 2 + 7 + 3 + 6 - 2 - 6 + 7 + 5 + 9 - 5 + 1 - 3 - 4 + 2 - 3 - 1",
    "correct_answer": 42,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "9 + 8 - 9 + 7 + 5 - 8 - 7 - 2 - 9 + 8 - 5 + 2 + 2 + 6 - 6 + 7 + 3 + 5 + 6 - 9",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "5602 - 1959",
    "correct_answer": 3643,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "168 * 144",
    "correct_answer": 24192,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "15 + 29 - 12 + 11 - 18 - 19 - 23 - 6 + 9 - 21 + 5 - 4 + 7 - 18 - 5 - 25 + 30 + 19 + 22 + 1 + 20 - 21 - 6 + 11 + 21 - 24",
    "correct_answer": -2,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "11 - 31",
    "correct_answer": -20,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "4 + 6 + 4 + 6 + 4 - 7 - 9 + 6 - 9 - 6 + 2 + 6 - 1 + 9 - 2 - 9",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "79 + 93 * 38 - 90 * 22",
    "correct_answer": 1633,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "2 - 9 - 5 + 2 - 3 + 7 - 6 + 9 + 1 + 7 + 2 + 7 - 8 + 3 + 6 - 8 + 8 + 5 + 5 - 1 - 3 + 4 + 2 - 2 - 6 + 5 - 8 + 7 + 7 - 6 - 7 + 6 + 1 + 7 + 9 + 3 - 9 + 1",
    "correct_answer": 35,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "25 - 5 - 20 - 21 - 14 + 21 - 20 - 19 + 28 - 6 + 3 + 3 - 5 + 8 + 9 - 5 - 30 - 23 - 2 - 19 + 28 + 14",
    "correct_answer": -50,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(39 + 90) * (15 - 68)",
    "correct_answer": -6837,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "5 + 4 - 2 - 7 - 5 + 8 - 6 - 3 + 3 + 5 + 7 - 4 + 8 + 5 - 7 + 5 - 2 + 2 - 7 - 7 + 8",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "283 * 671",
    "correct_answer": 189893,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "4482 - 4734",
    "correct_answer": -252,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "2412 + 8118",
    "correct_answer": 10530,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "42 + 73 - 77",
    "correct_answer": 38,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "63 * 99",
    "correct_answer": 6237,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "4 + 2 - 9 + 3 - 5 + 1 + 5 + 4 - 8 + 8 + 7 - 6 - 2 + 2 - 7 - 9 + 4 - 9 - 3 - 6 - 9 - 9 + 5 + 7 + 4 + 7 - 6 - 7 + 5",
    "correct_answer": -27,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "81 + 72 * 54 - 67 * 17",
    "correct_answer": 2830,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "18 + 29 - 3 + 25 + 2 - 12 + 8 + 7 + 17 - 14 - 7 - 22 + 28 - 10 - 19 - 12 - 4 - 27 + 21 + 3 - 5 - 2 - 6",
    "correct_answer": 15,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "4 + 7 - 9 + 2 + 9 + 7 + 5 + 1 - 4 - 1 + 9 + 9 + 4 - 5 + 3 + 9 - 1 - 5 - 5 - 1 - 4 - 4 - 1 + 6 + 9 + 3 + 5 - 1 - 1",
    "correct_answer": 50,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(74 + 94) * (26 - 87)",
    "correct_answer": -10248,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "20 + 14 - 12 - 22 - 30 - 1 + 11 + 26 + 3 - 3 - 5 + 6 - 13 - 27 + 30 + 17 + 29 - 28 - 12 - 2 + 26 - 11 + 12 + 11 - 26 + 21 - 16",
    "correct_answer": 18,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "35 + 37",
    "correct_answer": 72,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "292 - 349",
    "correct_answer": -57,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "945 + 597 + 437 - 51 * 761",
    "correct_answer": -36832,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "881 % 8",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "6345 - 6211",
    "correct_answer": 134,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "2 - 7 - 7 - 7 + 8 + 8 - 8 + 6 + 2 - 6 + 3 - 1 - 7 + 3 + 1 + 1 + 6 - 9 + 3 - 4 - 2 - 4",
    "correct_answer": -19,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "455 * 60",
    "correct_answer": 27300,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "415 - 614",
    "correct_answer": -199,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "7 + 8 + 10 - 20 - 28 + 24 + 3 + 28 - 23 - 15 + 10 + 13 - 27 + 18 - 28 + 20 + 15 + 9 - 22 - 19 - 16 + 20 - 21 - 25 + 13 - 23",
    "correct_answer": -69,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "5794 + 5740",
    "correct_answer": 11534,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "74 + 65 - 28",
    "correct_answer": 111,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "5668 + 1439",
    "correct_answer": 7107,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "21 - 43 + 53",
    "correct_answer": 31,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "936 * 58",
    "correct_answer": 54288,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "9 + 14 + 20 + 6 + 6 + 7 - 7 + 6 - 7 + 20 + 13 + 16 - 25 + 30 + 29 - 9 + 3 - 10 + 30 + 6 - 9",
    "correct_answer": 148,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "159 * 943",
    "correct_answer": 149937,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "564 + 964 - 495 - 440 * 765",
    "correct_answer": -335567,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "381 - 558",
    "correct_answer": -177,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "51 * 81",
    "correct_answer": 4131,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "711 * 68",
    "correct_answer": 48348,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "60 - 56",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "5 + 6 + 7 - 2 + 2 - 2 - 7 - 7 + 2 - 9 - 3 - 3 + 2 + 3 - 9 - 3 + 8 + 7 - 7 - 7 + 1 + 5 - 2 + 1 + 4 + 6 - 3 + 8 + 4 + 1 - 8 - 5 - 8 - 5 + 9 + 2 + 6 + 6",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "33 - 42 + 15",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "2260 + 6916",
    "correct_answer": 9176,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "39 * 21",
    "correct_answer": 819,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "37 + 30 - 96",
    "correct_answer": -29,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "82 + 77 - 3",
    "correct_answer": 156,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "62 + 351 * 115 * 877 - 452",
    "correct_answer": 35399715,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "5 + 6 - 2 - 1 - 4 - 7 + 8 - 5 + 9 + 5 - 8 + 5 + 9 - 4 + 1 - 6 - 8",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "354 - 483",
    "correct_answer": -129,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "1 + 3 - 2 + 7 - 9 + 8 - 8 + 4 + 3 + 8 - 6 - 2 - 7 - 9 + 9 - 4 + 2 - 3 + 4 - 1 + 4",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(66 + 59) * (50 - 37)",
    "correct_answer": 1625,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "690 * 83",
    "correct_answer": 57270,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "14 - 22 + 11 + 5 - 23 + 12 - 23 - 18 + 22 - 28 + 7 + 26 + 25 + 18 + 20 + 26 + 12 - 18 - 17 - 4 + 24 - 12 - 10 - 6",
    "correct_answer": 41,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "775 * 26",
    "correct_answer": 20150,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "826 % 5",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "(46 + 87) * (64 - 40)",
    "correct_answer": 3192,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "51 * 95",
    "correct_answer": 4845,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "750 % 11",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "556 * 870",
    "correct_answer": 483720,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "897 + 161 + 367 - 218 + 194",
    "correct_answer": 1401,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "80 + 57 * 46 - 61 * 32",
    "correct_answer": 750,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "28 - 73",
    "correct_answer": -45,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "569 - 148 - 433 + 471 - 193",
    "correct_answer": 266,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "368 - 539",
    "correct_answer": -171,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "745 - 548 - 801 * 857 + 516",
