Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [68, -68, 24, 88, -93, 15, -90, -90, -100, 77]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> int:
    def dfs(nums):
        if len(nums) < 2:
            return 1
        left = [x for x in nums if x < nums[0]]
        right = [x for x in nums if x > nums[0]]
        (m, n) = (len(left), len(right))
        (a, b) = (dfs(left), dfs(right))
        return c[m + n][m] * a % mod * b % mod
    n = len(list_1)
    mod = 10 ** 9 + 7
    c = [[0] * n for _ in range(n)]
    c[0][0] = 1
    for i in range(1, n):
        c[i][0] = 1
        for j in range(1, i + 1):
            c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod
    python_result_1 = (dfs(list_1) - 1 + mod) % mod
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [-93, -14, 90, -12, 80, -69, -98, 97, 58, -23]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Define task_2_target_static = 81.
Trace the execution of task_2 with inputs target = task_2_target_static.
```python
from typing import List
def task_2(list_2: List[int], target: int) -> int:
    list_2.sort()
    (ans, n) = (0, len(list_2))
    for i in range(n - 2):
        (j, k) = (i + 1, n - 1)
        while j < k:
            x = list_2[i] + list_2[j] + list_2[k]
            if x < target:
                ans += k - j
                j += 1
            else:
                k -= 1
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [-21, 1, 60, -17, 39, -10, 54, -35, -28, -1]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    (i, n) = (0, len(list_3))
    while i + 1 < n and list_3[i] < list_3[i + 1]:
        i += 1
    if i == n - 1:
        python_result_3 = n * (n + 1) // 2
        return python_result_3
    ans = i + 2
    j = n - 1
    while j:
        while i >= 0 and list_3[i] >= list_3[j]:
            i -= 1
        ans += i + 2
        if list_3[j - 1] >= list_3[j]:
            break
        j -= 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -2}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_nums_static = [38, -17, -11, -33, 80, 56, -69, 68, -80, 2].
Trace the execution of task_1 with inputs nums = task_1_nums_static.
```python
from typing import List
def task_1(nums: List[int], val_1: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_1:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [55, -14, -77, 65, -92, 64, 63, -79, 70, 57]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> List[int]:
    n = len(list_2)
    leftSum = [0] * n
    for i in range(1, n):
        leftSum[i] = leftSum[i - 1] + list_2[i - 1]
    total = sum(list_2)
    answer = []
    for i in range(n):
        rightSum_i = total - list_2[i] - leftSum[i]
        answer.append(abs(leftSum[i] - rightSum_i))
    python_result_2 = answer
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [-53, 73, -84, 56, 5, 47, 37, 83, -16, 69]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    (i, n) = (0, len(list_3))
    while i + 1 < n and list_3[i] < list_3[i + 1]:
        i += 1
    if i == n - 1:
        python_result_3 = n * (n + 1) // 2
        return python_result_3
    ans = i + 2
    j = n - 1
    while j:
        while i >= 0 and list_3[i] >= list_3[j]:
            i -= 1
        ans += i + 2
        if list_3[j - 1] >= list_3[j]:
            break
        j -= 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -96}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_y_static = 7.
Define task_1_bound_static = 7.
Trace the execution of task_1 with inputs y = task_1_y_static, bound = task_1_bound_static.
```python
from typing import List
def task_1(val_1: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_1 == 1:
            break
        a *= val_1
    python_result_1 = list(ans)
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [-48, -95, -13, 51, 24, -98, 22, -2, -100, 85]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> int:
    g = []
    for x in list_2:
        (l, r) = (0, len(g))
        while l < r:
            mid = l + r >> 1
            if g[mid] < x:
                r = mid
            else:
                l = mid + 1
        if l == len(g):
            g.append(x)
        else:
            g[l] = x
    python_result_2 = len(g)
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [-95, -65, 32, -5, -1, -75, 76, 54, 60, -68]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    (i, n) = (0, len(list_3))
    while i + 1 < n and list_3[i] < list_3[i + 1]:
        i += 1
    if i == n - 1:
        python_result_3 = n * (n + 1) // 2
        return python_result_3
    ans = i + 2
    j = n - 1
    while j:
        while i >= 0 and list_3[i] >= list_3[j]:
            i -= 1
        ans += i + 2
        if list_3[j - 1] >= list_3[j]:
            break
        j -= 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [-37, -42, 1, 52, -64, 85, -51, -15, 73, -68]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Define task_1_queries_static = [30, 86, 55, 61, -58, 55, -45, -19, -6, 38].
Trace the execution of task_1 with inputs queries = task_1_queries_static.
```python
from typing import List
def task_1(list_1: List[int], queries: List[int]) -> List[int]:
    s = set()
    ans = []
    for q in queries[::-1]:
        if q not in s:
            ans.append(q)
            s.add(q)
    for w in list_1:
        if w not in s:
            ans.append(w)
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": 23}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_y_static = -12.
