contestId int64 0 1.01k | name stringlengths 2 58 | tags listlengths 0 11 | title stringclasses 523
values | time-limit stringclasses 8
values | memory-limit stringclasses 8
values | problem-description stringlengths 0 7.15k | input-specification stringlengths 0 2.05k | output-specification stringlengths 0 1.5k | demo-input listlengths 0 7 | demo-output listlengths 0 7 | note stringlengths 0 5.24k | test_cases listlengths 0 402 | timeConsumedMillis int64 0 8k | memoryConsumedBytes int64 0 537M | score float64 -1 3.99 | __index_level_0__ int64 0 621k |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | none | [
"none"
] | null | null | Dima came to the horse land. There are *n* horses living in the land. Each horse in the horse land has several enemies (enmity is a symmetric relationship). The horse land isn't very hostile, so the number of enemies of each horse is at most 3.
Right now the horse land is going through an election campaign. So the horses trusted Dima to split them into two parts. At that the horses want the following condition to hold: a horse shouldn't have more than one enemy in its party.
Help Dima split the horses into parties. Note that one of the parties can turn out to be empty. | The first line contains two integers *n*,<=*m* — the number of horses in the horse land and the number of enemy pairs.
Next *m* lines define the enemy pairs. The *i*-th line contains integers *a**i*,<=*b**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=*n*; *a**i*<=≠<=*b**i*), which mean that horse *a**i* is the enemy of horse *b**i*.
Consider the horses indexed in some way from 1 to *n*. It is guaranteed that each horse has at most three enemies. No pair of enemies occurs more than once in the input. | Print a line, consisting of *n* characters: the *i*-th character of the line must equal "0", if the horse number *i* needs to go to the first party, otherwise this character should equal "1".
If there isn't a way to divide the horses as required, print -1. | [
"3 3\n1 2\n3 2\n3 1\n",
"2 1\n2 1\n",
"10 6\n1 2\n1 3\n1 4\n2 3\n2 4\n3 4\n"
] | [
"100\n",
"00\n",
"0110000000\n"
] | none | [] | 62 | 0 | 0 | 3,479 | |
673 | Problems for Round | [
"greedy",
"implementation"
] | null | null | There are *n* problems prepared for the next Codeforces round. They are arranged in ascending order by their difficulty, and no two problems have the same difficulty. Moreover, there are *m* pairs of similar problems. Authors want to split problems between two division according to the following rules:
- Problemset of each division should be non-empty. - Each problem should be used in exactly one division (yes, it is unusual requirement). - Each problem used in division 1 should be harder than any problem used in division 2. - If two problems are similar, they should be used in different divisions.
Your goal is count the number of ways to split problem between two divisions and satisfy all the rules. Two ways to split problems are considered to be different if there is at least one problem that belongs to division 1 in one of them and to division 2 in the other.
Note, that the relation of similarity is not transitive. That is, if problem *i* is similar to problem *j* and problem *j* is similar to problem *k*, it doesn't follow that *i* is similar to *k*. | The first line of the input contains two integers *n* and *m* (2<=≤<=*n*<=≤<=100<=000, 0<=≤<=*m*<=≤<=100<=000) — the number of problems prepared for the round and the number of pairs of similar problems, respectively.
Each of the following *m* lines contains a pair of similar problems *u**i* and *v**i* (1<=≤<=*u**i*,<=*v**i*<=≤<=*n*,<=*u**i*<=≠<=*v**i*). It's guaranteed, that no pair of problems meets twice in the input. | Print one integer — the number of ways to split problems in two divisions. | [
"5 2\n1 4\n5 2\n",
"3 3\n1 2\n2 3\n1 3\n",
"3 2\n3 1\n3 2\n"
] | [
"2\n",
"0\n",
"1\n"
] | In the first sample, problems 1 and 2 should be used in division 2, while problems 4 and 5 in division 1. Problem 3 may be used either in division 1 or in division 2.
In the second sample, all pairs of problems are similar and there is no way to split problem between two divisions without breaking any rules.
Third sample reminds you that the similarity relation is not transitive. Problem 3 is similar to both 1 and 2, but 1 is not similar to 2, so they may be used together. | [
{
"input": "5 2\n1 4\n5 2",
"output": "2"
},
{
"input": "3 3\n1 2\n2 3\n1 3",
"output": "0"
},
{
"input": "3 2\n3 1\n3 2",
"output": "1"
},
{
"input": "2 0",
"output": "1"
},
{
"input": "2 1\n1 2",
"output": "1"
},
{
"input": "3 0",
"output": "2"
... | 46 | 5,120,000 | 0 | 3,494 | |
74 | Train | [
"dp",
"games",
"greedy"
] | B. Train | 2 | 256 | A stowaway and a controller play the following game.
The train is represented by *n* wagons which are numbered with positive integers from 1 to *n* from the head to the tail. The stowaway and the controller are initially in some two different wagons. Every minute the train can be in one of two conditions — moving or idle. Every minute the players move.
The controller's move is as follows. The controller has the movement direction — to the train's head or to its tail. During a move the controller moves to the neighbouring wagon correspondingly to its movement direction. If at the end of his move the controller enters the 1-st or the *n*-th wagon, that he changes the direction of his movement into the other one. In other words, the controller cyclically goes from the train's head to its tail and back again during all the time of a game, shifting during each move by one wagon. Note, that the controller always have exactly one possible move.
The stowaway's move depends from the state of the train. If the train is moving, then the stowaway can shift to one of neighbouring wagons or he can stay where he is without moving. If the train is at a station and is idle, then the stowaway leaves the train (i.e. he is now not present in any train wagon) and then, if it is not the terminal train station, he enters the train again into any of *n* wagons (not necessarily into the one he's just left and not necessarily into the neighbouring one). If the train is idle for several minutes then each such minute the stowaway leaves the train and enters it back.
Let's determine the order of the players' moves. If at the given minute the train is moving, then first the stowaway moves and then the controller does. If at this minute the train is idle, then first the stowaway leaves the train, then the controller moves and then the stowaway enters the train.
If at some point in time the stowaway and the controller happen to be in one wagon, then the controller wins: he makes the stowaway pay fine. If after a while the stowaway reaches the terminal train station, then the stowaway wins: he simply leaves the station during his move and never returns there again.
At any moment of time the players know each other's positions. The players play in the optimal way. Specifically, if the controller wins, then the stowaway plays so as to lose as late as possible. As all the possible moves for the controller are determined uniquely, then he is considered to play optimally always. Determine the winner. | The first line contains three integers *n*, *m* and *k*. They represent the number of wagons in the train, the stowaway's and the controller's initial positions correspondingly (2<=≤<=*n*<=≤<=50, 1<=≤<=*m*,<=*k*<=≤<=*n*, *m*<=≠<=*k*).
The second line contains the direction in which a controller moves. "to head" means that the controller moves to the train's head and "to tail" means that the controller moves to its tail. It is guaranteed that in the direction in which the controller is moving, there is at least one wagon. Wagon 1 is the head, and wagon *n* is the tail.
The third line has the length from 1 to 200 and consists of symbols "0" and "1". The *i*-th symbol contains information about the train's state at the *i*-th minute of time. "0" means that in this very minute the train moves and "1" means that the train in this very minute stands idle. The last symbol of the third line is always "1" — that's the terminal train station. | If the stowaway wins, print "Stowaway" without quotes. Otherwise, print "Controller" again without quotes, then, separated by a space, print the number of a minute, at which the stowaway will be caught. | [
"5 3 2\nto head\n0001001\n",
"3 2 1\nto tail\n0001\n"
] | [
"Stowaway",
"Controller 2"
] | none | [
{
"input": "5 3 2\nto head\n0001001",
"output": "Stowaway"
},
{
"input": "3 2 1\nto tail\n0001",
"output": "Controller 2"
},
{
"input": "4 2 1\nto tail\n1000001",
"output": "Controller 6"
},
{
"input": "2 1 2\nto head\n111111",
"output": "Stowaway"
},
{
"input": "... | 124 | 307,200 | 3.968428 | 3,516 |
779 | Pupils Redistribution | [
"constructive algorithms",
"math"
] | null | null | In Berland each high school student is characterized by academic performance — integer value between 1 and 5.
In high school 0xFF there are two groups of pupils: the group *A* and the group *B*. Each group consists of exactly *n* students. An academic performance of each student is known — integer value between 1 and 5.
The school director wants to redistribute students between groups so that each of the two groups has the same number of students whose academic performance is equal to 1, the same number of students whose academic performance is 2 and so on. In other words, the purpose of the school director is to change the composition of groups, so that for each value of academic performance the numbers of students in both groups are equal.
To achieve this, there is a plan to produce a series of exchanges of students between groups. During the single exchange the director selects one student from the class *A* and one student of class *B*. After that, they both change their groups.
Print the least number of exchanges, in order to achieve the desired equal numbers of students for each academic performance. | The first line of the input contains integer number *n* (1<=≤<=*n*<=≤<=100) — number of students in both groups.
The second line contains sequence of integer numbers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=5), where *a**i* is academic performance of the *i*-th student of the group *A*.
The third line contains sequence of integer numbers *b*1,<=*b*2,<=...,<=*b**n* (1<=≤<=*b**i*<=≤<=5), where *b**i* is academic performance of the *i*-th student of the group *B*. | Print the required minimum number of exchanges or -1, if the desired distribution of students can not be obtained. | [
"4\n5 4 4 4\n5 5 4 5\n",
"6\n1 1 1 1 1 1\n5 5 5 5 5 5\n",
"1\n5\n3\n",
"9\n3 2 5 5 2 3 3 3 2\n4 1 4 1 1 2 4 4 1\n"
] | [
"1\n",
"3\n",
"-1\n",
"4\n"
] | none | [
{
"input": "4\n5 4 4 4\n5 5 4 5",
"output": "1"
},
{
"input": "6\n1 1 1 1 1 1\n5 5 5 5 5 5",
"output": "3"
},
{
"input": "1\n5\n3",
"output": "-1"
},
{
"input": "9\n3 2 5 5 2 3 3 3 2\n4 1 4 1 1 2 4 4 1",
"output": "4"
},
{
"input": "1\n1\n2",
"output": "-1"
... | 15 | 0 | 0 | 3,521 | |
626 | Block Towers | [
"brute force",
"greedy",
"math",
"number theory"
] | null | null | Students in a class are making towers of blocks. Each student makes a (non-zero) tower by stacking pieces lengthwise on top of each other. *n* of the students use pieces made of two blocks and *m* of the students use pieces made of three blocks.
The students don’t want to use too many blocks, but they also want to be unique, so no two students’ towers may contain the same number of blocks. Find the minimum height necessary for the tallest of the students' towers. | The first line of the input contains two space-separated integers *n* and *m* (0<=≤<=*n*,<=*m*<=≤<=1<=000<=000, *n*<=+<=*m*<=><=0) — the number of students using two-block pieces and the number of students using three-block pieces, respectively. | Print a single integer, denoting the minimum possible height of the tallest tower. | [
"1 3\n",
"3 2\n",
"5 0\n"
] | [
"9\n",
"8\n",
"10\n"
] | In the first case, the student using two-block pieces can make a tower of height 4, and the students using three-block pieces can make towers of height 3, 6, and 9 blocks. The tallest tower has a height of 9 blocks.
In the second case, the students can make towers of heights 2, 4, and 8 with two-block pieces and towers of heights 3 and 6 with three-block pieces, for a maximum height of 8 blocks. | [
{
"input": "1 3",
"output": "9"
},
{
"input": "3 2",
"output": "8"
},
{
"input": "5 0",
"output": "10"
},
{
"input": "4 2",
"output": "9"
},
{
"input": "0 1000000",
"output": "3000000"
},
{
"input": "1000000 1",
"output": "2000000"
},
{
"in... | 61 | 0 | -1 | 3,524 | |
733 | Parade | [
"math"
] | null | null | Very soon there will be a parade of victory over alien invaders in Berland. Unfortunately, all soldiers died in the war and now the army consists of entirely new recruits, many of whom do not even know from which leg they should begin to march. The civilian population also poorly understands from which leg recruits begin to march, so it is only important how many soldiers march in step.
There will be *n* columns participating in the parade, the *i*-th column consists of *l**i* soldiers, who start to march from left leg, and *r**i* soldiers, who start to march from right leg.
The beauty of the parade is calculated by the following formula: if *L* is the total number of soldiers on the parade who start to march from the left leg, and *R* is the total number of soldiers on the parade who start to march from the right leg, so the beauty will equal |*L*<=-<=*R*|.
No more than once you can choose one column and tell all the soldiers in this column to switch starting leg, i.e. everyone in this columns who starts the march from left leg will now start it from right leg, and vice versa. Formally, you can pick no more than one index *i* and swap values *l**i* and *r**i*.
Find the index of the column, such that switching the starting leg for soldiers in it will maximize the the beauty of the parade, or determine, that no such operation can increase the current beauty. | The first line contains single integer *n* (1<=≤<=*n*<=≤<=105) — the number of columns.
The next *n* lines contain the pairs of integers *l**i* and *r**i* (1<=≤<=*l**i*,<=*r**i*<=≤<=500) — the number of soldiers in the *i*-th column which start to march from the left or the right leg respectively. | Print single integer *k* — the number of the column in which soldiers need to change the leg from which they start to march, or 0 if the maximum beauty is already reached.
Consider that columns are numbered from 1 to *n* in the order they are given in the input data.
If there are several answers, print any of them. | [
"3\n5 6\n8 9\n10 3\n",
"2\n6 5\n5 6\n",
"6\n5 9\n1 3\n4 8\n4 5\n23 54\n12 32\n"
] | [
"3\n",
"1\n",
"0\n"
] | In the first example if you don't give the order to change the leg, the number of soldiers, who start to march from the left leg, would equal 5 + 8 + 10 = 23, and from the right leg — 6 + 9 + 3 = 18. In this case the beauty of the parade will equal |23 - 18| = 5.
If you give the order to change the leg to the third column, so the number of soldiers, who march from the left leg, will equal 5 + 8 + 3 = 16, and who march from the right leg — 6 + 9 + 10 = 25. In this case the beauty equals |16 - 25| = 9.
It is impossible to reach greater beauty by giving another orders. Thus, the maximum beauty that can be achieved is 9. | [
{
"input": "3\n5 6\n8 9\n10 3",
"output": "3"
},
{
"input": "2\n6 5\n5 6",
"output": "1"
},
{
"input": "6\n5 9\n1 3\n4 8\n4 5\n23 54\n12 32",
"output": "0"
},
{
"input": "2\n500 499\n500 500",
"output": "0"
},
{
"input": "1\n139 252",
"output": "0"
},
{
... | 358 | 2,662,400 | 3 | 3,532 | |
340 | Iahub and Permutations | [
"combinatorics",
"math"
] | null | null | Iahub is so happy about inventing bubble sort graphs that he's staying all day long at the office and writing permutations. Iahubina is angry that she is no more important for Iahub. When Iahub goes away, Iahubina comes to his office and sabotage his research work.