    "correct_answer": -685744,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "468 * 40",
    "correct_answer": 18720,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(59 + 64) * (65 - 78)",
    "correct_answer": -1599,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "789 * 75",
    "correct_answer": 59175,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(69 + 43) * (85 - 70)",
    "correct_answer": 1680,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "6038 - 2703",
    "correct_answer": 3335,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "726 * 466 - 374 + 350 * 740",
    "correct_answer": 596942,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "535 * 27",
    "correct_answer": 14445,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "30 * 87",
    "correct_answer": 2610,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "48 * 68",
    "correct_answer": 3264,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "9 - 7 - 2 - 9 - 8 + 9 + 5 - 5 + 6 + 6 - 6 - 2 - 8 + 7 - 6 - 2 - 8 - 8 - 4 - 3 - 4 - 7 - 3 + 5 + 2 + 7 - 3 - 4 + 8 + 2 - 9 - 8 - 3 + 7 - 3 + 3 - 9 + 7 - 7",
    "correct_answer": -55,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "70 + 68",
    "correct_answer": 138,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "5 + 9 + 4 - 6 - 9 - 4 + 2 + 6 - 6 + 8 + 5 - 4 + 6 - 3 + 5 + 2 + 9 - 2 + 6 - 8 - 1 - 6 + 8 + 8 - 8 + 4 + 7 - 1 + 5 - 5 + 7 - 2 - 5 - 4",
    "correct_answer": 32,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "27 + 20 * 31 - 56 * 73",
    "correct_answer": -3441,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "3849 - 6424",
    "correct_answer": -2575,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "237 * 356",
    "correct_answer": 84372,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "998 * 82",
    "correct_answer": 81836,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "362 % 9",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "95 - 43",
    "correct_answer": 52,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "31 + 73",
    "correct_answer": 104,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "(24 + 96) * (20 - 94)",
    "correct_answer": -8880,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "8408 - 5093",
    "correct_answer": 3315,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "(87 + 16) * (83 - 36)",
    "correct_answer": 4841,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "17 - 8 + 30 - 11 - 1 - 4 + 24 - 30 + 16 + 22 - 3 + 25 - 18 + 4 + 11 + 4 - 30 - 6 + 28 + 9 - 25 + 20 + 9",
    "correct_answer": 83,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "194 * 330 * 20 + 18 - 22",
    "correct_answer": 1280396,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "375 + 703 * 188 + 42 - 355",
    "correct_answer": 132226,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "96 + 71",
    "correct_answer": 167,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "97 - 60",
    "correct_answer": 37,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "37 - 30 + 78",
    "correct_answer": 85,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "4 - 27 + 3 - 22 + 1 + 12 - 1 + 9 - 5 - 14 - 8 - 27 - 25 + 11 - 30 - 22 - 2 - 7 - 16 - 22 + 3 + 14 - 6 - 23 - 7 - 11 - 20",
    "correct_answer": -238,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "868 - 627 + 349 + 60 + 436",
    "correct_answer": 1086,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "317 * 988 * 864 + 493 * 679",
    "correct_answer": 270936091,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "670 * 136 + 582 * 207 * 564",
    "correct_answer": 68038456,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "23 - 75",
    "correct_answer": -52,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "38 - 29",
    "correct_answer": 9,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "19 * 28",
    "correct_answer": 532,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "29 - 20 + 8 + 8 + 12 + 24 - 16 - 20 + 27 + 26 + 18 - 17 + 10 + 25 - 16 - 12 - 7 - 5 + 24 + 7 - 1 - 21",
    "correct_answer": 83,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(29 + 89) * (89 - 64)",
    "correct_answer": 2950,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "12 - 79 + 77",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "201 % 13",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "6 - 8 - 8 + 5 + 1 + 2 + 1 + 8 + 2 + 6 + 3 + 1 - 5 - 3 - 4 + 3 - 1 - 3 + 8 + 8 - 8 - 6 + 7 - 8 - 5 + 3 - 7 - 5 + 3 + 2 + 2 + 4 - 1 + 6 + 4 - 4 - 7 - 7",
    "correct_answer": -5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "29 - 16 - 26 + 27 - 24 - 9 - 27 + 14 + 17 - 10 + 10 + 9 - 16 + 29 + 21 + 9 - 24 - 6 - 7 + 22 + 3 + 5 + 23",
    "correct_answer": 53,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "5 - 4 + 7 + 9 + 1 - 2 - 7 - 1 + 3 + 9 + 9 + 4 - 7 - 7 + 9 - 7 - 8 + 6 - 6 - 1 - 1 + 7 - 7 - 9 + 7 + 9 - 8 + 8 - 1 + 9",
    "correct_answer": 26,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "197 + 793 + 623 - 566 - 903",
    "correct_answer": 144,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "7 - 3 - 4 + 7 - 7 - 7 - 8 + 1 + 8 + 2 + 9 - 5 + 1 + 3 - 5 + 2 - 7 + 3 - 4 + 1 + 2 + 8 - 2 - 3 + 2 + 5 - 2 - 9 - 4 + 7 - 1 + 7 - 9 - 7 - 8 + 4 - 9",
    "correct_answer": -25,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "21 + 4 - 1 + 6 - 20 + 16 + 28 - 11 + 1 - 19 - 18 - 9 - 14 - 23 + 24 - 27 - 9 + 6 - 11 - 2 + 29 - 29 - 30 - 14 - 26",
    "correct_answer": -128,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "300 * 28",
    "correct_answer": 8400,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "44 * 79",
    "correct_answer": 3476,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "22 - 53",
    "correct_answer": -31,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "26 * 47",
    "correct_answer": 1222,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "96 + 36 * 45 - 22 * 33",
    "correct_answer": 990,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "514 * 19",
    "correct_answer": 9766,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "500 + 931 * 152 + 574 + 325",
    "correct_answer": 142911,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1057 - 2537",
    "correct_answer": -1480,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "47 * 24",
    "correct_answer": 1128,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "58 + 3",
    "correct_answer": 61,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "2 + 12 - 7 + 13 - 28 - 26 + 24 + 12 - 2 + 12 - 14 - 24 - 29 - 21 - 7 + 18 + 18 + 24 - 16 - 9 - 10 + 15",
    "correct_answer": -43,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "249 * 398 - 732 - 495 * 158",
    "correct_answer": 20160,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "45 - 94",
    "correct_answer": -49,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "15 * 30",
    "correct_answer": 450,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "975 * 94",
    "correct_answer": 91650,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "3 - 7 + 1 + 9 + 3 - 7 + 3 + 4 + 3 + 3 - 2 - 8 + 8 - 2 + 2 - 1 - 3 + 9",
    "correct_answer": 18,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(57 + 16) * (64 - 95)",
    "correct_answer": -2263,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "580 * 78",
    "correct_answer": 45240,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "764 * 495",
    "correct_answer": 378180,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "36 * 33",
    "correct_answer": 1188,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(24 + 80) * (29 - 22)",
    "correct_answer": 728,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "90 + 59",
    "correct_answer": 149,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "221 + 678 * 604 + 710 + 893",
    "correct_answer": 411336,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "687 % 7",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "2975 - 7919",