Define task_2_bound_static = 65.
Trace the execution of task_2 with inputs y = task_2_y_static, bound = task_2_bound_static.
```python
from typing import List
def task_2(val_2: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_2 == 1:
            break
        a *= val_2
    python_result_2 = list(ans)
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [74, 74, -14, 88, 88, -55, 71, 20, -8, -80]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    (i, n) = (0, len(list_3))
    while i + 1 < n and list_3[i] < list_3[i + 1]:
        i += 1
    if i == n - 1:
        python_result_3 = n * (n + 1) // 2
        return python_result_3
    ans = i + 2
    j = n - 1
    while j:
        while i >= 0 and list_3[i] >= list_3[j]:
            i -= 1
        ans += i + 2
        if list_3[j - 1] >= list_3[j]:
            break
        j -= 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 53}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_1.
```python
def task_1(val_1: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_1:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_1:
        ans += 1
        s += k
        k += 1
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [50, -40, 73, 11, 95, -28, 97, -77, -23, 17]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> List[int]:
    ans = []
    (i, j) = (0, len(list_2) - 1)
    while i <= j:
        a = list_2[i] * list_2[i]
        b = list_2[j] * list_2[j]
        if a > b:
            ans.append(a)
            i += 1
        else:
            ans.append(b)
            j -= 1
    python_result_2 = ans[::-1]
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [-43, 54, -12, 31, -39, -80, -47, 55, 86, -7]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    (i, n) = (0, len(list_3))
    while i + 1 < n and list_3[i] < list_3[i + 1]:
        i += 1
    if i == n - 1:
        python_result_3 = n * (n + 1) // 2
        return python_result_3
    ans = i + 2
    j = n - 1
    while j:
        while i >= 0 and list_3[i] >= list_3[j]:
            i -= 1
        ans += i + 2
        if list_3[j - 1] >= list_3[j]:
            break
        j -= 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [68, -68, 25, -39, -50, -19, -88, -22, -66, -29]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> int:
    g = []
    for x in list_1:
        (l, r) = (0, len(g))
        while l < r:
            mid = l + r >> 1
            if g[mid] < x:
                r = mid
            else:
                l = mid + 1
        if l == len(g):
            g.append(x)
        else:
            g[l] = x
    python_result_1 = len(g)
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": -33}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_y_static = -32.
Define task_2_bound_static = 5.
Trace the execution of task_2 with inputs y = task_2_y_static, bound = task_2_bound_static.
```python
from typing import List
def task_2(val_2: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_2 == 1:
            break
        a *= val_2
    python_result_2 = list(ans)
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [59, 88, -65, -76, 52, 57, 72, 64, 85, -30]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    (i, n) = (0, len(list_3))
    while i + 1 < n and list_3[i] < list_3[i + 1]:
        i += 1
    if i == n - 1:
        python_result_3 = n * (n + 1) // 2
        return python_result_3
    ans = i + 2
    j = n - 1
    while j:
        while i >= 0 and list_3[i] >= list_3[j]:
            i -= 1
        ans += i + 2
        if list_3[j - 1] >= list_3[j]:
            break
        j -= 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 72}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_nums_static = [88, 74, 75, -78, 51, -82, -11, 40, 74, 67].
Trace the execution of task_1 with inputs nums = task_1_nums_static.
```python
from typing import List
def task_1(nums: List[int], val_1: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_1:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": 3}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_y_static = 6.
Define task_2_bound_static = 9.
Trace the execution of task_2 with inputs y = task_2_y_static, bound = task_2_bound_static.