The girl finds an important permutation for the research. The permutation contains *n* distinct integers *a*1, *a*2, ..., *a**n* (1<=≤<=*a**i*<=≤<=*n*). She replaces some of permutation elements with -1 value as a revenge.
When Iahub finds out his important permutation is broken, he tries to recover it. The only thing he remembers about the permutation is it didn't have any fixed point. A fixed point for a permutation is an element *a**k* which has value equal to *k* (*a**k*<==<=*k*). Your job is to proof to Iahub that trying to recover it is not a good idea. Output the number of permutations which could be originally Iahub's important permutation, modulo 1000000007 (109<=+<=7). | The first line contains integer *n* (2<=≤<=*n*<=≤<=2000). On the second line, there are *n* integers, representing Iahub's important permutation after Iahubina replaces some values with -1.
It's guaranteed that there are no fixed points in the given permutation. Also, the given sequence contains at least two numbers -1 and each positive number occurs in the sequence at most once. It's guaranteed that there is at least one suitable permutation. | Output a single integer, the number of ways Iahub could recover his permutation, modulo 1000000007 (109<=+<=7). | [
"5\n-1 -1 4 3 -1\n"
] | [
"2\n"
] | For the first test example there are two permutations with no fixed points are [2, 5, 4, 3, 1] and [5, 1, 4, 3, 2]. Any other permutation would have at least one fixed point. | [
{
"input": "5\n-1 -1 4 3 -1",
"output": "2"
},
{
"input": "8\n2 4 5 3 -1 8 -1 6",
"output": "1"
},
{
"input": "7\n-1 -1 4 -1 7 1 6",
"output": "4"
},
{
"input": "6\n-1 -1 -1 -1 -1 -1",
"output": "265"
},
{
"input": "2\n-1 -1",
"output": "1"
},
{
"input... | 124 | 7,065,600 | 0 | 3,534 | |
0 | none | [
"none"
] | null | null | You are given an array *a*1,<=*a*2,<=...,<=*a**n* consisting of *n* integers, and an integer *k*. You have to split the array into exactly *k* non-empty subsegments. You'll then compute the minimum integer on each subsegment, and take the maximum integer over the *k* obtained minimums. What is the maximum possible integer you can get?
Definitions of subsegment and array splitting are given in notes. | The first line contains two integers *n* and *k* (1<=≤<=*k*<=≤<=*n*<=≤<=<=105) — the size of the array *a* and the number of subsegments you have to split the array to.
The second line contains *n* integers *a*1,<=<=*a*2,<=<=...,<=<=*a**n* (<=-<=109<=<=≤<=<=*a**i*<=≤<=<=109). | Print single integer — the maximum possible integer you can get if you split the array into *k* non-empty subsegments and take maximum of minimums on the subsegments. | [
"5 2\n1 2 3 4 5\n",
"5 1\n-4 -5 -3 -2 -1\n"
] | [
"5\n",
"-5\n"
] | A subsegment [*l*, *r*] (*l* ≤ *r*) of array *a* is the sequence *a*<sub class="lower-index">*l*</sub>, *a*<sub class="lower-index">*l* + 1</sub>, ..., *a*<sub class="lower-index">*r*</sub>.
Splitting of array *a* of *n* elements into *k* subsegments [*l*<sub class="lower-index">1</sub>, *r*<sub class="lower-index">1</sub>], [*l*<sub class="lower-index">2</sub>, *r*<sub class="lower-index">2</sub>], ..., [*l*<sub class="lower-index">*k*</sub>, *r*<sub class="lower-index">*k*</sub>] (*l*<sub class="lower-index">1</sub> = 1, *r*<sub class="lower-index">*k*</sub> = *n*, *l*<sub class="lower-index">*i*</sub> = *r*<sub class="lower-index">*i* - 1</sub> + 1 for all *i* > 1) is *k* sequences (*a*<sub class="lower-index">*l*<sub class="lower-index">1</sub></sub>, ..., *a*<sub class="lower-index">*r*<sub class="lower-index">1</sub></sub>), ..., (*a*<sub class="lower-index">*l*<sub class="lower-index">*k*</sub></sub>, ..., *a*<sub class="lower-index">*r*<sub class="lower-index">*k*</sub></sub>).
In the first example you should split the array into subsegments [1, 4] and [5, 5] that results in sequences (1, 2, 3, 4) and (5). The minimums are *min*(1, 2, 3, 4) = 1 and *min*(5) = 5. The resulting maximum is *max*(1, 5) = 5. It is obvious that you can't reach greater result.
In the second example the only option you have is to split the array into one subsegment [1, 5], that results in one sequence ( - 4, - 5, - 3, - 2, - 1). The only minimum is *min*( - 4, - 5, - 3, - 2, - 1) = - 5. The resulting maximum is - 5. | [
{
"input": "5 2\n1 2 3 4 5",
"output": "5"
},
{
"input": "5 1\n-4 -5 -3 -2 -1",
"output": "-5"
},
{
"input": "10 2\n10 9 1 -9 -7 -9 3 8 -10 5",
"output": "10"
},
{
"input": "10 4\n-8 -1 2 -3 9 -8 4 -3 5 9",
"output": "9"
},
{
"input": "1 1\n504262064",
"output... | 233 | 13,619,200 | 3 | 3,550 | |
858 | Tests Renumeration | [
"greedy",
"implementation"
] | null | null | The All-Berland National Olympiad in Informatics has just ended! Now Vladimir wants to upload the contest from the Olympiad as a gym to a popular Codehorses website.
Unfortunately, the archive with Olympiad's data is a mess. For example, the files with tests are named arbitrary without any logic.
Vladimir wants to rename the files with tests so that their names are distinct integers starting from 1 without any gaps, namely, "1", "2", ..., "*n*', where *n* is the total number of tests.
Some of the files contain tests from statements (examples), while others contain regular tests. It is possible that there are no examples, and it is possible that all tests are examples. Vladimir wants to rename the files so that the examples are the first several tests, all all the next files contain regular tests only.
The only operation Vladimir can perform is the "move" command. Vladimir wants to write a script file, each of the lines in which is "move file_1 file_2", that means that the file "file_1" is to be renamed to "file_2". If there is a file "file_2" at the moment of this line being run, then this file is to be rewritten. After the line "move file_1 file_2" the file "file_1" doesn't exist, but there is a file "file_2" with content equal to the content of "file_1" before the "move" command.
Help Vladimir to write the script file with the minimum possible number of lines so that after this script is run:
- all examples are the first several tests having filenames "1", "2", ..., "*e*", where *e* is the total number of examples; - all other files contain regular tests with filenames "*e*<=+<=1", "*e*<=+<=2", ..., "*n*", where *n* is the total number of all tests. | The first line contains single integer *n* (1<=≤<=*n*<=≤<=105) — the number of files with tests.
*n* lines follow, each describing a file with test. Each line has a form of "name_i type_i", where "name_i" is the filename, and "type_i" equals "1", if the *i*-th file contains an example test, and "0" if it contains a regular test. Filenames of each file are strings of digits and small English letters with length from 1 to 6 characters. The filenames are guaranteed to be distinct. | In the first line print the minimum number of lines in Vladimir's script file.
After that print the script file, each line should be "move file_1 file_2", where "file_1" is an existing at the moment of this line being run filename, and "file_2" — is a string of digits and small English letters with length from 1 to 6. | [
"5\n01 0\n2 1\n2extra 0\n3 1\n99 0\n",
"2\n1 0\n2 1\n",
"5\n1 0\n11 1\n111 0\n1111 1\n11111 0\n"
] | [
"4\nmove 3 1\nmove 01 5\nmove 2extra 4\nmove 99 3\n",
"3\nmove 1 3\nmove 2 1\nmove 3 2",
"5\nmove 1 5\nmove 11 1\nmove 1111 2\nmove 111 4\nmove 11111 3\n"
] | none | [
{
"input": "5\n01 0\n2 1\n2extra 0\n3 1\n99 0",
"output": "4\nmove 3 1\nmove 01 5\nmove 2extra 4\nmove 99 3"
},
{
"input": "2\n1 0\n2 1",
"output": "3\nmove 1 odt0m5\nmove 2 1\nmove odt0m5 2"
},
{
"input": "5\n1 0\n11 1\n111 0\n1111 1\n11111 0",
"output": "5\nmove 1 5\nmove 11 1\nmov... | 46 | 0 | 0 | 3,560 | |
818 | Multicolored Cars | [
"data structures",
"implementation"
] | null | null | Alice and Bob got very bored during a long car trip so they decided to play a game. From the window they can see cars of different colors running past them. Cars are going one after another.
The game rules are like this. Firstly Alice chooses some color *A*, then Bob chooses some color *B* (*A*<=≠<=*B*). After each car they update the number of cars of their chosen color that have run past them. Let's define this numbers after *i*-th car *cnt**A*(*i*) and *cnt**B*(*i*).
- If *cnt**A*(*i*)<=><=*cnt**B*(*i*) for every *i* then the winner is Alice. - If *cnt**B*(*i*)<=≥<=*cnt**A*(*i*) for every *i* then the winner is Bob. - Otherwise it's a draw.
Bob knows all the colors of cars that they will encounter and order of their appearance. Alice have already chosen her color *A* and Bob now wants to choose such color *B* that he will win the game (draw is not a win). Help him find this color.
If there are multiple solutions, print any of them. If there is no such color then print -1. | The first line contains two integer numbers *n* and *A* (1<=≤<=*n*<=≤<=105,<=1<=≤<=*A*<=≤<=106) – number of cars and the color chosen by Alice.
The second line contains *n* integer numbers *c*1,<=*c*2,<=...,<=*c**n* (1<=≤<=*c**i*<=≤<=106) — colors of the cars that Alice and Bob will encounter in the order of their appearance. | Output such color *B* (1<=≤<=*B*<=≤<=106) that if Bob chooses it then he will win the game. If there are multiple solutions, print any of them. If there is no such color then print -1.
It is guaranteed that if there exists any solution then there exists solution with (1<=≤<=*B*<=≤<=106). | [
"4 1\n2 1 4 2\n",
"5 2\n2 2 4 5 3\n",
"3 10\n1 2 3\n"
] | [
"2\n",
"-1\n",
"4\n"
] | Let's consider availability of colors in the first example:
- *cnt*<sub class="lower-index">2</sub>(*i*) ≥ *cnt*<sub class="lower-index">1</sub>(*i*) for every *i*, and color 2 can be the answer. - *cnt*<sub class="lower-index">4</sub>(2) < *cnt*<sub class="lower-index">1</sub>(2), so color 4 isn't the winning one for Bob. - All the other colors also have *cnt*<sub class="lower-index">*j*</sub>(2) < *cnt*<sub class="lower-index">1</sub>(2), thus they are not available.
In the third example every color is acceptable except for 10. | [
{
"input": "4 1\n2 1 4 2",
"output": "2"
},
{
"input": "5 2\n2 2 4 5 3",
"output": "-1"
},
{
"input": "3 10\n1 2 3",
"output": "4"
},
{
"input": "1 1\n2",
"output": "3"
},
{
"input": "1 2\n2",
"output": "-1"
},
{
"input": "10 6\n8 5 1 6 6 5 10 6 9 8",
... | 2,000 | 9,216,000 | 0 | 3,561 | |
899 | Shovel Sale | [
"constructive algorithms",
"math"
] | null | null | There are *n* shovels in Polycarp's shop. The *i*-th shovel costs *i* burles, that is, the first shovel costs 1 burle, the second shovel costs 2 burles, the third shovel costs 3 burles, and so on. Polycarps wants to sell shovels in pairs.
Visitors are more likely to buy a pair of shovels if their total cost ends with several 9s. Because of this, Polycarp wants to choose a pair of shovels to sell in such a way that the sum of their costs ends with maximum possible number of nines. For example, if he chooses shovels with costs 12345 and 37454, their total cost is 49799, it ends with two nines.
You are to compute the number of pairs of shovels such that their total cost ends with maximum possible number of nines. Two pairs are considered different if there is a shovel presented in one pair, but not in the other. | The first line contains a single integer *n* (2<=≤<=*n*<=≤<=109) — the number of shovels in Polycarp's shop. | Print the number of pairs of shovels such that their total cost ends with maximum possible number of nines.
Note that it is possible that the largest number of 9s at the end is 0, then you should count all such ways.
It is guaranteed that for every *n*<=≤<=109 the answer doesn't exceed 2·109. | [
"7\n",
"14\n",
"50\n"
] | [
"3\n",
"9\n",
"1\n"
] | In the first example the maximum possible number of nines at the end is one. Polycarp cah choose the following pairs of shovels for that purpose:
- 2 and 7; - 3 and 6; - 4 and 5.
In the second example the maximum number of nines at the end of total cost of two shovels is one. The following pairs of shovels suit Polycarp:
- 1 and 8; - 2 and 7; - 3 and 6; - 4 and 5; - 5 and 14; - 6 and 13; - 7 and 12; - 8 and 11; - 9 and 10.
In the third example it is necessary to choose shovels 49 and 50, because the sum of their cost is 99, that means that the total number of nines is equal to two, which is maximum possible for *n* = 50. | [
{
"input": "7",
"output": "3"
},
{
"input": "14",
"output": "9"
},
{
"input": "50",
"output": "1"
},
{
"input": "999999999",
"output": "499999999"
},
{
"input": "15",
"output": "11"
},
{
"input": "3",
"output": "3"
},
{
"input": "6500",
... | 46 | 0 | 0 | 3,563 | |
234 | Weather | [
"dp",
"implementation"
] | null | null | Scientists say a lot about the problems of global warming and cooling of the Earth. Indeed, such natural phenomena strongly influence all life on our planet.
Our hero Vasya is quite concerned about the problems. He decided to try a little experiment and observe how outside daily temperature changes. He hung out a thermometer on the balcony every morning and recorded the temperature. He had been measuring the temperature for the last *n* days. Thus, he got a sequence of numbers *t*1,<=*t*2,<=...,<=*t**n*, where the *i*-th number is the temperature on the *i*-th day.
Vasya analyzed the temperature statistics in other cities, and came to the conclusion that the city has no environmental problems, if first the temperature outside is negative for some non-zero number of days, and then the temperature is positive for some non-zero number of days. More formally, there must be a positive integer *k* (1<=≤<=*k*<=≤<=*n*<=-<=1) such that *t*1<=<<=0,<=*t*2<=<<=0,<=...,<=*t**k*<=<<=0 and *t**k*<=+<=1<=><=0,<=*t**k*<=+<=2<=><=0,<=...,<=*t**n*<=><=0. In particular, the temperature should never be zero. If this condition is not met, Vasya decides that his city has environmental problems, and gets upset.
You do not want to upset Vasya. Therefore, you want to select multiple values of temperature and modify them to satisfy Vasya's condition. You need to know what the least number of temperature values needs to be changed for that. | The first line contains a single integer *n* (2<=≤<=*n*<=≤<=105) — the number of days for which Vasya has been measuring the temperature.