    "correct_answer": -4944,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "637 * 257 + 593 * 111 + 791",
    "correct_answer": 230323,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2297 - 3874",
    "correct_answer": -1577,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "68 * 95",
    "correct_answer": 6460,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "10 + 74",
    "correct_answer": 84,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "86 + 94 * 76 - 14 * 36",
    "correct_answer": 6726,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "97 + 79 * 32 - 63 * 38",
    "correct_answer": 231,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "6 + 18 + 15 + 20 - 7 + 20 + 1 - 26 - 21 + 14 + 5 - 26 - 10 - 9 - 27 - 13 - 15 + 13 + 11 - 18 - 30 + 2 - 21 + 8 - 12",
    "correct_answer": -102,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "47 * 98",
    "correct_answer": 4606,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "98 + 79 * 44 - 56 * 74",
    "correct_answer": -570,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "16 - 53 + 46",
    "correct_answer": 9,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "150 * 661",
    "correct_answer": 99150,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "11 + 25 - 3 + 19 - 8 - 18 + 29 + 25 + 28 - 22 - 2 + 21 + 3 - 12 + 26 + 20 + 3 + 12 + 6 - 6 + 10 + 2 + 22 + 23 - 19",
    "correct_answer": 195,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "3 - 4 + 9 + 6 - 1 + 6 - 5 - 6 - 2 + 7 - 9 - 5 - 2 + 7 - 4 + 5 + 5 + 2 - 8 + 2 - 8 - 8 - 4 - 2 - 6 + 1 + 4 + 5 + 7 + 8 + 7 + 2 - 1 - 1",
    "correct_answer": 10,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "40 * 28",
    "correct_answer": 1120,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "71 + 5 - 59",
    "correct_answer": 17,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "86 + 46 - 10",
    "correct_answer": 122,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "24 + 22 - 23",
    "correct_answer": 23,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "(29 + 76) * (52 - 51)",
    "correct_answer": 105,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "19 * 50",
    "correct_answer": 950,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "48 + 28 - 57",
    "correct_answer": 19,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "30 - 5",
    "correct_answer": 25,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "222 * 505",
    "correct_answer": 112110,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "779 * 55",
    "correct_answer": 42845,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "7 + 3 - 9 + 6 + 7 - 5 - 1 - 1 - 4 + 9 + 2 - 3 + 2 - 8 + 6 - 9 + 8 - 3 - 7 + 4 + 2 + 8 + 8 + 8 - 3 - 3 - 6 + 7 - 6 + 8 - 4 + 7 + 3 + 2 + 2",
    "correct_answer": 37,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "24 * 17",
    "correct_answer": 408,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "61 - 45",
    "correct_answer": 16,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "427 - 307 + 203 - 926 * 971",
    "correct_answer": -898823,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "6 + 26 + 16 + 11 + 27 - 28 + 29 + 13 + 2 - 14 + 7 + 9 - 4 + 23 - 3 + 13 - 9 - 6 - 7 - 6 + 6 - 7 + 15 - 10",
    "correct_answer": 109,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "37 - 91",
    "correct_answer": -54,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "923 * 99",
    "correct_answer": 91377,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "359 + 999 + 226 * 90 - 628",
    "correct_answer": 21070,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "27 + 53 * 70 - 57 * 21",
    "correct_answer": 2540,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "(54 + 38) * (54 - 92)",
    "correct_answer": -3496,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "22 - 3 + 9 - 15 + 28 - 28 + 27 + 3 - 24 + 25 - 28 + 24 - 20 + 12 + 16 - 25 - 19 - 15 + 16 - 11 + 10 + 16 - 6",
    "correct_answer": 14,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "469 - 549",
    "correct_answer": -80,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "3655 - 4808",
    "correct_answer": -1153,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "15 + 45 - 56",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "29 + 18",
    "correct_answer": 47,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "322 - 351 * 412 + 170 * 365",
    "correct_answer": -82240,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "11 + 68 * 94 - 58 * 65",
    "correct_answer": 2633,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "1 + 7 + 8 + 4 - 3 - 5 + 6 + 7 + 3 + 2 + 8 - 9 - 3 - 9 - 5 + 1 - 5 - 1 - 8 + 6 - 8 - 9",
    "correct_answer": -12,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "12 - 11 - 10 + 7 + 18 - 1 + 22 - 26 + 13 - 28 - 11 - 7 + 4 - 19 + 1 - 24 - 30 + 27 + 14 - 22 + 7 - 15 + 13",
    "correct_answer": -66,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "2939 - 4026",
    "correct_answer": -1087,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "5 + 11 + 22 + 9 + 8 - 21 - 11 - 28 - 3 + 29 + 2 - 29 - 17 - 7 - 2 - 9 + 1 + 24 + 6 - 28 + 1 - 9 - 1 + 30",
    "correct_answer": -17,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "99 + 38",
    "correct_answer": 137,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "8 + 1 + 7 - 1 - 5 + 7 + 7 + 1 - 8 + 2 + 1 - 6 + 2 - 2 - 4 - 3 + 5 - 8 + 8 - 3 + 1 + 7",
    "correct_answer": 17,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "137 % 12",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "15 + 347 * 681 - 983 * 342",
    "correct_answer": -99864,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "176 + 605 - 159 * 482 - 148",
    "correct_answer": -76005,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "29 * 29",
    "correct_answer": 841,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "61 * 35",
    "correct_answer": 2135,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "4 + 2 + 7 + 7 + 9 - 1 + 7 - 2 + 1 + 2 - 1 - 1 - 2 - 6 + 2 - 8 - 8 + 5 + 3 - 9 + 9 + 1 + 5 + 7 + 4 + 7 - 6 - 4 - 7 + 2 + 2 + 5 + 6 - 2 + 3",
    "correct_answer": 43,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "802 * 733",
    "correct_answer": 587866,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "(81 + 62) * (56 - 16)",
    "correct_answer": 5720,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "31 * 23",
    "correct_answer": 713,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "12 + 19 + 10 + 7 - 4 - 22 - 19 + 9 + 4 - 3 + 13 + 3 + 30 + 11 - 1 + 6 - 26 + 2 - 3 - 24 - 5 + 13 + 8 + 13 + 10 + 29 + 7",
    "correct_answer": 99,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "47 + 29 * 19 - 40 * 86",
    "correct_answer": -2842,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "4 - 8 - 8 - 9 + 4 + 6 + 3 + 9 - 7 - 6 + 1 + 1 - 7 + 9 + 1 + 8 + 5 + 8 - 5 + 9 - 3 - 6 - 2 + 1 + 6 - 3 + 7 + 2 + 7",
    "correct_answer": 27,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "1 + 4 + 2 - 8 + 2 + 2 + 9 + 2 + 8 - 2 + 2 - 3 - 2 - 5 - 1 - 5 + 1",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "334 + 598 - 461 + 388 * 220",
    "correct_answer": 85831,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "896 * 747",
    "correct_answer": 669312,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "4 - 8 - 8 + 5 + 7 - 9 + 2 - 7 + 5 + 8 - 7 + 6 + 1 + 5 - 5 + 7 + 4 - 3 - 2 + 3 + 6 - 8 + 8 - 7 - 4 - 5 - 5 + 7 + 8 - 9 + 4 - 3 + 1 - 4 - 1 - 4 + 9 + 7 + 4",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "2 - 5 - 24 + 4 - 1 - 29 - 18 - 2 + 19 - 11 + 3 + 6 + 23 - 28 + 15 + 26 - 8 + 26 + 19 + 25 - 1 - 9 - 24 - 3 - 11 + 27",
    "correct_answer": 21,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "153 % 18",
    "correct_answer": 9,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "611 % 19",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "17 - 1 + 3 - 16 - 13 - 29 - 20 - 27 + 16 + 26 + 15 + 25 + 10 - 12 + 14 + 26 + 7 + 12 - 13 + 23 - 29 - 11 - 24 + 16 + 11 + 16 + 24",