```python
from typing import List
def task_2(val_2: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_2 == 1:
            break
        a *= val_2
    python_result_2 = list(ans)
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [85, -63, 85, 68, -55, 44, 99, 70, -24, -37]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    (i, n) = (0, len(list_3))
    while i + 1 < n and list_3[i] < list_3[i + 1]:
        i += 1
    if i == n - 1:
        python_result_3 = n * (n + 1) // 2
        return python_result_3
    ans = i + 2
    j = n - 1
    while j:
        while i >= 0 and list_3[i] >= list_3[j]:
            i -= 1
        ans += i + 2
        if list_3[j - 1] >= list_3[j]:
            break
        j -= 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [80, -47, 100, -26, 59, 28, 46, 87, 84, -28]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> List[int]:
    n = len(list_1)
    left = [-1] * n
    right = [n] * n
    stk = []
    for (i, x) in enumerate(list_1):
        while stk and list_1[stk[-1]] <= x:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    for i in range(n - 1, -1, -1):
        while stk and list_1[stk[-1]] <= list_1[i]:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    python_result_1 = [r - l - 1 for (l, r) in zip(left, right)]
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [41, -81, 93, -49, -73, 74, 26, -59, 77, 27]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> List[int]:
    n = len(list_2)
    left = [-1] * n
    right = [n] * n
    stk = []
    for (i, x) in enumerate(list_2):
        while stk and list_2[stk[-1]] <= x:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    for i in range(n - 1, -1, -1):
        while stk and list_2[stk[-1]] <= list_2[i]:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    python_result_2 = [r - l - 1 for (l, r) in zip(left, right)]
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [-88, 41, 52, 50, 87, 39, -67, 44, -38, -25]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    (i, n) = (0, len(list_3))
    while i + 1 < n and list_3[i] < list_3[i + 1]:
        i += 1
    if i == n - 1:
        python_result_3 = n * (n + 1) // 2
        return python_result_3
    ans = i + 2
    j = n - 1
    while j:
        while i >= 0 and list_3[i] >= list_3[j]:
            i -= 1
        ans += i + 2
        if list_3[j - 1] >= list_3[j]:
            break
        j -= 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [72, 89, 20, 73, 29, -52, 48, -72, 22, -85]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Define task_1_queries_static = [100, -53, 45, 33, 47, 99, 65, 11, 96, 51].
Trace the execution of task_1 with inputs queries = task_1_queries_static.
```python
from typing import List
def task_1(list_1: List[int], queries: List[int]) -> List[int]:
    s = set()
    ans = []
    for q in queries[::-1]:
        if q not in s:
            ans.append(q)
            s.add(q)
    for w in list_1:
        if w not in s:
            ans.append(w)
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": 87}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_y_static = 18.
Define task_2_bound_static = 46.
Trace the execution of task_2 with inputs y = task_2_y_static, bound = task_2_bound_static.
```python
from typing import List
def task_2(val_2: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_2 == 1:
            break
        a *= val_2
    python_result_2 = list(ans)
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [18, -87, -63, -82, -25, -3, 31, -100, -3, -83]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    (i, n) = (0, len(list_3))
    while i + 1 < n and list_3[i] < list_3[i + 1]:
        i += 1
    if i == n - 1:
        python_result_3 = n * (n + 1) // 2
        return python_result_3
    ans = i + 2
    j = n - 1
    while j:
        while i >= 0 and list_3[i] >= list_3[j]:
            i -= 1
        ans += i + 2
        if list_3[j - 1] >= list_3[j]:
            break
        j -= 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [-59, -85, -14, 89, 84, 53, -58, 5, -2, -75]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> List[int]:
    def reverse(arr, j):
        i = 0
        while i < j:
            (arr[i], arr[j]) = (arr[j], arr[i])
            (i, j) = (i + 1, j - 1)
    n = len(list_1)
    ans = []
    for i in range(n - 1, 0, -1):
        j = i
        while j > 0 and list_1[j] != i + 1:
            j -= 1
        if j < i:
            if j > 0:
                ans.append(j + 1)
                reverse(list_1, j)
            ans.append(i + 1)
            reverse(list_1, i)
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": -31}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_tokens_static = [7, -92, 69, -64, 64, -49, 38, -82, -64, -59].
Trace the execution of task_2 with inputs tokens = task_2_tokens_static.
```python
from typing import List
def task_2(tokens: List[int], val_2: int) -> int:
    tokens.sort()
    ans = score = 0
    (i, j) = (0, len(tokens) - 1)
    while i <= j:
        if val_2 >= tokens[i]:
            val_2 -= tokens[i]
            (score, i) = (score + 1, i + 1)
            ans = max(ans, score)
        elif score:
            val_2 += tokens[j]
            (score, j) = (score - 1, j - 1)
        else:
            break
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [-100, -55, 23, 97, -7, -10, 41, 34, 44, 81]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    (i, n) = (0, len(list_3))
    while i + 1 < n and list_3[i] < list_3[i + 1]:
        i += 1
    if i == n - 1:
        python_result_3 = n * (n + 1) // 2
        return python_result_3
    ans = i + 2
    j = n - 1
    while j:
        while i >= 0 and list_3[i] >= list_3[j]:
            i -= 1
        ans += i + 2
        if list_3[j - 1] >= list_3[j]:
            break
        j -= 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [-29, 60, -7, -72, -91, 91, -54, 20, 34, 44]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> int:
    def f(x: int) -> int:
        i = 2
        (cnt, s) = (2, x + 1)
        while i <= x // i:
            if x % i == 0:
                cnt += 1
                s += i
                if i * i != x:
                    cnt += 1
                    s += x // i
            i += 1
        return s if cnt == 4 else 0
    python_result_1 = sum((f(x) for x in list_1))
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [-99, -6, -60, -99, -24, -18, 27, -27, -64, -49]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Define task_2_queries_static = [37, 47, 14, -89, 8, 14, -38, 47, -67, -66].