The second line contains a sequence of *n* integers *t*1,<=*t*2,<=...,<=*t**n* (|*t**i*|<=≤<=109) — the sequence of temperature values. Numbers *t**i* are separated by single spaces. | Print a single integer — the answer to the given task. | [
"4\n-1 1 -2 1\n",
"5\n0 -1 1 2 -5\n"
] | [
"1\n",
"2\n"
] | Note to the first sample: there are two ways to change exactly one number so that the sequence met Vasya's condition. You can either replace the first number 1 by any negative number or replace the number -2 by any positive number. | [
{
"input": "4\n-1 1 -2 1",
"output": "1"
},
{
"input": "5\n0 -1 1 2 -5",
"output": "2"
},
{
"input": "6\n0 0 0 0 0 0",
"output": "6"
},
{
"input": "6\n-1 -2 -3 -4 5 6",
"output": "0"
},
{
"input": "8\n1 2 -1 0 10 2 12 13",
"output": "3"
},
{
"input": "... | 342 | 15,872,000 | 3 | 3,565 | |
400 | Inna and Huge Candy Matrix | [
"implementation",
"math"
] | null | null | Inna and Dima decided to surprise Sereja. They brought a really huge candy matrix, it's big even for Sereja! Let's number the rows of the giant matrix from 1 to *n* from top to bottom and the columns — from 1 to *m*, from left to right. We'll represent the cell on the intersection of the *i*-th row and *j*-th column as (*i*,<=*j*). Just as is expected, some cells of the giant candy matrix contain candies. Overall the matrix has *p* candies: the *k*-th candy is at cell (*x**k*,<=*y**k*).
The time moved closer to dinner and Inna was already going to eat *p* of her favourite sweets from the matrix, when suddenly Sereja (for the reason he didn't share with anyone) rotated the matrix *x* times clockwise by 90 degrees. Then he performed the horizontal rotate of the matrix *y* times. And then he rotated the matrix *z* times counterclockwise by 90 degrees. The figure below shows how the rotates of the matrix looks like.
Inna got really upset, but Duma suddenly understood two things: the candies didn't get damaged and he remembered which cells contained Inna's favourite sweets before Sereja's strange actions. Help guys to find the new coordinates in the candy matrix after the transformation Sereja made! | The first line of the input contains fix integers *n*, *m*, *x*, *y*, *z*, *p* (1<=≤<=*n*,<=*m*<=≤<=109; 0<=≤<=*x*,<=*y*,<=*z*<=≤<=109; 1<=≤<=*p*<=≤<=105).
Each of the following *p* lines contains two integers *x**k*, *y**k* (1<=≤<=*x**k*<=≤<=*n*; 1<=≤<=*y**k*<=≤<=*m*) — the initial coordinates of the *k*-th candy. Two candies can lie on the same cell. | For each of the *p* candies, print on a single line its space-separated new coordinates. | [
"3 3 3 1 1 9\n1 1\n1 2\n1 3\n2 1\n2 2\n2 3\n3 1\n3 2\n3 3\n"
] | [
"1 3\n1 2\n1 1\n2 3\n2 2\n2 1\n3 3\n3 2\n3 1\n"
] | Just for clarity. Horizontal rotating is like a mirroring of the matrix. For matrix: | [
{
"input": "3 3 3 1 1 9\n1 1\n1 2\n1 3\n2 1\n2 2\n2 3\n3 1\n3 2\n3 3",
"output": "1 3\n1 2\n1 1\n2 3\n2 2\n2 1\n3 3\n3 2\n3 1"
},
{
"input": "5 5 0 0 0 1\n1 4",
"output": "1 4"
},
{
"input": "14 76 376219315 550904689 16684615 24\n11 21\n1 65\n5 25\n14 63\n11 30\n1 19\n5 7\n9 51\n2 49\n1... | 46 | 0 | 0 | 3,567 | |
0 | none | [
"none"
] | null | null | For an array $b$ of length $m$ we define the function $f$ as
where $\oplus$ is [bitwise exclusive OR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
For example, $f(1,2,4,8)=f(1\oplus2,2\oplus4,4\oplus8)=f(3,6,12)=f(3\oplus6,6\oplus12)=f(5,10)=f(5\oplus10)=f(15)=15$
You are given an array $a$ and a few queries. Each query is represented as two integers $l$ and $r$. The answer is the maximum value of $f$ on all continuous subsegments of the array $a_l, a_{l+1}, \ldots, a_r$. | The first line contains a single integer $n$ ($1 \le n \le 5000$) — the length of $a$.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$) — the elements of the array.
The third line contains a single integer $q$ ($1 \le q \le 100\,000$) — the number of queries.
Each of the next $q$ lines contains a query represented as two integers $l$, $r$ ($1 \le l \le r \le n$). | Print $q$ lines — the answers for the queries. | [
"3\n8 4 1\n2\n2 3\n1 2\n",
"6\n1 2 4 8 16 32\n4\n1 6\n2 5\n3 4\n1 2\n"
] | [
"5\n12\n",
"60\n30\n12\n3\n"
] | In first sample in both queries the maximum value of the function is reached on the subsegment that is equal to the whole segment.
In second sample, optimal segment for first query are $[3,6]$, for second query — $[2,5]$, for third — $[3,4]$, for fourth — $[1,2]$. | [
{
"input": "3\n8 4 1\n2\n2 3\n1 2",
"output": "5\n12"
},
{
"input": "6\n1 2 4 8 16 32\n4\n1 6\n2 5\n3 4\n1 2",
"output": "60\n30\n12\n3"
}
] | 93 | 0 | 0 | 3,574 | |
817 | Imbalanced Array | [
"data structures",
"divide and conquer",
"dsu",
"sortings"
] | null | null | You are given an array *a* consisting of *n* elements. The imbalance value of some subsegment of this array is the difference between the maximum and minimum element from this segment. The imbalance value of the array is the sum of imbalance values of all subsegments of this array.
For example, the imbalance value of array [1,<=4,<=1] is 9, because there are 6 different subsegments of this array:
- [1] (from index 1 to index 1), imbalance value is 0; - [1,<=4] (from index 1 to index 2), imbalance value is 3; - [1,<=4,<=1] (from index 1 to index 3), imbalance value is 3; - [4] (from index 2 to index 2), imbalance value is 0; - [4,<=1] (from index 2 to index 3), imbalance value is 3; - [1] (from index 3 to index 3), imbalance value is 0;
You have to determine the imbalance value of the array *a*. | The first line contains one integer *n* (1<=≤<=*n*<=≤<=106) — size of the array *a*.
The second line contains *n* integers *a*1,<=*a*2... *a**n* (1<=≤<=*a**i*<=≤<=106) — elements of the array. | Print one integer — the imbalance value of *a*. | [
"3\n1 4 1\n"
] | [
"9\n"
] | none | [
{
"input": "3\n1 4 1",
"output": "9"
},
{
"input": "10\n1 1 1 1 1 1 1 1 1 1",
"output": "0"
},
{
"input": "10\n1 4 4 3 5 2 4 2 4 5",
"output": "123"
},
{
"input": "10\n9 6 8 5 5 2 8 9 2 2",
"output": "245"
},
{
"input": "30\n4 5 2 2 5 2 3 4 3 3 2 1 3 4 4 5 3 3 1 5... | 2,000 | 12,083,200 | 0 | 3,599 | |
0 | none | [
"none"
] | null | null | One day in the IT lesson Anna and Maria learned about the lexicographic order.
String *x* is lexicographically less than string *y*, if either *x* is a prefix of *y* (and *x*<=≠<=*y*), or there exists such *i* (1<=≤<=*i*<=≤<=*min*(|*x*|,<=|*y*|)), that *x**i*<=<<=*y**i*, and for any *j* (1<=≤<=*j*<=<<=*i*) *x**j*<==<=*y**j*. Here |*a*| denotes the length of the string *a*. The lexicographic comparison of strings is implemented by operator < in modern programming languages.
The teacher gave Anna and Maria homework. She gave them a string of length *n*. They should write out all substrings of the given string, including the whole initial string, and the equal substrings (for example, one should write out the following substrings from the string "aab": "a", "a", "aa", "ab", "aab", "b"). The resulting strings should be sorted in the lexicographical order. The cunning teacher doesn't want to check all these strings. That's why she said to find only the *k*-th string from the list. Help Anna and Maria do the homework. | The first line contains a non-empty string that only consists of small Latin letters ("a"-"z"), whose length does not exceed 105. The second line contains the only integer *k* (1<=≤<=*k*<=≤<=105). | Print the string Anna and Maria need — the *k*-th (in the lexicographical order) substring of the given string. If the total number of substrings is less than *k*, print a string saying "No such line." (without the quotes). | [
"aa\n2\n",
"abc\n5\n",
"abab\n7\n"
] | [
"a\n",
"bc\n",
"b\n"
] | In the second sample before string "bc" follow strings "a", "ab", "abc", "b". | [
{
"input": "aa\n2",
"output": "a"
},
{
"input": "abc\n5",
"output": "bc"
},
{
"input": "abab\n7",
"output": "b"
},
{
"input": "codeforces\n1",
"output": "c"
},
{
"input": "cccc\n8",
"output": "ccc"
},
{
"input": "abcdefghijklmnopqrstuvwxyz\n27",
"o... | 2,000 | 15,052,800 | 0 | 3,609 | |
290 | Greedy Petya | [
"*special",
"dfs and similar",
"graphs",
"greedy"
] | null | null | Petya is an unexperienced programming contestant. Recently he has come across the following problem:
You are given a non-directed graph which consists of *n* nodes and *m* edges. Your task is to determine whether the graph contains a Hamiltonian path.
Petya wrote a quick bug-free code which he believes solves this problem. After that Petya decided to give this problem for April Fools Day contest. Unfortunately, Petya might have made a mistake, and it's quite possible that his algorithm is wrong. But this isn't a good excuse to leave the contest without submitting this problem, is it? | The first line contains two integers *n*,<=*m* (1<=≤<=*n*<=≤<=20; 0<=≤<=*m*<=≤<=400). Next *m* lines contain pairs of integers *v**i*,<=*u**i* (1<=≤<=*v**i*,<=*u**i*<=≤<=*n*). | Follow the format of Petya's code output. | [
"2 3\n1 2\n2 1\n1 1\n",
"3 0\n",
"10 20\n3 10\n4 6\n4 9\n7 5\n8 8\n3 10\n9 7\n5 2\n9 2\n10 6\n10 4\n1 1\n7 2\n8 4\n7 2\n1 8\n5 4\n10 2\n8 5\n5 2\n"
] | [
"Yes\n",
"No\n",
"No\n"
] | none | [] | 62 | 0 | 0 | 3,619 | |
1,003 | Binary String Constructing | [
"constructive algorithms"
] | null | null | You are given three integers $a$, $b$ and $x$. Your task is to construct a binary string $s$ of length $n = a + b$ such that there are exactly $a$ zeroes, exactly $b$ ones and exactly $x$ indices $i$ (where $1 \le i < n$) such that $s_i \ne s_{i + 1}$. It is guaranteed that the answer always exists.
For example, for the string "01010" there are four indices $i$ such that $1 \le i < n$ and $s_i \ne s_{i + 1}$ ($i = 1, 2, 3, 4$). For the string "111001" there are two such indices $i$ ($i = 3, 5$).
Recall that binary string is a non-empty sequence of characters where each character is either 0 or 1. | The first line of the input contains three integers $a$, $b$ and $x$ ($1 \le a, b \le 100, 1 \le x < a + b)$. | Print only one string $s$, where $s$ is any binary string satisfying conditions described above. It is guaranteed that the answer always exists. | [
"2 2 1\n",
"3 3 3\n",
"5 3 6\n"
] | [
"1100\n",
"101100\n",
"01010100\n"
] | All possible answers for the first example:
- 1100; - 0011.
All possible answers for the second example:
- 110100; - 101100; - 110010; - 100110; - 011001; - 001101; - 010011; - 001011. | [
{
"input": "2 2 1",
"output": "1100"
},
{
"input": "3 3 3",
"output": "101100"
},
{
"input": "5 3 6",
"output": "01010100"
},
{
"input": "100 1 2",
"output": "01000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
},
{
... | 327 | 30,208,000 | 0 | 3,628 | |
300 | Coach | [
"brute force",
"dfs and similar",
"graphs"
] | null | null | A programming coach has *n* students to teach. We know that *n* is divisible by 3. Let's assume that all students are numbered from 1 to *n*, inclusive.
Before the university programming championship the coach wants to split all students into groups of three. For some pairs of students we know that they want to be on the same team. Besides, if the *i*-th student wants to be on the same team with the *j*-th one, then the *j*-th student wants to be on the same team with the *i*-th one. The coach wants the teams to show good results, so he wants the following condition to hold: if the *i*-th student wants to be on the same team with the *j*-th, then the *i*-th and the *j*-th students must be on the same team. Also, it is obvious that each student must be on exactly one team.
Help the coach and divide the teams the way he wants. | The first line of the input contains integers *n* and *m* (3<=≤<=*n*<=≤<=48, . Then follow *m* lines, each contains a pair of integers *a**i*,<=*b**i* (1<=≤<=*a**i*<=<<=*b**i*<=≤<=*n*) — the pair *a**i*,<=*b**i* means that students with numbers *a**i* and *b**i* want to be on the same team.
It is guaranteed that *n* is divisible by 3. It is guaranteed that each pair *a**i*,<=*b**i* occurs in the input at most once. | If the required division into teams doesn't exist, print number -1. Otherwise, print lines. In each line print three integers *x**i*, *y**i*, *z**i* (1<=≤<=*x**i*,<=*y**i*,<=*z**i*<=≤<=*n*) — the *i*-th team.
If there are multiple answers, you are allowed to print any of them. | [
"3 0\n",
"6 4\n1 2\n2 3\n3 4\n5 6\n",
"3 3\n1 2\n2 3\n1 3\n"
] | [
"3 2 1 \n",
"-1\n",
"3 2 1 \n"
] | none | [
{
"input": "3 0",
"output": "3 2 1 "
},
{
"input": "6 4\n1 2\n2 3\n3 4\n5 6",
"output": "-1"
},
{
"input": "3 3\n1 2\n2 3\n1 3",
"output": "3 2 1 "
},
{
"input": "6 3\n1 2\n3 4\n5 6",
"output": "-1"
},
{
"input": "15 9\n1 4\n1 6\n2 7\n2 11\n4 6\n5 12\n7 11\n9 14\n... | 62 | 0 | -1 | 3,630 | |
613 | Peter and Snow Blower | [
"binary search",
"geometry",
"ternary search"
] | null | null | Peter got a new snow blower as a New Year present. Of course, Peter decided to try it immediately. After reading the instructions he realized that it does not work like regular snow blowing machines. In order to make it work, you need to tie it to some point that it does not cover, and then switch it on. As a result it will go along a circle around this point and will remove all the snow from its path.