    "correct_answer": 66,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "422 * 122",
    "correct_answer": 51484,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "279 * 62",
    "correct_answer": 17298,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "91 * 91",
    "correct_answer": 8281,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "46 * 91",
    "correct_answer": 4186,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "406 - 613",
    "correct_answer": -207,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "6315 + 7311",
    "correct_answer": 13626,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "3 + 1 - 2 - 5 - 4 + 5 - 1 - 3 - 6 + 4 - 1 + 4 + 1 - 6 + 6 + 1 - 4 + 5 + 1 - 7 - 9 - 5 - 4 + 4 + 3 + 4 - 3 + 3 + 9 - 9",
    "correct_answer": -15,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "34 * 41",
    "correct_answer": 1394,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "1 - 17 + 11 - 11 - 6 + 26 - 13 + 19 + 7 - 11 + 24 + 16 - 21 - 23 + 30 + 16 - 24 + 15 + 7 - 9 - 29 - 14 + 4 + 12 - 30 - 20",
    "correct_answer": -40,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "92 * 70",
    "correct_answer": 6440,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "5592 + 7437",
    "correct_answer": 13029,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "495 % 5",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "(90 + 21) * (50 - 95)",
    "correct_answer": -4995,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "826 % 10",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "637 + 951 * 716 + 935 * 484",
    "correct_answer": 1134093,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "341 * 718 * 938 + 825 * 745",
    "correct_answer": 230272669,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "239 - 298",
    "correct_answer": -59,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "(10 + 67) * (44 - 17)",
    "correct_answer": 2079,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "70 * 57",
    "correct_answer": 3990,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "6370 + 3430",
    "correct_answer": 9800,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "702 + 145 + 751 - 480 * 740",
    "correct_answer": -353602,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(54 + 47) * (67 - 98)",
    "correct_answer": -3131,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "12 - 11 + 3 - 25 - 6 + 9 + 11 - 30 + 20 - 17 + 7 + 16 + 5 - 4 + 9 + 5 - 2 - 1 + 13 - 27 + 9 - 7 - 22",
    "correct_answer": -33,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "9 + 4 + 8 - 7 - 5 + 3 + 8 - 2 - 1 - 3 - 5 + 2 + 3 - 7 - 4 + 6 + 6 - 2 + 1 - 6 + 1 - 5 - 5 + 3 + 3 + 1 + 7 + 8 + 4 - 3 + 9 - 4 - 3 + 5 + 8 - 4 - 7",
    "correct_answer": 26,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "41 * 66",
    "correct_answer": 2706,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "696 * 54",
    "correct_answer": 37584,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "35 * 21",
    "correct_answer": 735,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "3147 - 3856",
    "correct_answer": -709,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "4588 + 1480",
    "correct_answer": 6068,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "16 - 23 + 29 - 27 - 18 - 16 - 15 + 8 + 22 - 11 + 5 + 20 + 28 - 2 - 8 - 21 + 10 + 17 - 27 + 29 + 2 + 6 - 1 - 25 - 29 + 15 - 7",
    "correct_answer": -23,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "59 + 12 - 85",
    "correct_answer": -14,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "682 + 489 - 914 * 750 - 409",
    "correct_answer": -684738,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "413 % 17",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "2 + 59",
    "correct_answer": 61,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "1 + 5 + 1 - 3 + 9 + 2 + 3 - 3 + 7 + 2 - 5 + 6 + 7 + 6 + 5 - 1 - 5 - 3 - 7 + 5 + 1 + 2 + 1 - 4 + 5 + 3 - 6 + 7 - 7 - 3 - 2 - 3",
    "correct_answer": 26,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "34 + 15",
    "correct_answer": 49,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "2 - 5 + 9 - 6 - 1 + 4 - 7 + 7 + 3 - 4 - 5 + 2 - 3 - 9 - 2 + 2 - 5 + 6 + 1 + 2 + 8 + 3 - 4 - 9 - 5 + 5 + 3 - 8 + 8 - 9 + 9 + 3 - 9 + 8 - 9 + 5 + 9 - 2",
    "correct_answer": -3,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(87 + 93) * (97 - 34)",
    "correct_answer": 11340,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "448 - 520",
    "correct_answer": -72,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "10 + 76",
    "correct_answer": 86,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "332 + 421 + 454 + 412 * 686",
    "correct_answer": 283839,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "8248 - 4559",
    "correct_answer": 3689,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "483 - 213 + 728 - 60 - 642",
    "correct_answer": 296,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "23 * 41",
    "correct_answer": 943,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "25 * 42",
    "correct_answer": 1050,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "4 - 2 - 3 - 2 - 3 + 8 - 3 - 6 + 3 - 1 - 6 - 2 + 2 - 5 + 3 - 4 + 6 + 2 + 8 - 7 - 6 + 4 - 9 + 1 + 3 - 4 + 5 + 7 - 5 - 8 - 6 - 3 - 1",
    "correct_answer": -30,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "604 * 88",
    "correct_answer": 53152,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "1981 + 3332",
    "correct_answer": 5313,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "16 + 25 + 22 - 19 + 17 + 10 + 28 - 25 + 13 - 27 - 20 + 25 + 2 + 3 + 29 + 15 - 17 - 9 + 15 - 21 - 24 + 10 - 28",
    "correct_answer": 40,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "7 - 2 + 2 + 8 - 6 - 9 - 2 - 4 + 4 + 9 - 6 - 9 + 1 - 2 - 7 + 6 - 1 + 5 - 1 + 9 - 9 + 5 + 5 - 4 + 4 + 6 - 7 - 6 - 1 - 5 + 8 - 1",
    "correct_answer": -3,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "92 - 645 + 763 * 537 + 382",
    "correct_answer": 409560,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "8 - 6 - 9 - 9 - 2 + 9 + 8 - 1 + 3 + 3 + 5 - 7 + 4 - 8 - 1 + 4 + 3 - 4 + 6 - 1",
    "correct_answer": 5,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "73 * 68",
    "correct_answer": 4964,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "24 - 4 + 27 + 20 - 8 + 10 - 16 + 11 - 1 - 19 + 18 - 26 + 1 + 29 + 14 + 4 + 11 - 24 - 1 + 10 - 20 + 12 - 21 - 29 + 7",
    "correct_answer": 29,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "738 * 818",
    "correct_answer": 603684,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "257 % 8",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "4902 + 7878",
    "correct_answer": 12780,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "330 + 55 - 521 - 775 - 958",
    "correct_answer": -1869,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "412 * 273",
    "correct_answer": 112476,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "3 - 9 + 4 - 4 + 7 + 3 + 6 - 3 - 7 - 9 + 6 + 5 + 6 + 7 + 1 + 2 + 9 - 8 - 4 - 9 + 2 - 6 + 9 - 7 - 9 + 8 + 4 + 4 + 7 - 3 - 1 - 5 - 7 - 9 - 1",
    "correct_answer": -8,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "8 + 2 + 4 - 5 - 6 - 3 + 6 - 7 + 5 + 9 - 4 - 7 + 9 - 2 + 2 + 4 + 7 + 9 + 9 - 2 - 6 - 1 - 7 - 3 + 9 + 1 - 6 + 3 - 5 + 4 + 2 + 7 + 1 + 4 + 5",
    "correct_answer": 46,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "42 + 65 * 64 - 67 * 59",
    "correct_answer": 249,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "35 + 34 * 46 - 82 * 96",
    "correct_answer": -6273,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "340 * 40",
    "correct_answer": 13600,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "30 * 21",