Trace the execution of task_2 with inputs queries = task_2_queries_static.
```python
from typing import List
def task_2(list_2: List[int], queries: List[int]) -> List[int]:
    s = set()
    ans = []
    for q in queries[::-1]:
        if q not in s:
            ans.append(q)
            s.add(q)
    for w in list_2:
        if w not in s:
            ans.append(w)
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": 36}.
Task 3:
Let val_3 be the result of preprocessing task_3_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_3.
```python
def task_3(val_3: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_3:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_3:
        ans += 1
        s += k
        k += 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 99}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_1.
```python
def task_1(val_1: int) -> int:
    ans = 0
    (mi, mx) = (-2 ** 31, 2 ** 31 - 1)
    while val_1:
        if ans < mi // 10 + 1 or ans > mx // 10:
            python_result_1 = 0
            return python_result_1
        y = val_1 % 10
        if val_1 < 0 and y > 0:
            y -= 10
        ans = ans * 10 + y
        val_1 = (val_1 - y) // 10
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": 5}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_nums_static = [72, 50, -67, 92, 38, -74, 72, -93, 76, 71].
Trace the execution of task_2 with inputs nums = task_2_nums_static.
```python
from typing import List
def task_2(nums: List[int], val_2: int) -> int:
    nums.sort()
    n = len(nums)
    m = n >> 1
    ans = abs(nums[m] - val_2)
    if nums[m] > val_2:
        for i in range(m - 1, -1, -1):
            if nums[i] <= val_2:
                break
            ans += nums[i] - val_2
    else:
        for i in range(m + 1, n):
            if nums[i] >= val_2:
                break
            ans += val_2 - nums[i]
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": 81}.
Task 3:
Let val_3 be the result of preprocessing task_3_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_3.
```python
def task_3(val_3: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_3:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_3:
        ans += 1
        s += k
        k += 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [-4, 0, -32, -7, 11, 55, 98, 19, 67, 25]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> int:
    n = len(list_1)
    stk = []
    left = [-1] * n
    right = [n] * n
    for (i, h) in enumerate(list_1):
        while stk and list_1[stk[-1]] >= h:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    for i in range(n - 1, -1, -1):
        h = list_1[i]
        while stk and list_1[stk[-1]] >= h:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    python_result_1 = max((h * (right[i] - left[i] - 1) for (i, h) in enumerate(list_1)))
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [9, 8, 19, 92, -92, -26, -9, 92, -47, 82]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> List[int]:
    f = True
    while f:
        f = False
        t = list_2[:]
        for i in range(1, len(t) - 1):
            if t[i] > t[i - 1] and t[i] > t[i + 1]:
                list_2[i] -= 1
                f = True
            if t[i] < t[i - 1] and t[i] < t[i + 1]:
                list_2[i] += 1
                f = True
    python_result_2 = list_2
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": 66}.
Task 3:
Let val_3 be the result of preprocessing task_3_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_3.
```python
def task_3(val_3: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_3:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_3:
        ans += 1
        s += k
        k += 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -21}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_plants_static = [57, -14, 14, 59, 72, 12, 40, -60, 37, -9].
Define task_1_capacityB_static = -24.
Trace the execution of task_1 with inputs plants = task_1_plants_static, capacityB = task_1_capacityB_static.
```python
from typing import List
def task_1(plants: List[int], val_1: int, capacityB: int) -> int:
    (a, b) = (val_1, capacityB)
    ans = 0
    (i, j) = (0, len(plants) - 1)
    while i < j:
        if a < plants[i]:
            ans += 1
            a = val_1
        a -= plants[i]
        if b < plants[j]:
            ans += 1
            b = capacityB
        b -= plants[j]
        (i, j) = (i + 1, j - 1)
    ans += i == j and max(a, b) < plants[i]
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [-51, 90, 43, -81, -58, 23, 87, -53, -26, 83]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> int:
    (i, j) = (0, len(list_2) - 1)
    (a, b) = (list_2[i], list_2[j])
    ans = 0
    while i < j:
        if a < b:
            i += 1
            a += list_2[i]
            ans += 1
        elif b < a:
            j -= 1
            b += list_2[j]
            ans += 1
        else:
            (i, j) = (i + 1, j - 1)
            (a, b) = (list_2[i], list_2[j])
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": 3}.
Task 3:
Let val_3 be the result of preprocessing task_3_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_3.
```python
def task_3(val_3: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_3:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_3:
        ans += 1
        s += k
        k += 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [28, -44, -79, 28, 7, 20, -32, 86, 72, 29]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> int:
    g = []
    for x in list_1:
        (l, r) = (0, len(g))
        while l < r:
            mid = l + r >> 1
            if g[mid] < x:
                r = mid
            else:
                l = mid + 1
        if l == len(g):
            g.append(x)
        else:
            g[l] = x
    python_result_1 = len(g)
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [-41, 73, 8, -42, -100, 6, -91, 10, 49, -1]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Define task_2_k_static = -37.