Formally, we assume that Peter's machine is a polygon on a plane. Then, after the machine is switched on, it will make a circle around the point to which Peter tied it (this point lies strictly outside the polygon). That is, each of the points lying within or on the border of the polygon will move along the circular trajectory, with the center of the circle at the point to which Peter tied his machine.
Peter decided to tie his car to point *P* and now he is wondering what is the area of the region that will be cleared from snow. Help him. | The first line of the input contains three integers — the number of vertices of the polygon *n* (), and coordinates of point *P*.
Each of the next *n* lines contains two integers — coordinates of the vertices of the polygon in the clockwise or counterclockwise order. It is guaranteed that no three consecutive vertices lie on a common straight line.
All the numbers in the input are integers that do not exceed 1<=000<=000 in their absolute value. | Print a single real value number — the area of the region that will be cleared. Your answer will be considered correct if its absolute or relative error does not exceed 10<=-<=6.
Namely: let's assume that your answer is *a*, and the answer of the jury is *b*. The checker program will consider your answer correct, if . | [
"3 0 0\n0 1\n-1 2\n1 2\n",
"4 1 -1\n0 0\n1 2\n2 0\n1 1\n"
] | [
"12.566370614359172464\n",
"21.991148575128551812\n"
] | In the first sample snow will be removed from that area: | [
{
"input": "3 0 0\n0 1\n-1 2\n1 2",
"output": "12.566370614359172464"
},
{
"input": "4 1 -1\n0 0\n1 2\n2 0\n1 1",
"output": "21.991148575128551812"
},
{
"input": "3 0 0\n-1 1\n0 3\n1 1",
"output": "25.132741228718344928"
},
{
"input": "3 -4 2\n-3 2\n5 -5\n5 3",
"output": ... | 46 | 0 | 0 | 3,642 | |
440 | Balancer | [
"greedy",
"implementation"
] | null | null | Petya has *k* matches, placed in *n* matchboxes lying in a line from left to right. We know that *k* is divisible by *n*. Petya wants all boxes to have the same number of matches inside. For that, he can move a match from its box to the adjacent one in one move. How many such moves does he need to achieve the desired configuration? | The first line contains integer *n* (1<=≤<=*n*<=≤<=50000). The second line contains *n* non-negative numbers that do not exceed 109, the *i*-th written number is the number of matches in the *i*-th matchbox. It is guaranteed that the total number of matches is divisible by *n*. | Print the total minimum number of moves. | [
"6\n1 6 2 5 3 7\n"
] | [
"12\n"
] | none | [
{
"input": "6\n1 6 2 5 3 7",
"output": "12"
},
{
"input": "6\n6 6 6 0 0 0",
"output": "27"
},
{
"input": "6\n0 0 0 6 6 6",
"output": "27"
},
{
"input": "6\n6 6 0 0 6 6",
"output": "12"
},
{
"input": "5\n0 0 0 0 0",
"output": "0"
},
{
"input": "10\n0 10... | 500 | 921,600 | 0 | 3,646 | |
452 | Magic Trick | [
"combinatorics",
"math",
"probabilities"
] | null | null | Alex enjoys performing magic tricks. He has a trick that requires a deck of *n* cards. He has *m* identical decks of *n* different cards each, which have been mixed together. When Alex wishes to perform the trick, he grabs *n* cards at random and performs the trick with those. The resulting deck looks like a normal deck, but may have duplicates of some cards.
The trick itself is performed as follows: first Alex allows you to choose a random card from the deck. You memorize the card and put it back in the deck. Then Alex shuffles the deck, and pulls out a card. If the card matches the one you memorized, the trick is successful.
You don't think Alex is a very good magician, and that he just pulls a card randomly from the deck. Determine the probability of the trick being successful if this is the case. | First line of the input consists of two integers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=1000), separated by space — number of cards in each deck, and number of decks. | On the only line of the output print one floating point number – probability of Alex successfully performing the trick. Relative or absolute error of your answer should not be higher than 10<=-<=6. | [
"2 2\n",
"4 4\n",
"1 2\n"
] | [
"0.6666666666666666\n",
"0.4000000000000000\n",
"1.0000000000000000\n"
] | In the first sample, with probability <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/64c94d13eeb330b494061e86538db66574ad0f7d.png" style="max-width: 100.0%;max-height: 100.0%;"/> Alex will perform the trick with two cards with the same value from two different decks. In this case the trick is guaranteed to succeed.
With the remaining <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/14b21b617fcd2e25700376368355f7bbf975d8de.png" style="max-width: 100.0%;max-height: 100.0%;"/> probability he took two different cards, and the probability of pulling off the trick is <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/eb946338365d9781f7d2e9ec692c26702d0ae3a7.png" style="max-width: 100.0%;max-height: 100.0%;"/>.
The resulting probability is <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/f54a03c9fa9df64ba08161730756d50b780a5f43.png" style="max-width: 100.0%;max-height: 100.0%;"/> | [
{
"input": "2 2",
"output": "0.6666666666666666"
},
{
"input": "4 4",
"output": "0.4000000000000000"
},
{
"input": "1 2",
"output": "1.0000000000000000"
},
{
"input": "2 1",
"output": "0.5000000000000000"
},
{
"input": "10 10",
"output": "0.1818181818181818"
... | 155 | 1,638,400 | 3 | 3,648 | |
851 | Arpa and an exam about geometry | [
"geometry",
"math"
] | null | null | Arpa is taking a geometry exam. Here is the last problem of the exam.
You are given three points *a*,<=*b*,<=*c*.
Find a point and an angle such that if we rotate the page around the point by the angle, the new position of *a* is the same as the old position of *b*, and the new position of *b* is the same as the old position of *c*.
Arpa is doubting if the problem has a solution or not (i.e. if there exists a point and an angle satisfying the condition). Help Arpa determine if the question has a solution or not. | The only line contains six integers *a**x*,<=*a**y*,<=*b**x*,<=*b**y*,<=*c**x*,<=*c**y* (|*a**x*|,<=|*a**y*|,<=|*b**x*|,<=|*b**y*|,<=|*c**x*|,<=|*c**y*|<=≤<=109). It's guaranteed that the points are distinct. | Print "Yes" if the problem has a solution, "No" otherwise.
You can print each letter in any case (upper or lower). | [
"0 1 1 1 1 0\n",
"1 1 0 0 1000 1000\n"
] | [
"Yes\n",
"No\n"
] | In the first sample test, rotate the page around (0.5, 0.5) by <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/9d845923f4d356a48d8ede337db0303821311f0c.png" style="max-width: 100.0%;max-height: 100.0%;"/>.
In the second sample test, you can't find any solution. | [
{
"input": "0 1 1 1 1 0",
"output": "Yes"
},
{
"input": "1 1 0 0 1000 1000",
"output": "No"
},
{
"input": "1 0 2 0 3 0",
"output": "No"
},
{
"input": "3 4 0 0 4 3",
"output": "Yes"
},
{
"input": "-1000000000 1 0 0 1000000000 1",
"output": "Yes"
},
{
"i... | 61 | 5,529,600 | 0 | 3,660 | |
920 | SUM and REPLACE | [
"brute force",
"data structures",
"dsu",
"number theory"
] | null | null | Let *D*(*x*) be the number of positive divisors of a positive integer *x*. For example, *D*(2)<==<=2 (2 is divisible by 1 and 2), *D*(6)<==<=4 (6 is divisible by 1, 2, 3 and 6).
You are given an array *a* of *n* integers. You have to process two types of queries:
1. REPLACE *l* *r* — for every replace *a**i* with *D*(*a**i*); 1. SUM *l* *r* — calculate .
Print the answer for each SUM query. | The first line contains two integers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=3·105) — the number of elements in the array and the number of queries to process, respectively.
The second line contains *n* integers *a*1, *a*2, ..., *a**n* (1<=≤<=*a**i*<=≤<=106) — the elements of the array.
Then *m* lines follow, each containing 3 integers *t**i*, *l**i*, *r**i* denoting *i*-th query. If *t**i*<==<=1, then *i*-th query is REPLACE *l**i* *r**i*, otherwise it's SUM *l**i* *r**i* (1<=≤<=*t**i*<=≤<=2, 1<=≤<=*l**i*<=≤<=*r**i*<=≤<=*n*).
There is at least one SUM query. | For each SUM query print the answer to it. | [
"7 6\n6 4 1 10 3 2 4\n2 1 7\n2 4 5\n1 3 5\n2 4 4\n1 5 7\n2 1 7\n"
] | [
"30\n13\n4\n22\n"
] | none | [
{
"input": "7 6\n6 4 1 10 3 2 4\n2 1 7\n2 4 5\n1 3 5\n2 4 4\n1 5 7\n2 1 7",
"output": "30\n13\n4\n22"
},
{
"input": "4 2\n1 1 1 3\n1 1 4\n2 1 4",
"output": "5"
},
{
"input": "10 2\n1 1 1 1 1 1 1 1 1 9\n1 1 10\n2 1 10",
"output": "12"
},
{
"input": "4 2\n1 1 3 1\n1 1 4\n2 1 4"... | 2,000 | 19,558,400 | 0 | 3,673 | |
665 | Buses Between Cities | [
"implementation"
] | null | null | Buses run between the cities *A* and *B*, the first one is at 05:00 AM and the last one departs not later than at 11:59 PM. A bus from the city *A* departs every *a* minutes and arrives to the city *B* in a *t**a* minutes, and a bus from the city *B* departs every *b* minutes and arrives to the city *A* in a *t**b* minutes.
The driver Simion wants to make his job diverse, so he counts the buses going towards him. Simion doesn't count the buses he meet at the start and finish.
You know the time when Simion departed from the city *A* to the city *B*. Calculate the number of buses Simion will meet to be sure in his counting. | The first line contains two integers *a*,<=*t**a* (1<=≤<=*a*,<=*t**a*<=≤<=120) — the frequency of the buses from the city *A* to the city *B* and the travel time. Both values are given in minutes.
The second line contains two integers *b*,<=*t**b* (1<=≤<=*b*,<=*t**b*<=≤<=120) — the frequency of the buses from the city *B* to the city *A* and the travel time. Both values are given in minutes.
The last line contains the departure time of Simion from the city *A* in the format hh:mm. It is guaranteed that there are a bus from the city *A* at that time. Note that the hours and the minutes are given with exactly two digits. | Print the only integer *z* — the number of buses Simion will meet on the way. Note that you should not count the encounters in cities *A* and *B*. | [
"10 30\n10 35\n05:20\n",
"60 120\n24 100\n13:00\n"
] | [
"5\n",
"9\n"
] | In the first example Simion departs form the city *A* at 05:20 AM and arrives to the city *B* at 05:50 AM. He will meet the first 5 buses from the city *B* that departed in the period [05:00 AM - 05:40 AM]. Also Simion will meet a bus in the city *B* at 05:50 AM, but he will not count it.
Also note that the first encounter will be between 05:26 AM and 05:27 AM (if we suggest that the buses are go with the sustained speed). | [
{
"input": "10 30\n10 35\n05:20",
"output": "5"
},
{
"input": "60 120\n24 100\n13:00",
"output": "9"
},
{
"input": "30 60\n60 60\n22:30",
"output": "2"
},
{
"input": "30 60\n10 60\n23:30",
"output": "8"
},
{
"input": "5 45\n4 60\n21:00",
"output": "26"
},
... | 186 | 23,244,800 | 3 | 3,674 | |
412 | Pattern | [
"implementation",
"strings"
] | null | null | Developers often face with regular expression patterns. A pattern is usually defined as a string consisting of characters and metacharacters that sets the rules for your search. These patterns are most often used to check whether a particular string meets the certain rules.
In this task, a pattern will be a string consisting of small English letters and question marks ('?'). The question mark in the pattern is a metacharacter that denotes an arbitrary small letter of the English alphabet. We will assume that a string matches the pattern if we can transform the string into the pattern by replacing the question marks by the appropriate characters. For example, string aba matches patterns: ???, ??a, a?a, aba.
Programmers that work for the R1 company love puzzling each other (and themselves) with riddles. One of them is as follows: you are given *n* patterns of the same length, you need to find a pattern that contains as few question marks as possible, and intersects with each of the given patterns. Two patterns intersect if there is a string that matches both the first and the second pattern. Can you solve this riddle? | The first line contains a single integer *n* (1<=≤<=*n*<=≤<=105) — the number of patterns. Next *n* lines contain the patterns.
It is guaranteed that the patterns can only consist of small English letters and symbols '?'. All patterns are non-empty and have the same length. The total length of all the patterns does not exceed 105 characters. | In a single line print the answer to the problem — the pattern with the minimal number of signs '?', which intersects with each of the given ones. If there are several answers, print any of them. | [
"2\n?ab\n??b\n",
"2\na\nb\n",
"1\n?a?b\n"
] | [
"xab\n",
"?\n",
"cacb\n"
] | Consider the first example. Pattern xab intersects with each of the given patterns. Pattern ??? also intersects with each of the given patterns, but it contains more question signs, hence it is not an optimal answer. Clearly, xab is the optimal answer, because it doesn't contain any question sign. There are a lot of other optimal answers, for example: aab, bab, cab, dab and so on. | [
{
"input": "2\n?ab\n??b",
"output": "xab"
},
{
"input": "2\na\nb",
"output": "?"
},
{
"input": "1\n?a?b",
"output": "cacb"
},
{
"input": "1\n?",
"output": "x"
},
{
"input": "3\nabacaba\nabacaba\nabacaba",
"output": "abacaba"
},
{
"input": "3\nabc?t\n?b... | 218 | 4,198,400 | 3 | 3,678 | |
312 | Whose sentence is it? | [
"implementation",
"strings"
] | null | null | One day, liouzhou_101 got a chat record of Freda and Rainbow. Out of curiosity, he wanted to know which sentences were said by Freda, and which were said by Rainbow. According to his experience, he thought that Freda always said "lala." at the end of her sentences, while Rainbow always said "miao." at the beginning of his sentences. For each sentence in the chat record, help liouzhou_101 find whose sentence it is. | The first line of the input contains an integer *n* (1<=≤<=*n*<=≤<=10), number of sentences in the chat record. Each of the next *n* lines contains a sentence. A sentence is a string that contains only Latin letters (A-Z, a-z), underline (_), comma (,), point (.) and space ( ). Its length doesn’t exceed 100. | For each sentence, output "Freda's" if the sentence was said by Freda, "Rainbow's" if the sentence was said by Rainbow, or "OMG>.< I don't know!" if liouzhou_101 can’t recognize whose sentence it is. He can’t recognize a sentence if it begins with "miao." and ends with "lala.", or satisfies neither of the conditions. | [
"5\nI will go to play with you lala.\nwow, welcome.\nmiao.lala.\nmiao.\nmiao .\n"
] | [
"Freda's\nOMG>.< I don't know!\nOMG>.< I don't know!\nRainbow's\nOMG>.< I don't know!\n"
] | none | [
{
"input": "5\nI will go to play with you lala.\nwow, welcome.\nmiao.lala.\nmiao.\nmiao .",
"output": "Freda's\nOMG>.< I don't know!\nOMG>.< I don't know!\nRainbow's\nOMG>.< I don't know!"