    "correct_answer": 630,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "89 + 79 * 85 - 65 * 86",
    "correct_answer": 1214,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "522 * 34",
    "correct_answer": 17748,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "11 + 7 + 27 + 15 - 9 - 26 + 17 + 22 - 20 + 14 + 4 - 9 + 25 - 13 - 22 - 3 - 5 - 25 + 8 + 26 - 5 - 29 + 2 + 1 + 9",
    "correct_answer": 22,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "228 % 12",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "26 - 7 - 19 - 15 + 14 - 29 + 7 + 19 - 14 - 29 - 1 + 11 - 13 - 8 + 9 + 2 - 1 - 5 - 25 + 9 - 12 + 27 + 4 + 4 - 17 + 20",
    "correct_answer": -43,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "15 + 24 + 24 - 16 + 22 + 15 + 17 + 5 - 30 + 29 + 6 + 20 + 13 - 16 - 4 - 14 + 23 - 25 - 2 - 24 - 11 + 4",
    "correct_answer": 75,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "453 % 10",
    "correct_answer": 3,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "294 - 514",
    "correct_answer": -220,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "8 - 4 + 9 - 8 - 5 - 4 + 7 + 8 + 7 + 8 - 8 - 6 - 5 + 9 + 7 - 5 - 5 + 2 + 4 - 8 - 6 + 3 + 6 + 8 - 1 - 5 - 9 - 6 + 5 + 1 + 6 - 1 + 8 + 6",
    "correct_answer": 26,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "711 * 39",
    "correct_answer": 27729,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "90 + 94 * 98 - 97 * 21",
    "correct_answer": 7265,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "(22 + 57) * (84 - 92)",
    "correct_answer": -632,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "690 * 490",
    "correct_answer": 338100,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "275 % 13",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "10 - 26 - 9 + 9 + 15 + 15 - 12 - 9 + 24 - 16 + 3 - 20 - 9 + 27 - 18 + 9 - 15 + 3 + 20 - 30 + 13 - 8 + 18 + 18 - 8 + 14",
    "correct_answer": 18,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "315 - 512 - 763 * 935 + 627",
    "correct_answer": -712975,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "4824 - 6857",
    "correct_answer": -2033,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "13 * 403 - 847 * 134 - 558",
    "correct_answer": -108817,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "7 + 2 + 2 + 6 - 1 + 6 + 4 + 5 + 8 - 2 - 2 + 7 + 9 + 6 - 7 + 7 + 5 + 5 - 9 - 3 + 2",
    "correct_answer": 57,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(10 + 66) * (84 - 58)",
    "correct_answer": 1976,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "267 * 92",
    "correct_answer": 24564,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "667 % 14",
    "correct_answer": 9,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "8412 + 6225",
    "correct_answer": 14637,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "4607 - 6655",
    "correct_answer": -2048,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "91 * 72",
    "correct_answer": 6552,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "95 + 82 - 4",
    "correct_answer": 173,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "504 * 44",
    "correct_answer": 22176,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "777 - 530 * 586 + 609 + 607",
    "correct_answer": -308587,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(88 + 16) * (27 - 54)",
    "correct_answer": -2808,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "1 + 13 + 23 - 2 - 21 - 6 - 17 - 14 + 2 + 14 - 25 + 18 - 4 - 2 - 8 + 7 - 17 - 3 + 25 + 19 + 7 + 20 + 1 - 11 - 6 + 26",
    "correct_answer": 40,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "9 + 2 + 4 + 8 + 8 - 4 - 5 - 3 + 6 + 2 + 9 - 3 + 6 - 3 + 4 - 1 - 7 - 2",
    "correct_answer": 30,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "4977 - 9537",
    "correct_answer": -4560,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "83 + 19 - 31",
    "correct_answer": 71,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "6 + 4 + 9 - 9 + 2 + 8 - 5 + 8 + 8 - 7 - 7 - 2 + 4 + 7 - 5 + 7 + 6 - 1 + 2 + 9 - 4 - 9 + 6 - 2 - 7 - 5 - 3 + 7 - 9 - 5 - 8 + 8",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "410 * 11",
    "correct_answer": 4510,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "860 * 78",
    "correct_answer": 67080,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "67 * 50",
    "correct_answer": 3350,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "264 * 59",
    "correct_answer": 15576,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(52 + 62) * (74 - 68)",
    "correct_answer": 684,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "97 * 76",
    "correct_answer": 7372,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "8 + 1 - 9 + 1 - 7 + 4 + 2 + 5 + 4 + 1 + 4 + 9 - 6 - 6 - 1 + 3 + 2 + 3 + 7 + 2 + 5 + 3",
    "correct_answer": 35,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "2425 + 8193",
    "correct_answer": 10618,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "12 + 28 + 19 + 15 + 27 + 15 + 20 - 27 + 28 - 22 - 7 + 18 + 10 - 23 - 7 - 21 - 20 + 12 + 2 + 25 - 8",
    "correct_answer": 96,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "469 * 671",
    "correct_answer": 314699,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "797 + 525 * 126 - 687 + 193",
    "correct_answer": 66453,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "32 * 40",
    "correct_answer": 1280,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "18 - 24 - 28 + 20 - 24 + 7 + 5 + 3 + 26 - 6 + 10 + 4 - 11 - 9 + 18 - 25 - 21 - 2 - 2 + 28 + 15 - 20 + 21 - 21",
    "correct_answer": -18,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(11 + 31) * (38 - 55)",
    "correct_answer": -714,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "30 - 21 + 10 - 25 - 7 + 10 + 17 + 26 + 1 + 5 + 9 - 1 - 10 - 2 - 6 + 11 + 23 + 27 - 24 - 17 + 14 - 20",
    "correct_answer": 50,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "52 * 31",
    "correct_answer": 1612,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "525 - 706 + 293 - 74 - 363",
    "correct_answer": -325,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "18 + 15 + 14 - 28 - 10 - 14 - 14 - 23 + 25 + 23 + 19 + 20 - 29 - 6 - 27 - 5 + 19 - 4 - 14 + 28 - 17 - 14 + 11 - 1 - 28 + 24 - 26",
    "correct_answer": -44,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "8307 + 3435",
    "correct_answer": 11742,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "854 * 18",
    "correct_answer": 15372,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "48 + 37 - 50",
    "correct_answer": 35,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "753 * 618",
    "correct_answer": 465354,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "3 - 2 - 3 - 6 - 9 - 2 + 9 - 7 + 9 + 7 + 1 - 2 - 5 + 1 - 5 + 1 + 7 - 9 + 8 + 9 + 6 - 7 - 5 - 7 - 2 + 3 + 3 - 3 - 7 + 3 + 3",
    "correct_answer": -8,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "22 + 44 * 40 - 31 * 45",
    "correct_answer": 387,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "7370 + 1072",
    "correct_answer": 8442,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "54 - 86",
    "correct_answer": -32,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "871 * 264 - 447 + 592 + 574",
    "correct_answer": 230663,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(63 + 47) * (75 - 55)",
    "correct_answer": 2200,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "78 + 77",
    "correct_answer": 155,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "643 + 956 * 738 + 302 * 189",
    "correct_answer": 763249,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "111 + 956 * 952 * 881 - 496",
    "correct_answer": 801808287,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "22 - 12 - 23 - 30 + 27 - 29 - 20 - 12 - 26 - 24 + 18 + 27 + 20 - 20 + 7 - 1 - 3 - 25 - 18 + 17 + 26 - 22 + 16",
    "correct_answer": -85,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "99 * 63",