Trace the execution of task_2 with inputs k = task_2_k_static.
```python
from typing import List
def task_2(list_2: List[int], k: int) -> int:
    list_2.sort()
    n = len(list_2)
    m = n >> 1
    ans = abs(list_2[m] - k)
    if list_2[m] > k:
        for i in range(m - 1, -1, -1):
            if list_2[i] <= k:
                break
            ans += list_2[i] - k
    else:
        for i in range(m + 1, n):
            if list_2[i] >= k:
                break
            ans += k - list_2[i]
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": 7}.
Task 3:
Let val_3 be the result of preprocessing task_3_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_3.
```python
def task_3(val_3: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_3:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_3:
        ans += 1
        s += k
        k += 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -27}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_nums_static = [22, -7, 0, 13, -50, 15, -89, -67, -36, -68].
Trace the execution of task_1 with inputs nums = task_1_nums_static.
```python
from typing import List
def task_1(nums: List[int], val_1: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_1:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [-28, -59, 82, 99, -90, -28, 28, 54, 73, 32]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> List[int]:
    f = True
    while f:
        f = False
        t = list_2[:]
        for i in range(1, len(t) - 1):
            if t[i] > t[i - 1] and t[i] > t[i + 1]:
                list_2[i] -= 1
                f = True
            if t[i] < t[i - 1] and t[i] < t[i + 1]:
                list_2[i] += 1
                f = True
    python_result_2 = list_2
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": 9}.
Task 3:
Let val_3 be the result of preprocessing task_3_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_3.
```python
def task_3(val_3: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_3:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_3:
        ans += 1
        s += k
        k += 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -15}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_y_static = -24.
Define task_1_bound_static = 82.
Trace the execution of task_1 with inputs y = task_1_y_static, bound = task_1_bound_static.
```python
from typing import List
def task_1(val_1: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_1 == 1:
            break
        a *= val_1
    python_result_1 = list(ans)
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [-86, -41, 92, 1, 58, 75, 39, -97, -15, -36]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Define task_2_queries_static = [-61, -95, 11, 17, 26, 95, 43, -87, -63, 18].
Trace the execution of task_2 with inputs queries = task_2_queries_static.
```python
from typing import List
def task_2(list_2: List[int], queries: List[int]) -> List[int]:
    s = set()
    ans = []
    for q in queries[::-1]:
        if q not in s:
            ans.append(q)
            s.add(q)
    for w in list_2:
        if w not in s:
            ans.append(w)
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": 62}.
Task 3:
Let val_3 be the result of preprocessing task_3_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_3.
```python
def task_3(val_3: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_3:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_3:
        ans += 1
        s += k
        k += 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 57}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_nums_static = [85, -82, -28, 77, -70, -80, -91, -91, 28, -84].
Trace the execution of task_1 with inputs nums = task_1_nums_static.
```python
from typing import List
def task_1(nums: List[int], val_1: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_1:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": -84}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_nums_static = [9, 97, -83, -21, -32, 34, 47, 36, 78, 58].
Trace the execution of task_2 with inputs nums = task_2_nums_static.
```python
from typing import List
def task_2(nums: List[int], val_2: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_2:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": 89}.
Task 3:
Let val_3 be the result of preprocessing task_3_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_3.
```python
def task_3(val_3: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_3:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_3:
        ans += 1
        s += k
        k += 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 54}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_plants_static = [86, 90, 1, -90, 55, 65, 54, 11, 5, -78].
Define task_1_capacityB_static = -73.
Trace the execution of task_1 with inputs plants = task_1_plants_static, capacityB = task_1_capacityB_static.
```python
from typing import List
def task_1(plants: List[int], val_1: int, capacityB: int) -> int:
    (a, b) = (val_1, capacityB)
    ans = 0
    (i, j) = (0, len(plants) - 1)
    while i < j:
        if a < plants[i]:
            ans += 1
            a = val_1
        a -= plants[i]
        if b < plants[j]:
            ans += 1
            b = capacityB
        b -= plants[j]
        (i, j) = (i + 1, j - 1)
    ans += i == j and max(a, b) < plants[i]
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [35, 11, 17, 11, -98, -26, -57, 6, -46, -26]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> int:
    n = len(list_2)
    f = [1] * n
    g = [1] * n
    for i in range(1, n):
        if list_2[i] > list_2[i - 1]:
            f[i] = f[i - 1] + 1
    ans = 0
    for i in range(n - 2, -1, -1):
        if list_2[i] > list_2[i + 1]:
            g[i] = g[i + 1] + 1
            if f[i] > 1:
                ans = max(ans, f[i] + g[i] - 1)
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": 35}.