},
{
"input": "10\nLpAEKiHVJrzSZqBVSSyY\nYECGBlala.\nUZeGpeM.UCwiHmmA\nqt_,.b_.LSwJtJ.\nFAnXZtHlala.\nmiao.iape... | 124 | 2,048,000 | -1 | 3,681 | |
932 | Palindromic Supersequence | [
"constructive algorithms"
] | null | null | You are given a string *A*. Find a string *B*, where *B* is a palindrome and *A* is a subsequence of *B*.
A subsequence of a string is a string that can be derived from it by deleting some (not necessarily consecutive) characters without changing the order of the remaining characters. For example, "cotst" is a subsequence of "contest".
A palindrome is a string that reads the same forward or backward.
The length of string *B* should be at most 104. It is guaranteed that there always exists such string.
You do not need to find the shortest answer, the only restriction is that the length of string *B* should not exceed 104. | First line contains a string *A* (1<=≤<=|*A*|<=≤<=103) consisting of lowercase Latin letters, where |*A*| is a length of *A*. | Output single line containing *B* consisting of only lowercase Latin letters. You do not need to find the shortest answer, the only restriction is that the length of string *B* should not exceed 104. If there are many possible *B*, print any of them. | [
"aba\n",
"ab\n"
] | [
"aba",
"aabaa"
] | In the first example, "aba" is a subsequence of "aba" which is a palindrome.
In the second example, "ab" is a subsequence of "aabaa" which is a palindrome. | [
{
"input": "aba",
"output": "abaaba"
},
{
"input": "ab",
"output": "abba"
},
{
"input": "krnyoixirslfszfqivgkaflgkctvbvksipwomqxlyqxhlbceuhbjbfnhofcgpgwdseffycthmlpcqejgskwjkbkbbmifnurnwyhevsoqzmtvzgfiqajfrgyuzxnrtxectcnlyoisbglpdbjbslxlpoymrcxmdtqhcnlvtqdwftuzgbdxsyscwbrguostbelnvtaqdmk... | 77 | 5,632,000 | 3 | 3,694 | |
670 | Game of Robots | [
"implementation"
] | null | null | In late autumn evening *n* robots gathered in the cheerful company of friends. Each robot has a unique identifier — an integer from 1 to 109.
At some moment, robots decided to play the game "Snowball". Below there are the rules of this game. First, all robots stand in a row. Then the first robot says his identifier. After that the second robot says the identifier of the first robot and then says his own identifier. Then the third robot says the identifier of the first robot, then says the identifier of the second robot and after that says his own. This process continues from left to right until the *n*-th robot says his identifier.
Your task is to determine the *k*-th identifier to be pronounced. | The first line contains two positive integers *n* and *k* (1<=≤<=*n*<=≤<=100<=000, 1<=≤<=*k*<=≤<=*min*(2·109,<=*n*·(*n*<=+<=1)<=/<=2).
The second line contains the sequence *id*1,<=*id*2,<=...,<=*id**n* (1<=≤<=*id**i*<=≤<=109) — identifiers of roborts. It is guaranteed that all identifiers are different. | Print the *k*-th pronounced identifier (assume that the numeration starts from 1). | [
"2 2\n1 2\n",
"4 5\n10 4 18 3\n"
] | [
"1\n",
"4\n"
] | In the first sample identifiers of robots will be pronounced in the following order: 1, 1, 2. As *k* = 2, the answer equals to 1.
In the second test case identifiers of robots will be pronounced in the following order: 10, 10, 4, 10, 4, 18, 10, 4, 18, 3. As *k* = 5, the answer equals to 4. | [
{
"input": "2 2\n1 2",
"output": "1"
},
{
"input": "4 5\n10 4 18 3",
"output": "4"
},
{
"input": "1 1\n4",
"output": "4"
},
{
"input": "2 1\n5 1",
"output": "5"
},
{
"input": "2 2\n1 4",
"output": "1"
},
{
"input": "2 3\n6 7",
"output": "7"
},
... | 1,013 | 268,390,400 | 0 | 3,695 | |
644 | Hostname Aliases | [
"*special",
"binary search",
"data structures",
"implementation",
"sortings",
"strings"
] | null | null | There are some websites that are accessible through several different addresses. For example, for a long time Codeforces was accessible with two hostnames codeforces.com and codeforces.ru.
You are given a list of page addresses being queried. For simplicity we consider all addresses to have the form http://<hostname>[/<path>], where:
- <hostname> — server name (consists of words and maybe some dots separating them), - /<path> — optional part, where <path> consists of words separated by slashes.
We consider two <hostname> to correspond to one website if for each query to the first <hostname> there will be exactly the same query to the second one and vice versa — for each query to the second <hostname> there will be the same query to the first one. Take a look at the samples for further clarifications.
Your goal is to determine the groups of server names that correspond to one website. Ignore groups consisting of the only server name.
Please note, that according to the above definition queries http://<hostname> and http://<hostname>/ are different. | The first line of the input contains a single integer *n* (1<=≤<=*n*<=≤<=100<=000) — the number of page queries. Then follow *n* lines each containing exactly one address. Each address is of the form http://<hostname>[/<path>], where:
- <hostname> consists of lowercase English letters and dots, there are no two consecutive dots, <hostname> doesn't start or finish with a dot. The length of <hostname> is positive and doesn't exceed 20. - <path> consists of lowercase English letters, dots and slashes. There are no two consecutive slashes, <path> doesn't start with a slash and its length doesn't exceed 20.
Addresses are not guaranteed to be distinct. | First print *k* — the number of groups of server names that correspond to one website. You should count only groups of size greater than one.
Next *k* lines should contain the description of groups, one group per line. For each group print all server names separated by a single space. You are allowed to print both groups and names inside any group in arbitrary order. | [
"10\nhttp://abacaba.ru/test\nhttp://abacaba.ru/\nhttp://abacaba.com\nhttp://abacaba.com/test\nhttp://abacaba.de/\nhttp://abacaba.ru/test\nhttp://abacaba.de/test\nhttp://abacaba.com/\nhttp://abacaba.com/t\nhttp://abacaba.com/test\n",
"14\nhttp://c\nhttp://ccc.bbbb/aba..b\nhttp://cba.com\nhttp://a.c/aba..b/a\nhttp:... | [
"1\nhttp://abacaba.de http://abacaba.ru \n",
"2\nhttp://cba.com http://ccc.bbbb \nhttp://a.a.a http://a.c http://abc \n"
] | none | [
{
"input": "10\nhttp://abacaba.ru/test\nhttp://abacaba.ru/\nhttp://abacaba.com\nhttp://abacaba.com/test\nhttp://abacaba.de/\nhttp://abacaba.ru/test\nhttp://abacaba.de/test\nhttp://abacaba.com/\nhttp://abacaba.com/t\nhttp://abacaba.com/test",
"output": "1\nhttp://abacaba.de http://abacaba.ru "
},
{
"... | 0 | 0 | -1 | 3,703 | |
0 | none | [
"none"
] | null | null | A couple of friends, Axel and Marston are travelling across the country of Bitland. There are *n* towns in Bitland, with some pairs of towns connected by one-directional roads. Each road in Bitland is either a pedestrian road or a bike road. There can be multiple roads between any pair of towns, and may even be a road from a town to itself. However, no pair of roads shares the starting and the destination towns along with their types simultaneously.
The friends are now located in the town 1 and are planning the travel route. Axel enjoys walking, while Marston prefers biking. In order to choose a route diverse and equally interesting for both friends, they have agreed upon the following procedure for choosing the road types during the travel:
- The route starts with a pedestrian route.- Suppose that a beginning of the route is written in a string *s* of letters P (pedestrain road) and B (biking road). Then, the string is appended to *s*, where stands for the string *s* with each character changed to opposite (that is, all pedestrian roads changed to bike roads, and vice versa).
In the first few steps the route will look as follows: P, PB, PBBP, PBBPBPPB, PBBPBPPBBPPBPBBP, and so on.
After that the friends start travelling from the town 1 via Bitlandian roads, choosing the next road according to the next character of their route type each time. If it is impossible to choose the next road, the friends terminate their travel and fly home instead.
Help the friends to find the longest possible route that can be travelled along roads of Bitland according to the road types choosing procedure described above. If there is such a route with more than 1018 roads in it, print -1 instead. | The first line contains two integers *n* and *m* (1<=≤<=*n*<=≤<=500, 0<=≤<=*m*<=≤<=2*n*2) — the number of towns and roads in Bitland respectively.
Next *m* lines describe the roads. *i*-th of these lines contains three integers *v**i*, *u**i* and *t**i* (1<=≤<=*v**i*,<=*u**i*<=≤<=*n*, 0<=≤<=*t**i*<=≤<=1), where *v**i* and *u**i* denote start and destination towns indices of the *i*-th road, and *t**i* decribes the type of *i*-th road (0 for a pedestrian road, 1 for a bike road). It is guaranteed that for each pair of distinct indices *i*, *j* such that 1<=≤<=*i*,<=*j*<=≤<=*m*, either *v**i*<=≠<=*v**j*, or *u**i*<=≠<=*u**j*, or *t**i*<=≠<=*t**j* holds. | If it is possible to find a route with length strictly greater than 1018, print -1. Otherwise, print the maximum length of a suitable path. | [
"2 2\n1 2 0\n2 2 1\n",
"2 3\n1 2 0\n2 2 1\n2 2 0\n"
] | [
"3\n",
"-1\n"
] | In the first sample we can obtain a route of length 3 by travelling along the road 1 from town 1 to town 2, and then following the road 2 twice from town 2 to itself.
In the second sample we can obtain an arbitrarily long route by travelling the road 1 first, and then choosing road 2 or 3 depending on the necessary type. | [] | 0 | 0 | -1 | 3,729 | |
63 | Settlers' Training | [
"implementation"
] | B. Settlers' Training | 2 | 256 | In a strategic computer game "Settlers II" one has to build defense structures to expand and protect the territory. Let's take one of these buildings. At the moment the defense structure accommodates exactly *n* soldiers. Within this task we can assume that the number of soldiers in the defense structure won't either increase or decrease.
Every soldier has a rank — some natural number from 1 to *k*. 1 stands for a private and *k* stands for a general. The higher the rank of the soldier is, the better he fights. Therefore, the player profits from having the soldiers of the highest possible rank.
To increase the ranks of soldiers they need to train. But the soldiers won't train for free, and each training session requires one golden coin. On each training session all the *n* soldiers are present.
At the end of each training session the soldiers' ranks increase as follows. First all the soldiers are divided into groups with the same rank, so that the least possible number of groups is formed. Then, within each of the groups where the soldiers below the rank *k* are present, exactly one soldier increases his rank by one.
You know the ranks of all *n* soldiers at the moment. Determine the number of golden coins that are needed to increase the ranks of all the soldiers to the rank *k*. | The first line contains two integers *n* and *k* (1<=≤<=*n*,<=*k*<=≤<=100). They represent the number of soldiers and the number of different ranks correspondingly. The second line contains *n* numbers in the non-decreasing order. The *i*-th of them, *a**i*, represents the rank of the *i*-th soldier in the defense building (1<=≤<=*i*<=≤<=*n*, 1<=≤<=*a**i*<=≤<=*k*). | Print a single integer — the number of golden coins needed to raise all the soldiers to the maximal rank. | [
"4 4\n1 2 2 3\n",
"4 3\n1 1 1 1\n"
] | [
"4",
"5"
] | In the first example the ranks will be raised in the following manner:
1 2 2 3 → 2 2 3 4 → 2 3 4 4 → 3 4 4 4 → 4 4 4 4
Thus totals to 4 training sessions that require 4 golden coins. | [
{
"input": "4 4\n1 2 2 3",
"output": "4"
},
{
"input": "4 3\n1 1 1 1",
"output": "5"
},
{
"input": "3 3\n1 2 3",
"output": "2"
},
{
"input": "1 1\n1",
"output": "0"
},
{
"input": "1 5\n1",
"output": "4"
},
{
"input": "1 5\n4",
"output": "1"
},
... | 124 | 102,400 | 3.968809 | 3,736 |
769 | Year of University Entrance | [
"*special",
"implementation",
"sortings"
] | null | null | There is the faculty of Computer Science in Berland. In the social net "TheContact!" for each course of this faculty there is the special group whose name equals the year of university entrance of corresponding course of students at the university.
Each of students joins the group of his course and joins all groups for which the year of student's university entrance differs by no more than *x* from the year of university entrance of this student, where *x* — some non-negative integer. A value *x* is not given, but it can be uniquely determined from the available data. Note that students don't join other groups.
You are given the list of groups which the student Igor joined. According to this information you need to determine the year of Igor's university entrance. | The first line contains the positive odd integer *n* (1<=≤<=*n*<=≤<=5) — the number of groups which Igor joined.
The next line contains *n* distinct integers *a*1,<=*a*2,<=...,<=*a**n* (2010<=≤<=*a**i*<=≤<=2100) — years of student's university entrance for each group in which Igor is the member.
It is guaranteed that the input data is correct and the answer always exists. Groups are given randomly. | Print the year of Igor's university entrance. | [
"3\n2014 2016 2015\n",
"1\n2050\n"
] | [
"2015\n",
"2050\n"
] | In the first test the value *x* = 1. Igor entered the university in 2015. So he joined groups members of which are students who entered the university in 2014, 2015 and 2016.
In the second test the value *x* = 0. Igor entered only the group which corresponds to the year of his university entrance. | [
{
"input": "3\n2014 2016 2015",
"output": "2015"
},
{
"input": "1\n2050",
"output": "2050"
},
{
"input": "1\n2010",
"output": "2010"
},
{
"input": "1\n2011",
"output": "2011"
},
{
"input": "3\n2010 2011 2012",
"output": "2011"
},
{
"input": "3\n2049 20... | 46 | 4,300,800 | 3 | 3,740 | |
980 | The Number Games | [
"data structures",
"greedy",
"trees"
] | null | null | The nation of Panel holds an annual show called The Number Games, where each district in the nation will be represented by one contestant.
The nation has $n$ districts numbered from $1$ to $n$, each district has exactly one path connecting it to every other district. The number of fans of a contestant from district $i$ is equal to $2^i$.
This year, the president decided to reduce the costs. He wants to remove $k$ contestants from the games. However, the districts of the removed contestants will be furious and will not allow anyone to cross through their districts.
The president wants to ensure that all remaining contestants are from districts that can be reached from one another. He also wishes to maximize the total number of fans of the participating contestants.
Which contestants should the president remove? | The first line of input contains two integers $n$ and $k$ ($1 \leq k < n \leq 10^6$) — the number of districts in Panel, and the number of contestants the president wishes to remove, respectively.