    "correct_answer": 6237,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "19 + 16 * 28 - 48 * 24",
    "correct_answer": -685,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "433 * 56",
    "correct_answer": 24248,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "28 - 17 + 15 + 29 - 9 + 21 + 21 - 29 + 3 - 12 - 30 + 12 + 1 - 19 - 3 + 24 - 26 - 3 - 15 + 21 + 21 - 6 + 20",
    "correct_answer": 47,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "20 + 782 + 811 * 952 * 220",
    "correct_answer": 169856642,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "3 - 3 - 7 - 6 - 6 - 5 - 2 - 1 + 3 - 6 - 6 + 1 - 7 + 1 + 2 - 3 - 6 + 5 + 6 + 5 + 8",
    "correct_answer": -24,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "19 - 18 + 26 - 12 - 6 + 6 - 7 - 23 + 29 - 6 + 1 - 19 - 22 - 7 - 25 - 10 + 9 - 22 + 8 - 11 - 26 + 5 + 20 - 18 - 22",
    "correct_answer": -131,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "36 + 59 * 53 - 38 * 55",
    "correct_answer": 1073,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "375 * 736 - 506 + 514 * 876",
    "correct_answer": 725758,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "7 - 12",
    "correct_answer": -5,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "69 * 49",
    "correct_answer": 3381,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "433 * 254 * 259 - 172 + 403",
    "correct_answer": 28485569,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "962 % 4",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "386 * 67",
    "correct_answer": 25862,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "26 + 1 - 19 - 25 - 28 - 17 - 13 + 21 + 2 + 17 + 25 + 5 + 6 - 4 + 12 + 20 + 13 + 27 - 28 - 25 - 2 + 11 + 30 - 13 - 16 + 26 - 9",
    "correct_answer": 43,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "4 - 8 + 3 - 6 - 1 + 4 - 8 - 9 + 3 - 9 + 9 - 2 - 5 + 8 + 4 - 1 + 8 - 5 - 5 + 6 - 5 + 5 + 1 - 3 + 3 + 6 + 4 - 8 - 2 - 1",
    "correct_answer": -10,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "451 * 39",
    "correct_answer": 17589,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "19 - 11 - 6 - 27 + 24 + 20 + 24 + 13 - 5 - 1 + 6 - 26 + 20 - 21 + 30 + 22 + 19 + 20 + 9 + 20 - 8 + 24 + 15 - 9 + 11 - 6 - 12",
    "correct_answer": 164,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "635 * 74",
    "correct_answer": 46990,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "618 * 23",
    "correct_answer": 14214,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "47 * 32",
    "correct_answer": 1504,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(86 + 40) * (79 - 50)",
    "correct_answer": 3654,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "110 + 547 - 711 + 369 - 752",
    "correct_answer": -437,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "9 - 4 + 7 + 8 - 5 + 1 + 5 + 9 - 2 - 2 - 3 - 4 - 9 - 2 - 7 + 3 - 3 - 4 - 4 - 9",
    "correct_answer": -16,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "65 - 63",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "3146 - 3384",
    "correct_answer": -238,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "568 * 25",
    "correct_answer": 14200,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "614 * 114 + 957 - 76 - 213",
    "correct_answer": 70664,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "6883 - 8859",
    "correct_answer": -1976,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "(49 + 48) * (49 - 80)",
    "correct_answer": -3007,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "11 + 29 - 27 + 5 - 5 - 8 + 23 + 4 - 19 - 26 - 26 - 11 + 6 + 16 + 29 + 12 - 1 - 23 - 28 - 25 + 24 - 29 + 26 - 20",
    "correct_answer": -63,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "(69 + 80) * (66 - 32)",
    "correct_answer": 5066,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "37 - 66",
    "correct_answer": -29,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "36 + 58",
    "correct_answer": 94,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "191 * 580 - 891 * 915 - 178",
    "correct_answer": -704663,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1876 - 2803",
    "correct_answer": -927,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "31 + 37 * 66 - 23 * 12",
    "correct_answer": 2197,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "757 * 956",
    "correct_answer": 723692,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "88 + 55",
    "correct_answer": 143,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "734 * 403 * 820 + 636 * 397",
    "correct_answer": 242810132,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "655 * 813",
    "correct_answer": 532515,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "9 - 4 - 8 + 5 + 2 + 5 - 7 - 9 + 7 + 1 - 8 + 7 - 7 - 3 - 1 + 3 - 6 + 6",
    "correct_answer": -8,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "480 * 522",
    "correct_answer": 250560,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "4525 - 6039",
    "correct_answer": -1514,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "126 % 14",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "(34 + 98) * (89 - 13)",
    "correct_answer": 10032,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "407 * 194",
    "correct_answer": 78958,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "48 * 72",
    "correct_answer": 3456,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "9808 - 3501",
    "correct_answer": 6307,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "934 * 27",
    "correct_answer": 25218,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "9 + 4 + 21 + 5 - 26 + 16 - 2 - 14 - 24 + 1 + 10 - 7 - 29 - 15 + 10 - 22 + 19 - 12 - 3 + 11 + 5 - 23",
    "correct_answer": -66,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "28 + 19 - 4 + 19 - 1 + 23 + 7 + 22 - 10 - 17 - 30 - 14 - 30 - 3 - 27 - 4 - 21 + 13 - 10 + 14 + 19 + 29 - 13 - 12 - 21",
    "correct_answer": -24,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "2 + 7 + 1 - 3 + 2 + 2 + 9 - 5 + 2 - 5 + 8 - 1 - 5 - 4 + 8 - 3 - 3 - 5 - 4 - 1 - 7 - 6 - 1 - 7 + 3 + 4 + 8 - 7 + 7 + 2 - 6 + 4 + 1 + 3 + 4 + 9 - 4 - 7",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "26 + 26 - 19 - 22 - 11 - 6 + 22 - 18 + 1 - 25 + 15 - 28 + 15 - 22 - 17 - 1 - 2 + 22 + 29 + 12 + 21 + 26 + 7 - 21 + 15 - 1 + 12",
    "correct_answer": 56,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "864 * 97",
    "correct_answer": 83808,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "768 * 47",
    "correct_answer": 36096,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "391 * 81",
    "correct_answer": 31671,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "491 * 155",
    "correct_answer": 76105,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "13 + 27 + 29 + 10 - 18 + 30 + 24 - 5 + 13 - 13 + 27 + 21 + 25 + 1 + 11 - 30 + 6 - 18 + 15 - 27 - 16 - 1 + 25",
    "correct_answer": 149,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "15 - 84 + 84",
    "correct_answer": 15,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "456 - 523",
    "correct_answer": -67,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "77 - 42",
    "correct_answer": 35,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "955 % 9",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "949 * 56 * 120 - 445 - 106",
    "correct_answer": 6376729,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "28 - 6 + 5 + 25 - 12 - 24 + 28 + 15 + 26 + 21 - 22 + 25 - 20 + 1 + 8 + 12 - 27 - 14 - 4 - 18 + 8",
    "correct_answer": 55,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "884 * 170 - 67 - 279 - 615",
    "correct_answer": 149319,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2958 - 3685",
    "correct_answer": -727,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "9 - 1 + 6 - 6 - 1 - 6 - 1 - 1 + 3 + 2 + 2 + 4 - 6 + 6 - 6 + 8 + 1 - 7 - 9 + 4 - 2 + 5 - 1 + 9 + 4 + 1 - 4 + 3 + 6 + 7 + 5 - 7 + 1 + 1 + 8",