Task 3:
Let val_3 be the result of preprocessing task_3_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_3.
```python
def task_3(val_3: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_3:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_3:
        ans += 1
        s += k
        k += 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -100}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_nums_static = [-45, 99, 82, -8, 88, -97, -89, -97, 72, 18].
Trace the execution of task_1 with inputs nums = task_1_nums_static.
```python
from typing import List
def task_1(nums: List[int], val_1: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_1:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": -97}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_nums_static = [-16, -50, -79, -56, -56, -58, -44, 64, 55, 18].
Trace the execution of task_2 with inputs nums = task_2_nums_static.
```python
from typing import List
def task_2(nums: List[int], val_2: int) -> int:
    nums.sort()
    n = len(nums)
    m = n >> 1
    ans = abs(nums[m] - val_2)
    if nums[m] > val_2:
        for i in range(m - 1, -1, -1):
            if nums[i] <= val_2:
                break
            ans += nums[i] - val_2
    else:
        for i in range(m + 1, n):
            if nums[i] >= val_2:
                break
            ans += val_2 - nums[i]
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": 10}.
Task 3:
Let val_3 be the result of preprocessing task_3_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_3.
```python
def task_3(val_3: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_3:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_3:
        ans += 1
        s += k
        k += 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 54}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_nums_static = [-81, 52, 42, -80, -23, -28, -49, 10, 14, 83].
Trace the execution of task_1 with inputs nums = task_1_nums_static.
```python
from typing import List
def task_1(nums: List[int], val_1: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_1:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": 97}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_y_static = -84.
Define task_2_bound_static = 76.
Trace the execution of task_2 with inputs y = task_2_y_static, bound = task_2_bound_static.
```python
from typing import List
def task_2(val_2: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_2 == 1:
            break
        a *= val_2
    python_result_2 = list(ans)
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": 18}.
Task 3:
Let val_3 be the result of preprocessing task_3_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_3.
```python
def task_3(val_3: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_3:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_3:
        ans += 1
        s += k
        k += 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [-26, 73, 96, -96, 19, 42, 99, 78, 35, -54]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> int:
    def dfs(nums):
        if len(nums) < 2:
            return 1
        left = [x for x in nums if x < nums[0]]
        right = [x for x in nums if x > nums[0]]
        (m, n) = (len(left), len(right))
        (a, b) = (dfs(left), dfs(right))
        return c[m + n][m] * a % mod * b % mod
    n = len(list_1)
    mod = 10 ** 9 + 7
    c = [[0] * n for _ in range(n)]
    c[0][0] = 1
    for i in range(1, n):
        c[i][0] = 1
        for j in range(1, i + 1):
            c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod
    python_result_1 = (dfs(list_1) - 1 + mod) % mod
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [26, -86, 29, 17, -54, -28, -71, -65, -30, -70]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> List[int]:
    stk = []
    n = len(list_2)
    ans = [0] * n
    for i in range(n - 1, -1, -1):
        while stk and list_2[stk[-1]] <= list_2[i]:
            stk.pop()
        if stk:
            ans[i] = stk[-1] - i
        stk.append(i)
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": 22}.
Task 3:
Let val_3 be the result of preprocessing task_3_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_3.
```python
def task_3(val_3: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_3:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_3:
        ans += 1
        s += k
        k += 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 11}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_initialExperience_static = -66.
Define task_1_energy_static = [22, -17, -29, 7, -10, -42, -46, -63, -12, 82].
Define task_1_experience_static = [95, -58, -50, -31, 90, 18, -17, 41, 93, 39].
Trace the execution of task_1 with inputs initialExperience = task_1_initialExperience_static, energy = task_1_energy_static, experience = task_1_experience_static.
```python
from typing import List
def task_1(val_1: int, initialExperience: int, energy: List[int], experience: List[int]) -> int:
    sum_energy = sum(energy)
    energy_hours = max(0, sum_energy + 1 - val_1)
    exp_hours = 0
    current_exp = initialExperience
    for e in experience:
        if current_exp <= e:
            delta = e + 1 - current_exp
            exp_hours += delta
            current_exp += delta
        current_exp += e
    python_result_1 = energy_hours + exp_hours
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": -8}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_arr_static = [-75, 47, -16, 97, 50, 11, -87, 58, 30, 37].
Trace the execution of task_2 with inputs arr = task_2_arr_static.
```python
from typing import List
def task_2(arr: List[int], val_2: int) -> int:
    if arr[0] > val_2:
        python_result_2 = val_2
        return python_result_2
    (left, right) = (0, len(arr))
    while left < right:
        mid = left + right >> 1
        if arr[mid] - mid - 1 >= val_2:
            right = mid
        else:
            left = mid + 1
    python_result_2 = arr[left - 1] + val_2 - (arr[left - 1] - (left - 1) - 1)
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": 39}.