The next $n-1$ lines each contains two integers $a$ and $b$ ($1 \leq a, b \leq n$, $a \ne b$), that describe a road that connects two different districts $a$ and $b$ in the nation. It is guaranteed that there is exactly one path between every two districts. | Print $k$ space-separated integers: the numbers of the districts of which the contestants should be removed, in increasing order of district number. | [
"6 3\n2 1\n2 6\n4 2\n5 6\n2 3\n",
"8 4\n2 6\n2 7\n7 8\n1 2\n3 1\n2 4\n7 5\n"
] | [
"1 3 4\n",
"1 3 4 5\n"
] | In the first sample, the maximum possible total number of fans is $2^2 + 2^5 + 2^6 = 100$. We can achieve it by removing the contestants of the districts 1, 3, and 4. | [
{
"input": "6 3\n2 1\n2 6\n4 2\n5 6\n2 3",
"output": "1 3 4"
},
{
"input": "8 4\n2 6\n2 7\n7 8\n1 2\n3 1\n2 4\n7 5",
"output": "1 3 4 5"
},
{
"input": "2 1\n1 2",
"output": "1"
},
{
"input": "3 1\n2 1\n2 3",
"output": "1"
},
{
"input": "3 2\n1 3\n1 2",
"output... | 140 | 20,172,800 | 0 | 3,743 | |
645 | Mischievous Mess Makers | [
"greedy",
"math"
] | null | null | It is a balmy spring afternoon, and Farmer John's *n* cows are ruminating about link-cut cacti in their stalls. The cows, labeled 1 through *n*, are arranged so that the *i*-th cow occupies the *i*-th stall from the left. However, Elsie, after realizing that she will forever live in the shadows beyond Bessie's limelight, has formed the Mischievous Mess Makers and is plotting to disrupt this beautiful pastoral rhythm. While Farmer John takes his *k* minute long nap, Elsie and the Mess Makers plan to repeatedly choose two distinct stalls and swap the cows occupying those stalls, making no more than one swap each minute.
Being the meticulous pranksters that they are, the Mischievous Mess Makers would like to know the maximum messiness attainable in the *k* minutes that they have. We denote as *p**i* the label of the cow in the *i*-th stall. The messiness of an arrangement of cows is defined as the number of pairs (*i*,<=*j*) such that *i*<=<<=*j* and *p**i*<=><=*p**j*. | The first line of the input contains two integers *n* and *k* (1<=≤<=*n*,<=*k*<=≤<=100<=000) — the number of cows and the length of Farmer John's nap, respectively. | Output a single integer, the maximum messiness that the Mischievous Mess Makers can achieve by performing no more than *k* swaps. | [
"5 2\n",
"1 10\n"
] | [
"10\n",
"0\n"
] | In the first sample, the Mischievous Mess Makers can swap the cows in the stalls 1 and 5 during the first minute, then the cows in stalls 2 and 4 during the second minute. This reverses the arrangement of cows, giving us a total messiness of 10.
In the second sample, there is only one cow, so the maximum possible messiness is 0. | [
{
"input": "5 2",
"output": "10"
},
{
"input": "1 10",
"output": "0"
},
{
"input": "100000 2",
"output": "399990"
},
{
"input": "1 1",
"output": "0"
},
{
"input": "8 3",
"output": "27"
},
{
"input": "7 1",
"output": "11"
},
{
"input": "1000... | 62 | 1,331,200 | 3 | 3,749 | |
174 | Problem About Equation | [
"math"
] | null | null | A group of *n* merry programmers celebrate Robert Floyd's birthday. Polucarpus has got an honourable task of pouring Ber-Cola to everybody. Pouring the same amount of Ber-Cola to everybody is really important. In other words, the drink's volume in each of the *n* mugs must be the same.
Polycarpus has already began the process and he partially emptied the Ber-Cola bottle. Now the first mug has *a*1 milliliters of the drink, the second one has *a*2 milliliters and so on. The bottle has *b* milliliters left and Polycarpus plans to pour them into the mugs so that the main equation was fulfilled.
Write a program that would determine what volume of the drink Polycarpus needs to add into each mug to ensure that the following two conditions were fulfilled simultaneously:
- there were *b* milliliters poured in total. That is, the bottle need to be emptied; - after the process is over, the volumes of the drink in the mugs should be equal. | The first line contains a pair of integers *n*, *b* (2<=≤<=*n*<=≤<=100,<=1<=≤<=*b*<=≤<=100), where *n* is the total number of friends in the group and *b* is the current volume of drink in the bottle. The second line contains a sequence of integers *a*1,<=*a*2,<=...,<=*a**n* (0<=≤<=*a**i*<=≤<=100), where *a**i* is the current volume of drink in the *i*-th mug. | Print a single number "-1" (without the quotes), if there is no solution. Otherwise, print *n* float numbers *c*1,<=*c*2,<=...,<=*c**n*, where *c**i* is the volume of the drink to add in the *i*-th mug. Print the numbers with no less than 6 digits after the decimal point, print each *c**i* on a single line. Polycarpus proved that if a solution exists then it is unique.
Russian locale is installed by default on the testing computer. Make sure that your solution use the point to separate the integer part of a real number from the decimal, not a comma. | [
"5 50\n1 2 3 4 5\n",
"2 2\n1 100\n"
] | [
"12.000000\n11.000000\n10.000000\n9.000000\n8.000000\n",
"-1\n"
] | none | [
{
"input": "5 50\n1 2 3 4 5",
"output": "12.000000\n11.000000\n10.000000\n9.000000\n8.000000"
},
{
"input": "2 2\n1 100",
"output": "-1"
},
{
"input": "2 2\n1 1",
"output": "1.000000\n1.000000"
},
{
"input": "3 2\n1 2 1",
"output": "1.000000\n0.000000\n1.000000"
},
{
... | 248 | 6,758,400 | 3 | 3,756 | |
630 | Lucky Numbers | [
"combinatorics",
"math"
] | null | null | The numbers of all offices in the new building of the Tax Office of IT City will have lucky numbers.
Lucky number is a number that consists of digits 7 and 8 only. Find the maximum number of offices in the new building of the Tax Office given that a door-plate can hold a number not longer than *n* digits. | The only line of input contains one integer *n* (1<=≤<=*n*<=≤<=55) — the maximum length of a number that a door-plate can hold. | Output one integer — the maximum number of offices, than can have unique lucky numbers not longer than *n* digits. | [
"2\n"
] | [
"6"
] | none | [
{
"input": "2",
"output": "6"
},
{
"input": "1",
"output": "2"
},
{
"input": "3",
"output": "14"
},
{
"input": "5",
"output": "62"
},
{
"input": "12",
"output": "8190"
},
{
"input": "34",
"output": "34359738366"
},
{
"input": "43",
"out... | 31 | 0 | 3 | 3,762 | |
474 | Worms | [
"binary search",
"implementation"
] | null | null | It is lunch time for Mole. His friend, Marmot, prepared him a nice game for lunch.
Marmot brought Mole *n* ordered piles of worms such that *i*-th pile contains *a**i* worms. He labeled all these worms with consecutive integers: worms in first pile are labeled with numbers 1 to *a*1, worms in second pile are labeled with numbers *a*1<=+<=1 to *a*1<=+<=*a*2 and so on. See the example for a better understanding.
Mole can't eat all the worms (Marmot brought a lot) and, as we all know, Mole is blind, so Marmot tells him the labels of the best juicy worms. Marmot will only give Mole a worm if Mole says correctly in which pile this worm is contained.
Poor Mole asks for your help. For all juicy worms said by Marmot, tell Mole the correct answers. | The first line contains a single integer *n* (1<=≤<=*n*<=≤<=105), the number of piles.
The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=103, *a*1<=+<=*a*2<=+<=...<=+<=*a**n*<=≤<=106), where *a**i* is the number of worms in the *i*-th pile.
The third line contains single integer *m* (1<=≤<=*m*<=≤<=105), the number of juicy worms said by Marmot.
The fourth line contains *m* integers *q*1,<=*q*2,<=...,<=*q**m* (1<=≤<=*q**i*<=≤<=*a*1<=+<=*a*2<=+<=...<=+<=*a**n*), the labels of the juicy worms. | Print *m* lines to the standard output. The *i*-th line should contain an integer, representing the number of the pile where the worm labeled with the number *q**i* is. | [
"5\n2 7 3 4 9\n3\n1 25 11\n"
] | [
"1\n5\n3\n"
] | For the sample input:
- The worms with labels from [1, 2] are in the first pile. - The worms with labels from [3, 9] are in the second pile. - The worms with labels from [10, 12] are in the third pile. - The worms with labels from [13, 16] are in the fourth pile. - The worms with labels from [17, 25] are in the fifth pile. | [
{
"input": "5\n2 7 3 4 9\n3\n1 25 11",
"output": "1\n5\n3"
}
] | 77 | 2,355,200 | 0 | 3,772 | |
908 | New Year and Entity Enumeration | [
"bitmasks",
"combinatorics",
"dp",
"math"
] | null | null | You are given an integer *m*.
Let *M*<==<=2*m*<=-<=1.
You are also given a set of *n* integers denoted as the set *T*. The integers will be provided in base 2 as *n* binary strings of length *m*.
A set of integers *S* is called "good" if the following hold.
1. If , then . 1. If , then 1. 1. All elements of *S* are less than or equal to *M*.
Here, and refer to the bitwise XOR and bitwise AND operators, respectively.
Count the number of good sets *S*, modulo 109<=+<=7. | The first line will contain two integers *m* and *n* (1<=≤<=*m*<=≤<=1<=000, 1<=≤<=*n*<=≤<=*min*(2*m*,<=50)).
The next *n* lines will contain the elements of *T*. Each line will contain exactly *m* zeros and ones. Elements of *T* will be distinct. | Print a single integer, the number of good sets modulo 109<=+<=7. | [
"5 3\n11010\n00101\n11000\n",
"30 2\n010101010101010010101010101010\n110110110110110011011011011011\n"
] | [
"4\n",
"860616440\n"
] | An example of a valid set *S* is {00000, 00101, 00010, 00111, 11000, 11010, 11101, 11111}. | [
{
"input": "5 3\n11010\n00101\n11000",
"output": "4"
},
{
"input": "30 2\n010101010101010010101010101010\n110110110110110011011011011011",
"output": "860616440"
},
{
"input": "30 10\n001000000011000111000010010000\n000001100001010000000000000100\n000110100010100000000000101000\n110000010... | 608 | 13,107,200 | 3 | 3,775 | |
131 | Opposites Attract | [
"implementation",
"math"
] | null | null | Everybody knows that opposites attract. That is the key principle of the "Perfect Matching" dating agency. The "Perfect Matching" matchmakers have classified each registered customer by his interests and assigned to the *i*-th client number *t**i* (<=-<=10<=≤<=*t**i*<=≤<=10). Of course, one number can be assigned to any number of customers.
"Perfect Matching" wants to advertise its services and publish the number of opposite couples, that is, the couples who have opposite values of *t*. Each couple consists of exactly two clients. The customer can be included in a couple an arbitrary number of times. Help the agency and write the program that will find the sought number by the given sequence *t*1,<=*t*2,<=...,<=*t**n*. For example, if *t*<==<=(1,<=<=-<=1,<=1,<=<=-<=1), then any two elements *t**i* and *t**j* form a couple if *i* and *j* have different parity. Consequently, in this case the sought number equals 4.
Of course, a client can't form a couple with him/herself. | The first line of the input data contains an integer *n* (1<=≤<=*n*<=≤<=105) which represents the number of registered clients of the "Couple Matching". The second line contains a sequence of integers *t*1,<=*t*2,<=...,<=*t**n* (<=-<=10<=≤<=*t**i*<=≤<=10), *t**i* — is the parameter of the *i*-th customer that has been assigned to the customer by the result of the analysis of his interests. | Print the number of couples of customs with opposite *t*. The opposite number for *x* is number <=-<=*x* (0 is opposite to itself). Couples that only differ in the clients' order are considered the same.
Note that the answer to the problem can be large enough, so you must use the 64-bit integer type for calculations. Please, do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specificator. | [
"5\n-3 3 0 0 3\n",
"3\n0 0 0\n"
] | [
"3\n",
"3\n"
] | In the first sample the couples of opposite clients are: (1,2), (1,5) и (3,4).
In the second sample any couple of clients is opposite. | [
{
"input": "5\n-3 3 0 0 3",
"output": "3"
},
{
"input": "3\n0 0 0",
"output": "3"
},
{
"input": "1\n0",
"output": "0"
},
{
"input": "1\n5",
"output": "0"
},
{
"input": "2\n0 0",
"output": "1"
},
{
"input": "2\n-3 3",
"output": "1"
},
{
"inp... | 122 | 0 | 0 | 3,788 | |
350 | TL | [
"brute force",
"greedy",
"implementation"
] | null | null | Valera wanted to prepare a Codesecrof round. He's already got one problem and he wants to set a time limit (TL) on it.
Valera has written *n* correct solutions. For each correct solution, he knows its running time (in seconds). Valera has also wrote *m* wrong solutions and for each wrong solution he knows its running time (in seconds).
Let's suppose that Valera will set *v* seconds TL in the problem. Then we can say that a solution passes the system testing if its running time is at most *v* seconds. We can also say that a solution passes the system testing with some "extra" time if for its running time, *a* seconds, an inequality 2*a*<=≤<=*v* holds.
As a result, Valera decided to set *v* seconds TL, that the following conditions are met:
1. *v* is a positive integer; 1. all correct solutions pass the system testing; 1. at least one correct solution passes the system testing with some "extra" time; 1. all wrong solutions do not pass the system testing; 1. value *v* is minimum among all TLs, for which points 1, 2, 3, 4 hold.
Help Valera and find the most suitable TL or else state that such TL doesn't exist. | The first line contains two integers *n*, *m* (1<=≤<=*n*,<=*m*<=≤<=100). The second line contains *n* space-separated positive integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=100) — the running time of each of the *n* correct solutions in seconds. The third line contains *m* space-separated positive integers *b*1,<=*b*2,<=...,<=*b**m* (1<=≤<=*b**i*<=≤<=100) — the running time of each of *m* wrong solutions in seconds. | If there is a valid TL value, print it. Otherwise, print -1. | [
"3 6\n4 5 2\n8 9 6 10 7 11\n",
"3 1\n3 4 5\n6\n"
] | [
"5",
"-1\n"
] | none | [
{
"input": "3 6\n4 5 2\n8 9 6 10 7 11",
"output": "5"
},
{
"input": "3 1\n3 4 5\n6",
"output": "-1"
},
{
"input": "2 5\n45 99\n49 41 77 83 45",
"output": "-1"
},
{
"input": "50 50\n18 13 5 34 10 36 36 12 15 11 16 17 14 36 23 45 32 24 31 18 24 32 7 1 31 3 49 8 16 23 3 39 47 43... | 310 | 0 | 0 | 3,792 | |
160 | Find Pair | [
"implementation",
"math",
"sortings"
] | null | null | You've got another problem dealing with arrays. Let's consider an arbitrary sequence containing *n* (not necessarily different) integers *a*1, *a*2, ..., *a**n*. We are interested in all possible pairs of numbers (*a**i*, *a**j*), (1<=≤<=*i*,<=*j*<=≤<=*n*). In other words, let's consider all *n*2 pairs of numbers, picked from the given array.