    "correct_answer": 37,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "60 - 37 + 87",
    "correct_answer": 110,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "518 * 56",
    "correct_answer": 29008,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "92 - 40",
    "correct_answer": 52,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "428 % 6",
    "correct_answer": 2,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "1 + 98",
    "correct_answer": 99,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "844 % 16",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "495 - 710",
    "correct_answer": -215,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "4 - 3 - 1 - 8 + 6 - 7 - 7 - 7 - 3 + 3 + 6 - 7 + 8 + 5 + 4 + 2 + 2",
    "correct_answer": -3,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "17 - 10 - 26 + 28 - 8 + 25 - 15 + 20 - 17 - 1 + 23 - 22 - 2 - 22 - 25 - 14 + 3 - 2 + 20 - 22 + 4 - 20 - 25 - 7 - 5 + 8 + 8",
    "correct_answer": -87,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "77 + 91 - 11",
    "correct_answer": 157,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "42 + 29 * 30 - 42 * 24",
    "correct_answer": -96,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "282 * 994",
    "correct_answer": 280308,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "587 * 90",
    "correct_answer": 52830,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "731 * 372",
    "correct_answer": 271932,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "5777 + 5979",
    "correct_answer": 11756,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "46 * 45",
    "correct_answer": 2070,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "203 + 438 + 428 - 39 + 278",
    "correct_answer": 1308,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "108 * 98",
    "correct_answer": 10584,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "306 + 678 + 10 - 965 * 289",
    "correct_answer": -277891,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "95 + 6 - 56",
    "correct_answer": 45,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "311 - 332",
    "correct_answer": -21,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "2016 - 2770",
    "correct_answer": -754,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "99 * 67",
    "correct_answer": 6633,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "7779 + 7353",
    "correct_answer": 15132,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "335 - 433",
    "correct_answer": -98,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "932 * 83",
    "correct_answer": 77356,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "877 % 18",
    "correct_answer": 13,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "3 + 2 + 1 + 3 - 6 + 4 + 2 + 2 - 6 + 1 + 4 + 3 - 3 + 2 - 2 - 5 - 4 - 5 + 2 - 1 - 9 + 8 - 5 - 4 - 8 - 8 + 9 + 5 + 3 + 2 + 9 + 2 + 9 - 2 - 1 + 7",
    "correct_answer": 14,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "691 * 556 - 249 - 316 * 692",
    "correct_answer": 165275,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "6816 - 3725",
    "correct_answer": 3091,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "711 % 3",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "1802 + 5896",
    "correct_answer": 7698,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "886 % 7",
    "correct_answer": 4,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "(83 + 87) * (72 - 51)",
    "correct_answer": 3570,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "29 - 58",
    "correct_answer": -29,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "48 * 40",
    "correct_answer": 1920,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "29 + 13 + 22 - 22 - 7 - 12 - 18 + 26 + 1 + 29 - 9 + 3 + 27 - 13 - 8 - 16 - 25 - 3 + 10 - 24 - 4",
    "correct_answer": -1,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "354 * 518 * 840 + 357 - 639",
    "correct_answer": 154032198,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "95 * 39",
    "correct_answer": 3705,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "46 + 27 * 92 - 10 * 62",
    "correct_answer": 1910,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "740 * 40",
    "correct_answer": 29600,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "7 - 3 - 8 - 7 + 6 - 6 - 7 + 3 - 3 + 7 + 6 + 3 - 8 - 4 + 7 - 1 - 6 + 6 + 2 + 9 + 3 + 9 - 7 + 4 + 1 + 9 + 8 + 6 + 2 - 7 - 4 + 4 - 5",
    "correct_answer": 26,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "29 * 49",
    "correct_answer": 1421,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "54 - 53",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "652 * 678",
    "correct_answer": 442056,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "535 - 359 + 702 * 673 + 740",
    "correct_answer": 473362,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "2871 + 5389",
    "correct_answer": 8260,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "14 - 15 - 28 - 2 + 27 - 27 + 29 + 29 - 25 + 1 - 19 + 18 - 18 - 10 + 22 + 1 + 17 + 14 + 6 - 21 + 23 - 6 - 25 + 8 + 29 + 16",
    "correct_answer": 58,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "20 - 22 - 24 + 9 - 23 + 9 + 3 + 17 + 4 - 11 - 16 - 20 + 25 - 22 + 28 - 7 + 12 + 6 - 16 + 1 - 20 + 8",
    "correct_answer": -39,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "46 * 43",
    "correct_answer": 1978,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "(92 + 86) * (53 - 28)",
    "correct_answer": 4450,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "747 % 19",
    "correct_answer": 6,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "22 - 13 - 6 - 6 + 15 + 11 - 21 + 12 + 12 + 28 - 2 + 11 - 9 + 21 + 26 - 28 + 16 + 30 - 2 + 15 - 9 + 24 + 3",
    "correct_answer": 150,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "900 * 294 - 522 * 184 * 208",
    "correct_answer": -19713384,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "58 + 82 * 35 - 44 * 85",
    "correct_answer": -812,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "28 + 27 - 20 + 17 + 1 - 18 - 27 - 21 + 13 - 27 - 25 - 11 - 6 - 22 - 21 + 1 + 30 + 15 - 18 - 12 - 27 + 2 + 22 - 2 + 11 - 2",
    "correct_answer": -92,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "76 + 75 - 85",
    "correct_answer": 66,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "1 + 6 - 9 + 8 - 2 - 7 + 4 - 8 + 1 + 4 - 6 + 7 - 6 - 1 + 6 - 2 - 4 - 9 + 5 + 1 - 8",
    "correct_answer": -19,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "14 + 25 * 19 - 79 * 18",
    "correct_answer": -933,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "729 % 16",
    "correct_answer": 9,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "3 + 7 + 9 + 7 - 4 - 8 - 8 + 4 + 5 + 4 - 2 + 2 + 7 - 2 + 7 - 9 - 7 - 4 - 1 - 2 - 8 + 7",
    "correct_answer": 7,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "(22 + 31) * (79 - 43)",
    "correct_answer": 1908,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "7291 - 6759",
    "correct_answer": 532,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "5 + 3 + 5 - 5 - 7 - 5 - 9 + 7 + 1 + 7 - 1 + 5 + 6 + 8 - 1 - 5 + 4 - 9 + 1 - 4 + 6 - 7 - 3 - 3 - 6 + 1 - 6 + 6 + 1 + 7 + 3 + 3 + 8 - 8 + 8 - 3 + 2 + 2 - 5",
    "correct_answer": 12,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "176 % 15",
    "correct_answer": 11,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "35 + 21",
    "correct_answer": 56,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "91 + 97 * 50 - 45 * 33",
    "correct_answer": 3456,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "59 * 37",
    "correct_answer": 2183,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "38 * 59",
    "correct_answer": 2242,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "224 * 781 + 789 - 338 - 929",