Task 3:
Let val_3 be the result of preprocessing task_3_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_3.
```python
def task_3(val_3: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_3:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_3:
        ans += 1
        s += k
        k += 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 64}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_1.
```python
def task_1(val_1: int) -> int:
    while 1:
        (t, s, i) = (val_1, 0, 2)
        while i <= val_1 // i:
            while val_1 % i == 0:
                val_1 //= i
                s += i
            i += 1
        if val_1 > 1:
            s += val_1
        if s == t:
            python_result_1 = t
            return python_result_1
        val_1 = s
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": -3}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_nums_static = [22, 67, -67, 1, 45, -58, 37, -44, -53, -80].
Trace the execution of task_2 with inputs nums = task_2_nums_static.
```python
from typing import List
def task_2(nums: List[int], val_2: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_2:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": 80}.
Task 3:
Let val_3 be the result of preprocessing task_3_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_3.
```python
def task_3(val_3: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_3:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_3:
        ans += 1
        s += k
        k += 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [73, 39, 56, -82, -22, -14, -32, -4, -69, -95]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Define task_1_arr2_static = [-65, 38, -82, -30, 8, -13, -14, -17, 8, 12].
Trace the execution of task_1 with inputs arr2 = task_1_arr2_static.
```python
from typing import List
def task_1(list_1: List[int], arr2: List[int]) -> List[int]:
    (i, j) = (len(list_1) - 1, len(arr2) - 1)
    c = 0
    ans = []
    while i >= 0 or j >= 0 or c:
        a = 0 if i < 0 else list_1[i]
        b = 0 if j < 0 else arr2[j]
        x = a + b + c
        c = 0
        if x >= 2:
            x -= 2
            c -= 1
        elif x == -1:
            x = 1
            c += 1
        ans.append(x)
        (i, j) = (i - 1, j - 1)
    while len(ans) > 1 and ans[-1] == 0:
        ans.pop()
    python_result_1 = ans[::-1]
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": 95}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_2.
```python
def task_2(val_2: int) -> int:
    while 1:
        (t, s, i) = (val_2, 0, 2)
        while i <= val_2 // i:
            while val_2 % i == 0:
                val_2 //= i
                s += i
            i += 1
        if val_2 > 1:
            s += val_2
        if s == t:
            python_result_2 = t
            return python_result_2
        val_2 = s
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": 73}.
Task 3:
Let val_3 be the result of preprocessing task_3_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_3.
```python
def task_3(val_3: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_3:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_3:
        ans += 1
        s += k
        k += 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -80}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_nums_static = [-32, 30, -59, 38, -9, -30, 46, 46, -57, -63].
Trace the execution of task_1 with inputs nums = task_1_nums_static.
```python
from typing import List
def task_1(nums: List[int], val_1: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_1:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": 38}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_2.
```python
def task_2(val_2: int) -> int:
    ans = 0
    (mi, mx) = (-2 ** 31, 2 ** 31 - 1)
    while val_2:
        if ans < mi // 10 + 1 or ans > mx // 10:
            python_result_2 = 0
            return python_result_2
        y = val_2 % 10
        if val_2 < 0 and y > 0:
            y -= 10
        ans = ans * 10 + y
        val_2 = (val_2 - y) // 10
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": 18}.
Task 3:
Let val_3 be the result of preprocessing task_3_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_3.
```python
def task_3(val_3: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_3:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_3:
        ans += 1
        s += k
        k += 1
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 93}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_skills_static = [-18, -73, -44, -25, 27, -13, -56, 32, -93, -33].
Trace the execution of task_1 with inputs skills = task_1_skills_static.
```python
from typing import List
def task_1(skills: List[int], val_1: int) -> int:
    n = len(skills)
    val_1 = min(val_1, n - 1)
    i = cnt = 0
    for j in range(1, n):
        if skills[i] < skills[j]:
            i = j
            cnt = 1
        else:
            cnt += 1
        if cnt == val_1:
            break
    python_result_1 = i
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": [-37, -30, -92, -25, 28, -10, 83, -100, -82, -6]}.
Task 2:
Let list_2 be the result of preprocessing task_2_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Define task_2_trainers_static = [-97, -44, 28, 43, -16, -77, -16, 37, -4, 55].
Trace the execution of task_2 with inputs trainers = task_2_trainers_static.