For example, in sequence *a*<==<={3,<=1,<=5} are 9 pairs of numbers: (3,<=3),<=(3,<=1),<=(3,<=5),<=(1,<=3),<=(1,<=1),<=(1,<=5),<=(5,<=3),<=(5,<=1),<=(5,<=5).
Let's sort all resulting pairs lexicographically by non-decreasing. Let us remind you that pair (*p*1, *q*1) is lexicographically less than pair (*p*2, *q*2) only if either *p*1 < *p*2, or *p*1 = *p*2 and *q*1 < *q*2.
Then the sequence, mentioned above, will be sorted like that: (1,<=1),<=(1,<=3),<=(1,<=5),<=(3,<=1),<=(3,<=3),<=(3,<=5),<=(5,<=1),<=(5,<=3),<=(5,<=5)
Let's number all the pair in the sorted list from 1 to *n*2. Your task is formulated like this: you should find the *k*-th pair in the ordered list of all possible pairs of the array you've been given. | The first line contains two integers *n* and *k* (1<=≤<=*n*<=≤<=105,<=1<=≤<=*k*<=≤<=*n*2). The second line contains the array containing *n* integers *a*1, *a*2, ..., *a**n* (<=-<=109<=≤<=*a**i*<=≤<=109). The numbers in the array can coincide. All numbers are separated with spaces.
Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use cin, cout, streams or the %I64d specificator instead. | In the single line print two numbers — the sought *k*-th pair. | [
"2 4\n2 1\n",
"3 2\n3 1 5\n"
] | [
"2 2\n",
"1 3\n"
] | In the first sample the sorted sequence for the given array looks as: (1, 1), (1, 2), (2, 1), (2, 2). The 4-th of them is pair (2, 2).
The sorted sequence for the array from the second sample is given in the statement. The 2-nd pair there is (1, 3). | [
{
"input": "2 4\n2 1",
"output": "2 2"
},
{
"input": "3 2\n3 1 5",
"output": "1 3"
},
{
"input": "3 3\n1 1 2",
"output": "1 1"
},
{
"input": "1 1\n-4",
"output": "-4 -4"
},
{
"input": "3 7\n5 4 3",
"output": "5 3"
},
{
"input": "3 6\n10 1 3",
"outp... | 1,000 | 179,916,800 | 0 | 3,795 | |
765 | Code obfuscation | [
"greedy",
"implementation",
"strings"
] | null | null | Kostya likes Codeforces contests very much. However, he is very disappointed that his solutions are frequently hacked. That's why he decided to obfuscate (intentionally make less readable) his code before upcoming contest.
To obfuscate the code, Kostya first looks at the first variable name used in his program and replaces all its occurrences with a single symbol *a*, then he looks at the second variable name that has not been replaced yet, and replaces all its occurrences with *b*, and so on. Kostya is well-mannered, so he doesn't use any one-letter names before obfuscation. Moreover, there are at most 26 unique identifiers in his programs.
You are given a list of identifiers of some program with removed spaces and line breaks. Check if this program can be a result of Kostya's obfuscation. | In the only line of input there is a string *S* of lowercase English letters (1<=≤<=|*S*|<=≤<=500) — the identifiers of a program with removed whitespace characters. | If this program can be a result of Kostya's obfuscation, print "YES" (without quotes), otherwise print "NO". | [
"abacaba\n",
"jinotega\n"
] | [
"YES\n",
"NO\n"
] | In the first sample case, one possible list of identifiers would be "number string number character number string number". Here how Kostya would obfuscate the program:
- replace all occurences of number with a, the result would be "a string a character a string a",- replace all occurences of string with b, the result would be "a b a character a b a",- replace all occurences of character with c, the result would be "a b a c a b a",- all identifiers have been replaced, thus the obfuscation is finished. | [
{
"input": "abacaba",
"output": "YES"
},
{
"input": "jinotega",
"output": "NO"
},
{
"input": "aaaaaaaaaaa",
"output": "YES"
},
{
"input": "aba",
"output": "YES"
},
{
"input": "bab",
"output": "NO"
},
{
"input": "a",
"output": "YES"
},
{
"in... | 156 | 2,355,200 | 3 | 3,802 | |
522 | Closest Equals | [
"*special",
"data structures"
] | null | null | You are given sequence *a*1,<=*a*2,<=...,<=*a**n* and *m* queries *l**j*,<=*r**j* (1<=≤<=*l**j*<=≤<=*r**j*<=≤<=*n*). For each query you need to print the minimum distance between such pair of elements *a**x* and *a**y* (*x*<=≠<=*y*), that:
- both indexes of the elements lie within range [*l**j*,<=*r**j*], that is, *l**j*<=≤<=*x*,<=*y*<=≤<=*r**j*; - the values of the elements are equal, that is *a**x*<==<=*a**y*.
The text above understands distance as |*x*<=-<=*y*|. | The first line of the input contains a pair of integers *n*, *m* (1<=≤<=*n*,<=*m*<=≤<=5·105) — the length of the sequence and the number of queries, correspondingly.
The second line contains the sequence of integers *a*1,<=*a*2,<=...,<=*a**n* (<=-<=109<=≤<=*a**i*<=≤<=109).
Next *m* lines contain the queries, one per line. Each query is given by a pair of numbers *l**j*,<=*r**j* (1<=≤<=*l**j*<=≤<=*r**j*<=≤<=*n*) — the indexes of the query range limits. | Print *m* integers — the answers to each query. If there is no valid match for some query, please print -1 as an answer to this query. | [
"5 3\n1 1 2 3 2\n1 5\n2 4\n3 5\n",
"6 5\n1 2 1 3 2 3\n4 6\n1 3\n2 5\n2 4\n1 6\n"
] | [
"1\n-1\n2\n",
"2\n2\n3\n-1\n2\n"
] | none | [
{
"input": "5 3\n1 1 2 3 2\n1 5\n2 4\n3 5",
"output": "1\n-1\n2"
},
{
"input": "6 5\n1 2 1 3 2 3\n4 6\n1 3\n2 5\n2 4\n1 6",
"output": "2\n2\n3\n-1\n2"
},
{
"input": "10 6\n2 2 1 5 6 4 9 8 5 4\n1 2\n1 10\n2 10\n2 9\n5 5\n2 8",
"output": "1\n1\n4\n5\n-1\n-1"
},
{
"input": "1 1\... | 108 | 20,172,800 | 0 | 3,808 | |
920 | Connected Components? | [
"data structures",
"dfs and similar",
"dsu",
"graphs"
] | null | null | You are given an undirected graph consisting of *n* vertices and edges. Instead of giving you the edges that exist in the graph, we give you *m* unordered pairs (*x*,<=*y*) such that there is no edge between *x* and *y*, and if some pair of vertices is not listed in the input, then there is an edge between these vertices.
You have to find the number of connected components in the graph and the size of each component. A connected component is a set of vertices *X* such that for every two vertices from this set there exists at least one path in the graph connecting these vertices, but adding any other vertex to *X* violates this rule. | The first line contains two integers *n* and *m* (1<=≤<=*n*<=≤<=200000, ).
Then *m* lines follow, each containing a pair of integers *x* and *y* (1<=≤<=*x*,<=*y*<=≤<=*n*, *x*<=≠<=*y*) denoting that there is no edge between *x* and *y*. Each pair is listed at most once; (*x*,<=*y*) and (*y*,<=*x*) are considered the same (so they are never listed in the same test). If some pair of vertices is not listed in the input, then there exists an edge between those vertices. | Firstly print *k* — the number of connected components in this graph.
Then print *k* integers — the sizes of components. You should output these integers in non-descending order. | [
"5 5\n1 2\n3 4\n3 2\n4 2\n2 5\n"
] | [
"2\n1 4 "
] | none | [
{
"input": "5 5\n1 2\n3 4\n3 2\n4 2\n2 5",
"output": "2\n1 4 "
},
{
"input": "8 15\n2 1\n4 5\n2 4\n3 4\n2 5\n3 5\n2 6\n3 6\n5 6\n4 6\n2 7\n3 8\n2 8\n3 7\n6 7",
"output": "1\n8 "
},
{
"input": "12 58\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 10\n1 11\n1 12\n2 3\n2 4\n2 5\n2 6\n2 7\n2 8\n2 9\n... | 2,292 | 268,390,400 | 0 | 3,809 | |
0 | none | [
"none"
] | null | null | A factory produces thimbles in bulk. Typically, it can produce up to *a* thimbles a day. However, some of the machinery is defective, so it can currently only produce *b* thimbles each day. The factory intends to choose a *k*-day period to do maintenance and construction; it cannot produce any thimbles during this time, but will be restored to its full production of *a* thimbles per day after the *k* days are complete.
Initially, no orders are pending. The factory receives updates of the form *d**i*, *a**i*, indicating that *a**i* new orders have been placed for the *d**i*-th day. Each order requires a single thimble to be produced on precisely the specified day. The factory may opt to fill as many or as few of the orders in a single batch as it likes.
As orders come in, the factory owner would like to know the maximum number of orders he will be able to fill if he starts repairs on a given day *p**i*. Help the owner answer his questions. | The first line contains five integers *n*, *k*, *a*, *b*, and *q* (1<=≤<=*k*<=≤<=*n*<=≤<=200<=000, 1<=≤<=*b*<=<<=*a*<=≤<=10 000, 1<=≤<=*q*<=≤<=200<=000) — the number of days, the length of the repair time, the production rates of the factory, and the number of updates, respectively.
The next *q* lines contain the descriptions of the queries. Each query is of one of the following two forms:
- 1 *d**i* *a**i* (1<=≤<=*d**i*<=≤<=*n*, 1<=≤<=*a**i*<=≤<=10 000), representing an update of *a**i* orders on day *d**i*, or - 2 *p**i* (1<=≤<=*p**i*<=≤<=*n*<=-<=*k*<=+<=1), representing a question: at the moment, how many orders could be filled if the factory decided to commence repairs on day *p**i*?
It's guaranteed that the input will contain at least one query of the second type. | For each query of the second type, print a line containing a single integer — the maximum number of orders that the factory can fill over all *n* days. | [
"5 2 2 1 8\n1 1 2\n1 5 3\n1 2 1\n2 2\n1 4 2\n1 3 2\n2 1\n2 3\n",
"5 4 10 1 6\n1 1 5\n1 5 5\n1 3 2\n1 5 2\n2 1\n2 2\n"
] | [
"3\n6\n4\n",
"7\n1\n"
] | Consider the first sample.
We produce up to 1 thimble a day currently and will produce up to 2 thimbles a day after repairs. Repairs take 2 days.
For the first question, we are able to fill 1 order on day 1, no orders on days 2 and 3 since we are repairing, no orders on day 4 since no thimbles have been ordered for that day, and 2 orders for day 5 since we are limited to our production capacity, for a total of 3 orders filled.
For the third question, we are able to fill 1 order on day 1, 1 order on day 2, and 2 orders on day 5, for a total of 4 orders. | [
{
"input": "5 2 2 1 8\n1 1 2\n1 5 3\n1 2 1\n2 2\n1 4 2\n1 3 2\n2 1\n2 3",
"output": "3\n6\n4"
},
{
"input": "5 4 10 1 6\n1 1 5\n1 5 5\n1 3 2\n1 5 2\n2 1\n2 2",
"output": "7\n1"
},
{
"input": "1 1 2 1 1\n2 1",
"output": "0"
}
] | 93 | 0 | 0 | 3,815 | |
769 | k-Interesting Pairs Of Integers | [
"*special",
"bitmasks",
"brute force",
"meet-in-the-middle"
] | null | null | Vasya has the sequence consisting of *n* integers. Vasya consider the pair of integers *x* and *y* k-interesting, if their binary representation differs from each other exactly in *k* bits. For example, if *k*<==<=2, the pair of integers *x*<==<=5 and *y*<==<=3 is k-interesting, because their binary representation *x*=101 and *y*=011 differs exactly in two bits.
Vasya wants to know how many pairs of indexes (*i*, *j*) are in his sequence so that *i*<=<<=*j* and the pair of integers *a**i* and *a**j* is k-interesting. Your task is to help Vasya and determine this number. | The first line contains two integers *n* and *k* (2<=≤<=*n*<=≤<=105, 0<=≤<=*k*<=≤<=14) — the number of integers in Vasya's sequence and the number of bits in which integers in k-interesting pair should differ.
The second line contains the sequence *a*1,<=*a*2,<=...,<=*a**n* (0<=≤<=*a**i*<=≤<=104), which Vasya has. | Print the number of pairs (*i*, *j*) so that *i*<=<<=*j* and the pair of integers *a**i* and *a**j* is k-interesting. | [
"4 1\n0 3 2 1\n",
"6 0\n200 100 100 100 200 200\n"
] | [
"4\n",
"6\n"
] | In the first test there are 4 k-interesting pairs:
- (1, 3), - (1, 4), - (2, 3), - (2, 4).
In the second test *k* = 0. Consequently, integers in any k-interesting pair should be equal to themselves. Thus, for the second test there are 6 k-interesting pairs:
- (1, 5), - (1, 6), - (2, 3), - (2, 4), - (3, 4), - (5, 6). | [
{
"input": "4 1\n0 3 2 1",
"output": "4"
},
{
"input": "6 0\n200 100 100 100 200 200",
"output": "6"
},
{
"input": "2 0\n1 1",
"output": "1"
},
{
"input": "2 0\n0 0",
"output": "1"
},
{
"input": "2 0\n10000 10000",
"output": "1"
},
{
"input": "2 0\n0 1... | 62 | 4,915,200 | 0 | 3,817 | |
19 | Points | [
"data structures"
] | D. Points | 2 | 256 | Pete and Bob invented a new interesting game. Bob takes a sheet of paper and locates a Cartesian coordinate system on it as follows: point (0,<=0) is located in the bottom-left corner, *Ox* axis is directed right, *Oy* axis is directed up. Pete gives Bob requests of three types:
- add x y — on the sheet of paper Bob marks a point with coordinates (*x*,<=*y*). For each request of this type it's guaranteed that point (*x*,<=*y*) is not yet marked on Bob's sheet at the time of the request. - remove x y — on the sheet of paper Bob erases the previously marked point with coordinates (*x*,<=*y*). For each request of this type it's guaranteed that point (*x*,<=*y*) is already marked on Bob's sheet at the time of the request. - find x y — on the sheet of paper Bob finds all the marked points, lying strictly above and strictly to the right of point (*x*,<=*y*). Among these points Bob chooses the leftmost one, if it is not unique, he chooses the bottommost one, and gives its coordinates to Pete.