    "correct_answer": 174466,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "21 - 28 - 25 - 18 - 21 - 25 + 19 - 19 + 9 + 26 - 7 - 16 - 21 - 6 - 14 + 23 - 30 - 8 - 21 - 29 + 21 + 25 + 2 - 3 + 4",
    "correct_answer": -141,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "7 - 26 - 23 - 22 - 3 + 21 - 11 + 29 + 23 + 20 - 25 - 5 - 28 - 30 - 21 + 14 + 19 - 13 - 5 - 17 + 27 - 16 - 7 + 16 + 3 - 5",
    "correct_answer": -78,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "1916 + 4594",
    "correct_answer": 6510,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "27 - 5 - 26 + 29 + 26 + 24 - 29 - 12 - 6 + 3 - 14 - 15 + 29 - 26 - 2 - 19 - 10 + 2 - 7 - 27 - 6 - 27 + 25",
    "correct_answer": -66,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "9199 - 3469",
    "correct_answer": 5730,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "57 * 58",
    "correct_answer": 3306,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "11 + 23 - 1 - 26 - 17 + 5 - 11 - 17 - 25 - 26 + 21 + 2 - 5 + 4 - 26 - 3 - 2 - 24 + 19 - 4 + 13 + 17",
    "correct_answer": -72,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "270 % 17",
    "correct_answer": 15,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "5 + 12 - 23 + 10 - 4 + 25 + 7 + 12 + 21 - 24 - 8 + 9 - 15 + 5 + 14 - 26 - 19 - 19 - 24 - 11 - 20 - 23 - 27 + 24",
    "correct_answer": -99,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "7 - 19 + 14 - 24 - 27 + 11 - 21 - 13 - 30 + 3 + 17 + 7 + 22 + 15 + 7 + 19 - 18 - 13 - 30 + 28 - 25 + 30",
    "correct_answer": -40,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "32 - 61",
    "correct_answer": -29,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "740 * 161",
    "correct_answer": 119140,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "(73 + 22) * (19 - 69)",
    "correct_answer": -4750,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "(98 + 97) * (56 - 96)",
    "correct_answer": -7800,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "28 - 46",
    "correct_answer": -18,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "37 + 77 - 40",
    "correct_answer": 74,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "465 % 5",
    "correct_answer": 0,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "463 * 51",
    "correct_answer": 23613,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "815 * 76",
    "correct_answer": 61940,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "74 + 84 - 25",
    "correct_answer": 133,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "30 * 94",
    "correct_answer": 2820,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "145 - 101 * 737 + 453 + 276",
    "correct_answer": -73563,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "208 * 884",
    "correct_answer": 183872,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "21 * 45",
    "correct_answer": 945,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "37 + 59 * 29 - 83 * 26",
    "correct_answer": -410,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "65 - 921 + 158 * 960 + 475",
    "correct_answer": 151299,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "(95 + 48) * (83 - 68)",
    "correct_answer": 2145,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "(30 + 33) * (52 - 32)",
    "correct_answer": 1260,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "936 % 17",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "17 - 14 - 30 - 23 + 16 - 2 - 26 - 11 - 22 - 22 - 22 - 21 - 27 - 17 + 18 - 2 + 11 + 28 - 30 - 21 - 21 - 9",
    "correct_answer": -230,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "4371 - 5560",
    "correct_answer": -1189,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "81 * 57",
    "correct_answer": 4617,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "343 * 579 - 82 - 555 * 420",
    "correct_answer": -34585,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "7 - 20 + 21",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "70 * 36",
    "correct_answer": 2520,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "918 % 14",
    "correct_answer": 8,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "9 - 7 + 6 + 5 + 5 + 8 - 9 - 2 + 8 - 5 + 3 - 6 + 1 + 3 - 2 + 2 + 4 - 6 - 3 + 3 + 3 - 7 - 7 - 7 - 3 + 4 + 7 + 5 - 2 - 9",
    "correct_answer": 1,
    "difficulty": "union_balanced",
    "family": "single_digit_pm_chain"
  },
  {
    "expression": "417 % 19",
    "correct_answer": 18,
    "difficulty": "union_balanced",
    "family": "small_mod"
  },
  {
    "expression": "275 * 548 - 648 + 959 * 639",
    "correct_answer": 762853,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "4824 - 7290",
    "correct_answer": -2466,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "8 + 13 + 5 + 18 + 3 - 22 + 2 + 1 - 27 + 1 - 28 - 13 + 3 - 27 - 2 + 16 - 29 + 6 - 21 + 12 + 23",
    "correct_answer": -58,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "2887 - 3676",
    "correct_answer": -789,
    "difficulty": "union_balanced",
    "family": "negative_subtraction"
  },
  {
    "expression": "294 * 73",
    "correct_answer": 21462,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "5 + 25 - 12 + 11 - 17 + 26 + 4 - 11 + 2 - 10 - 12 + 2 - 28 + 10 + 13 - 10 - 30 - 10 + 6 + 30 + 4 - 11",
    "correct_answer": -13,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "22 + 46 * 48 - 43 * 49",
    "correct_answer": 123,
    "difficulty": "union_balanced",
    "family": "chain_mult_mix"
  },
  {
    "expression": "7 - 20 - 8 - 5 - 2 + 7 - 20 + 29 + 10 + 3 - 9 - 27 - 15 - 9 - 7 - 28 - 2 + 25 - 19 + 15 - 20",
    "correct_answer": -95,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "29 + 1 + 16 + 15 - 15 + 8 + 18 + 19 + 4 + 5 + 12 + 3 + 3 + 9 + 14 - 28 + 18 + 3 + 12 - 6 - 2 + 11 - 3 - 21 - 28 + 26",
    "correct_answer": 123,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "16 + 83 - 20",
    "correct_answer": 79,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "52 - 66 + 1",
    "correct_answer": -13,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "77 * 80",
    "correct_answer": 6160,
    "difficulty": "union_balanced",
    "family": "two_digit_mult"
  },
  {
    "expression": "320 * 646 + 108 * 686 - 795",
    "correct_answer": 280013,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  },
  {
    "expression": "1901 + 6067",
    "correct_answer": 7968,
    "difficulty": "union_balanced",
    "family": "four_digit_add_sub"
  },
  {
    "expression": "72 - 4 + 78",
    "correct_answer": 146,
    "difficulty": "union_balanced",
    "family": "two_step_easy"
  },
  {
    "expression": "26 - 4 + 3 + 10 - 1 + 13 - 5 + 13 - 21 - 2 + 26 + 19 + 16 - 6 + 6 + 14 - 15 + 24 + 15 + 18 + 3 - 3 - 7 + 3 - 12 + 23",
    "correct_answer": 156,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "33 - 6",
    "correct_answer": 27,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "61 - 71",
    "correct_answer": -10,
    "difficulty": "union_balanced",
    "family": "single_op_easy"
  },
  {
    "expression": "6 + 28 - 29 + 30 + 18 + 30 + 26 + 27 + 12 - 28 + 11 - 10 - 13 - 20 + 20 + 2 + 20 + 29 + 7 - 26 - 5 - 1 + 29 - 30 - 21 - 11",
    "correct_answer": 101,
    "difficulty": "union_balanced",
    "family": "small_int_pm_chain"
  },
  {
    "expression": "303 * 68",
    "correct_answer": 20604,
    "difficulty": "union_balanced",
    "family": "three_by_two_mult"
  },
  {
    "expression": "(36 + 32) * (10 - 98)",
    "correct_answer": -5984,
    "difficulty": "union_balanced",
    "family": "paren_mix"
  },
  {
    "expression": "684 * 509",
    "correct_answer": 348156,
    "difficulty": "union_balanced",
    "family": "three_by_three_mult"
  },
  {
    "expression": "56 - 141 * 367 + 607 * 793",
    "correct_answer": 429660,
    "difficulty": "union_balanced",
    "family": "precedence_chain"
  }
]