```python
from typing import List
def task_2(list_2: List[int], trainers: List[int]) -> int:
    list_2.sort()
    trainers.sort()
    (j, n) = (0, len(trainers))
    for (i, p) in enumerate(list_2):
        while j < n and trainers[j] < p:
            j += 1
        if j == n:
            python_result_2 = i
            return python_result_2
        j += 1
    python_result_2 = len(list_2)
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [8, -49, 29, 27, -82, -35, -84, -22, -58, -57]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [[0] * n for _ in range(n)]
    d = {x: i for (i, x) in enumerate(list_3)}
    for i in range(n):
        for j in range(i):
            f[i][j] = 2
    ans = 0
    for i in range(2, n):
        for j in range(1, i):
            t = list_3[i] - list_3[j]
            if t in d and (k := d[t]) < j:
                f[i][j] = max(f[i][j], f[j][k] + 1)
                ans = max(ans, f[i][j])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [-97, -24, -44, -44, -86, 10, -54, 26, 68, 97]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> int:
    ans = t = 1
    for (i, x) in enumerate(list_1[1:]):
        if list_1[i] < x:
            t += 1
            ans = max(ans, t)
        else:
            t = 1
    t = 1
    for (i, x) in enumerate(list_1[1:]):
        if list_1[i] > x:
            t += 1
            ans = max(ans, t)
        else:
            t = 1
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": -33}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_y_static = 87.
Define task_2_bound_static = 24.
Trace the execution of task_2 with inputs y = task_2_y_static, bound = task_2_bound_static.
```python
from typing import List
def task_2(val_2: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_2 == 1:
            break
        a *= val_2
    python_result_2 = list(ans)
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [22, 35, -47, 79, 69, -44, 67, 2, 65, -12]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [[0] * n for _ in range(n)]
    d = {x: i for (i, x) in enumerate(list_3)}
    for i in range(n):
        for j in range(i):
            f[i][j] = 2
    ans = 0
    for i in range(2, n):
        for j in range(1, i):
            t = list_3[i] - list_3[j]
            if t in d and (k := d[t]) < j:
                f[i][j] = max(f[i][j], f[j][k] + 1)
                ans = max(ans, f[i][j])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [-67, -52, -59, 79, 60, -71, 37, 98, -54, 15]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> List[int]:
    (i, j) = (0, len(list_1) - 1)
    while i < j:
        if list_1[i] % 2 == 0:
            i += 1
        elif list_1[j] % 2 == 1:
            j -= 1
        else:
            (list_1[i], list_1[j]) = (list_1[j], list_1[i])
            (i, j) = (i + 1, j - 1)
    python_result_1 = list_1
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": 8}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_y_static = 87.
Define task_2_bound_static = 33.
Trace the execution of task_2 with inputs y = task_2_y_static, bound = task_2_bound_static.
```python
from typing import List
def task_2(val_2: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_2 == 1:
            break
        a *= val_2
    python_result_2 = list(ans)
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [-79, 28, -20, -57, 13, -37, 37, 97, 96, 0]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [[0] * n for _ in range(n)]
    d = {x: i for (i, x) in enumerate(list_3)}
    for i in range(n):
        for j in range(i):
            f[i][j] = 2
    ans = 0
    for i in range(2, n):
        for j in range(1, i):
            t = list_3[i] - list_3[j]
            if t in d and (k := d[t]) < j:
                f[i][j] = max(f[i][j], f[j][k] + 1)
                ans = max(ans, f[i][j])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -46}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_nums_static = [-86, -11, 62, -96, 92, -51, -99, -15, 33, -29].
Trace the execution of task_1 with inputs nums = task_1_nums_static.
```python
from typing import List
def task_1(nums: List[int], val_1: int) -> int:
    nums.sort()
    n = len(nums)
    m = n >> 1
    ans = abs(nums[m] - val_1)
    if nums[m] > val_1:
        for i in range(m - 1, -1, -1):
            if nums[i] <= val_1:
                break
            ans += nums[i] - val_1
    else:
        for i in range(m + 1, n):
            if nums[i] >= val_1:
                break
            ans += val_1 - nums[i]
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Define task_2_input = {"result": 13}.
Task 2:
Let val_2 be the result of preprocessing task_2_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_nums_static = [-20, -37, 29, 98, -82, 54, 80, 65, 31, -86].
Trace the execution of task_2 with inputs nums = task_2_nums_static.
```python
from typing import List
def task_2(nums: List[int], val_2: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_2:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Define task_3_input = {"result": [12, 11, -34, -4, -20, -88, 46, 26, 14, -14]}.
Task 3:
Let list_3 be the result of preprocessing task_3_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [[0] * n for _ in range(n)]
    d = {x: i for (i, x) in enumerate(list_3)}
    for i in range(n):
        for j in range(i):
            f[i][j] = 2
    ans = 0
    for i in range(2, n):
        for j in range(1, i):
            t = list_3[i] - list_3[j]
            if t in d and (k := d[t]) < j:
                f[i][j] = max(f[i][j], f[j][k] + 1)
                ans = max(ans, f[i][j])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.