Bob managed to answer the requests, when they were 10, 100 or 1000, but when their amount grew up to 2·105, Bob failed to cope. Now he needs a program that will answer all Pete's requests. Help Bob, please! | The first input line contains number *n* (1<=≤<=*n*<=≤<=2·105) — amount of requests. Then there follow *n* lines — descriptions of the requests. add x y describes the request to add a point, remove x y — the request to erase a point, find x y — the request to find the bottom-left point. All the coordinates in the input file are non-negative and don't exceed 109. | For each request of type find x y output in a separate line the answer to it — coordinates of the bottommost among the leftmost marked points, lying strictly above and to the right of point (*x*,<=*y*). If there are no points strictly above and to the right of point (*x*,<=*y*), output -1. | [
"7\nadd 1 1\nadd 3 4\nfind 0 0\nremove 1 1\nfind 0 0\nadd 1 1\nfind 0 0\n",
"13\nadd 5 5\nadd 5 6\nadd 5 7\nadd 6 5\nadd 6 6\nadd 6 7\nadd 7 5\nadd 7 6\nadd 7 7\nfind 6 6\nremove 7 7\nfind 6 6\nfind 4 4\n"
] | [
"1 1\n3 4\n1 1\n",
"7 7\n-1\n5 5\n"
] | none | [] | 2,000 | 819,200 | 0 | 3,822 |
899 | Months and Years | [
"implementation"
] | null | null | Everybody in Russia uses Gregorian calendar. In this calendar there are 31 days in January, 28 or 29 days in February (depending on whether the year is leap or not), 31 days in March, 30 days in April, 31 days in May, 30 in June, 31 in July, 31 in August, 30 in September, 31 in October, 30 in November, 31 in December.
A year is leap in one of two cases: either its number is divisible by 4, but not divisible by 100, or is divisible by 400. For example, the following years are leap: 2000, 2004, but years 1900 and 2018 are not leap.
In this problem you are given *n* (1<=≤<=*n*<=≤<=24) integers *a*1,<=*a*2,<=...,<=*a**n*, and you have to check if these integers could be durations in days of *n* consecutive months, according to Gregorian calendar. Note that these months could belong to several consecutive years. In other words, check if there is a month in some year, such that its duration is *a*1 days, duration of the next month is *a*2 days, and so on. | The first line contains single integer *n* (1<=≤<=*n*<=≤<=24) — the number of integers.
The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (28<=≤<=*a**i*<=≤<=31) — the numbers you are to check. | If there are several consecutive months that fit the sequence, print "YES" (without quotes). Otherwise, print "NO" (without quotes).
You can print each letter in arbitrary case (small or large). | [
"4\n31 31 30 31\n",
"2\n30 30\n",
"5\n29 31 30 31 30\n",
"3\n31 28 30\n",
"3\n31 31 28\n"
] | [
"Yes\n\n",
"No\n\n",
"Yes\n\n",
"No\n\n",
"Yes\n\n"
] | In the first example the integers can denote months July, August, September and October.
In the second example the answer is no, because there are no two consecutive months each having 30 days.
In the third example the months are: February (leap year) — March — April – May — June.
In the fourth example the number of days in the second month is 28, so this is February. March follows February and has 31 days, but not 30, so the answer is NO.
In the fifth example the months are: December — January — February (non-leap year). | [
{
"input": "4\n31 31 30 31",
"output": "Yes"
},
{
"input": "2\n30 30",
"output": "No"
},
{
"input": "5\n29 31 30 31 30",
"output": "Yes"
},
{
"input": "3\n31 28 30",
"output": "No"
},
{
"input": "3\n31 31 28",
"output": "Yes"
},
{
"input": "24\n29 28 3... | 31 | 0 | 0 | 3,829 | |
653 | Bear and Compressing | [
"brute force",
"dfs and similar",
"dp",
"strings"
] | null | null | Limak is a little polar bear. Polar bears hate long strings and thus they like to compress them. You should also know that Limak is so young that he knows only first six letters of the English alphabet: 'a', 'b', 'c', 'd', 'e' and 'f'.
You are given a set of *q* possible operations. Limak can perform them in any order, any operation may be applied any number of times. The *i*-th operation is described by a string *a**i* of length two and a string *b**i* of length one. No two of *q* possible operations have the same string *a**i*.
When Limak has a string *s* he can perform the *i*-th operation on *s* if the first two letters of *s* match a two-letter string *a**i*. Performing the *i*-th operation removes first two letters of *s* and inserts there a string *b**i*. See the notes section for further clarification.
You may note that performing an operation decreases the length of a string *s* exactly by 1. Also, for some sets of operations there may be a string that cannot be compressed any further, because the first two letters don't match any *a**i*.
Limak wants to start with a string of length *n* and perform *n*<=-<=1 operations to finally get a one-letter string "a". In how many ways can he choose the starting string to be able to get "a"? Remember that Limak can use only letters he knows. | The first line contains two integers *n* and *q* (2<=≤<=*n*<=≤<=6, 1<=≤<=*q*<=≤<=36) — the length of the initial string and the number of available operations.
The next *q* lines describe the possible operations. The *i*-th of them contains two strings *a**i* and *b**i* (|*a**i*|<==<=2,<=|*b**i*|<==<=1). It's guaranteed that *a**i*<=≠<=*a**j* for *i*<=≠<=*j* and that all *a**i* and *b**i* consist of only first six lowercase English letters. | Print the number of strings of length *n* that Limak will be able to transform to string "a" by applying only operations given in the input. | [
"3 5\nab a\ncc c\nca a\nee c\nff d\n",
"2 8\naf e\ndc d\ncc f\nbc b\nda b\neb a\nbb b\nff c\n",
"6 2\nbb a\nba a\n"
] | [
"4\n",
"1\n",
"0\n"
] | In the first sample, we count initial strings of length 3 from which Limak can get a required string "a". There are 4 such strings: "abb", "cab", "cca", "eea". The first one Limak can compress using operation 1 two times (changing "ab" to a single "a"). The first operation would change "abb" to "ab" and the second operation would change "ab" to "a".
Other three strings may be compressed as follows:
- "cab" <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png" style="max-width: 100.0%;max-height: 100.0%;"/> "ab" <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png" style="max-width: 100.0%;max-height: 100.0%;"/> "a" - "cca" <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png" style="max-width: 100.0%;max-height: 100.0%;"/> "ca" <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png" style="max-width: 100.0%;max-height: 100.0%;"/> "a" - "eea" <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png" style="max-width: 100.0%;max-height: 100.0%;"/> "ca" <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png" style="max-width: 100.0%;max-height: 100.0%;"/> "a"
In the second sample, the only correct initial string is "eb" because it can be immediately compressed to "a". | [
{
"input": "3 5\nab a\ncc c\nca a\nee c\nff d",
"output": "4"
},
{
"input": "2 8\naf e\ndc d\ncc f\nbc b\nda b\neb a\nbb b\nff c",
"output": "1"
},
{
"input": "6 2\nbb a\nba a",
"output": "0"
},
{
"input": "2 5\nfe b\nbb a\naf b\nfd b\nbf c",
"output": "1"
},
{
"i... | 108 | 5,324,800 | 3 | 3,833 | |
963 | Alternating Sum | [
"math",
"number theory"
] | null | null | You are given two integers $a$ and $b$. Moreover, you are given a sequence $s_0, s_1, \dots, s_{n}$. All values in $s$ are integers $1$ or $-1$. It's known that sequence is $k$-periodic and $k$ divides $n+1$. In other words, for each $k \leq i \leq n$ it's satisfied that $s_{i} = s_{i - k}$.
Find out the non-negative remainder of division of $\sum \limits_{i=0}^{n} s_{i} a^{n - i} b^{i}$ by $10^{9} + 9$.
Note that the modulo is unusual! | The first line contains four integers $n, a, b$ and $k$ $(1 \leq n \leq 10^{9}, 1 \leq a, b \leq 10^{9}, 1 \leq k \leq 10^{5})$.
The second line contains a sequence of length $k$ consisting of characters '+' and '-'.
If the $i$-th character (0-indexed) is '+', then $s_{i} = 1$, otherwise $s_{i} = -1$.
Note that only the first $k$ members of the sequence are given, the rest can be obtained using the periodicity property. | Output a single integer — value of given expression modulo $10^{9} + 9$. | [
"2 2 3 3\n+-+\n",
"4 1 5 1\n-\n"
] | [
"7\n",
"999999228\n"
] | In the first example:
$(\sum \limits_{i=0}^{n} s_{i} a^{n - i} b^{i})$ = $2^{2} 3^{0} - 2^{1} 3^{1} + 2^{0} 3^{2}$ = 7
In the second example:
$(\sum \limits_{i=0}^{n} s_{i} a^{n - i} b^{i}) = -1^{4} 5^{0} - 1^{3} 5^{1} - 1^{2} 5^{2} - 1^{1} 5^{3} - 1^{0} 5^{4} = -781 \equiv 999999228 \pmod{10^{9} + 9}$. | [
{
"input": "2 2 3 3\n+-+",
"output": "7"
},
{
"input": "4 1 5 1\n-",
"output": "999999228"
},
{
"input": "1 1 4 2\n-+",
"output": "3"
},
{
"input": "3 1 4 4\n+--+",
"output": "45"
},
{
"input": "5 1 1 6\n++---+",
"output": "0"
},
{
"input": "5 2 2 6\n+... | 0 | 0 | -1 | 3,837 | |
550 | Two Substrings | [
"brute force",
"dp",
"greedy",
"implementation",
"strings"
] | null | null | You are given string *s*. Your task is to determine if the given string *s* contains two non-overlapping substrings "AB" and "BA" (the substrings can go in any order). | The only line of input contains a string *s* of length between 1 and 105 consisting of uppercase Latin letters. | Print "YES" (without the quotes), if string *s* contains two non-overlapping substrings "AB" and "BA", and "NO" otherwise. | [
"ABA\n",
"BACFAB\n",
"AXBYBXA\n"
] | [
"NO\n",
"YES\n",
"NO\n"
] | In the first sample test, despite the fact that there are substrings "AB" and "BA", their occurrences overlap, so the answer is "NO".
In the second sample test there are the following occurrences of the substrings: BACFAB.
In the third sample test there is no substring "AB" nor substring "BA". | [
{
"input": "ABA",
"output": "NO"
},
{
"input": "BACFAB",
"output": "YES"
},
{
"input": "AXBYBXA",
"output": "NO"
},
{
"input": "ABABAB",
"output": "YES"
},
{
"input": "BBBBBBBBBB",
"output": "NO"
},
{
"input": "ABBA",
"output": "YES"
},
{
"... | 46 | 0 | 0 | 3,840 | |
333 | Secrets | [
"greedy"
] | null | null | Gerald has been selling state secrets at leisure. All the secrets cost the same: *n* marks. The state which secrets Gerald is selling, has no paper money, only coins. But there are coins of all positive integer denominations that are powers of three: 1 mark, 3 marks, 9 marks, 27 marks and so on. There are no coins of other denominations. Of course, Gerald likes it when he gets money without the change. And all buyers respect him and try to give the desired sum without change, if possible. But this does not always happen.
One day an unlucky buyer came. He did not have the desired sum without change. Then he took out all his coins and tried to give Gerald a larger than necessary sum with as few coins as possible. What is the maximum number of coins he could get?
The formal explanation of the previous paragraph: we consider all the possible combinations of coins for which the buyer can not give Gerald the sum of *n* marks without change. For each such combination calculate the minimum number of coins that can bring the buyer at least *n* marks. Among all combinations choose the maximum of the minimum number of coins. This is the number we want. | The single line contains a single integer *n* (1<=≤<=*n*<=≤<=1017).
Please, do not use the %lld specifier to read or write 64 bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier. | In a single line print an integer: the maximum number of coins the unlucky buyer could have paid with. | [
"1\n",
"4\n"
] | [
"1\n",
"2\n"
] | In the first test case, if a buyer has exactly one coin of at least 3 marks, then, to give Gerald one mark, he will have to give this coin. In this sample, the customer can not have a coin of one mark, as in this case, he will be able to give the money to Gerald without any change.
In the second test case, if the buyer had exactly three coins of 3 marks, then, to give Gerald 4 marks, he will have to give two of these coins. The buyer cannot give three coins as he wants to minimize the number of coins that he gives. | [
{
"input": "1",
"output": "1"
},
{
"input": "4",
"output": "2"
},
{
"input": "3",
"output": "1"
},
{
"input": "8",
"output": "3"
},
{
"input": "10",
"output": "4"
},
{
"input": "100000000000000000",
"output": "33333333333333334"
},
{
"input... | 184 | 0 | 3 | 3,842 | |
22 | System Administrator | [
"graphs"
] | C. System Administrator | 1 | 256 | Bob got a job as a system administrator in X corporation. His first task was to connect *n* servers with the help of *m* two-way direct connection so that it becomes possible to transmit data from one server to any other server via these connections. Each direct connection has to link two different servers, each pair of servers should have at most one direct connection. Y corporation, a business rival of X corporation, made Bob an offer that he couldn't refuse: Bob was asked to connect the servers in such a way, that when server with index *v* fails, the transmission of data between some other two servers becomes impossible, i.e. the system stops being connected. Help Bob connect the servers. | The first input line contains 3 space-separated integer numbers *n*, *m*, *v* (3<=≤<=*n*<=≤<=105,<=0<=≤<=*m*<=≤<=105,<=1<=≤<=*v*<=≤<=*n*), *n* — amount of servers, *m* — amount of direct connections, *v* — index of the server that fails and leads to the failure of the whole system. | If it is impossible to connect the servers in the required way, output -1. Otherwise output *m* lines with 2 numbers each — description of all the direct connections in the system. Each direct connection is described by two numbers — indexes of two servers, linked by this direct connection. The servers are numbered from 1. If the answer is not unique, output any. | [
"5 6 3\n",
"6 100 1\n"
] | [
"1 2\n2 3\n3 4\n4 5\n1 3\n3 5\n",
"-1\n"
] | none | [
{
"input": "5 6 3",
"output": "1 3\n2 3\n4 3\n5 3\n1 2\n1 4"
},
{
"input": "6 100 1",
"output": "-1"
},
{
"input": "10 26 1",
"output": "2 1\n3 1\n4 1\n5 1\n6 1\n7 1\n8 1\n9 1\n10 1\n2 3\n2 4\n2 5\n2 6\n2 7\n2 8\n2 9\n3 4\n3 5\n3 6\n3 7\n3 8\n3 9\n4 5\n4 6\n4 7\n4 8"
},
{
"in... | 109 | 0 | 0 | 3,843 |
180 | Defragmentation | [
"implementation"
] | null | null | In this problem you have to implement an algorithm to defragment your hard disk. The hard disk consists of a sequence of clusters, numbered by integers from 1 to *n*. The disk has *m* recorded files, the *i*-th file occupies clusters with numbers *a**i*,<=1, *a**i*,<=2, ..., *a**i*,<=*n**i*. These clusters are not necessarily located consecutively on the disk, but the order in which they are given corresponds to their sequence in the file (cluster *a**i*,<=1 contains the first fragment of the *i*-th file, cluster *a**i*,<=2 has the second fragment, etc.). Also the disc must have one or several clusters which are free from files.
You are permitted to perform operations of copying the contents of cluster number *i* to cluster number *j* (*i* and *j* must be different). Moreover, if the cluster number *j* used to keep some information, it is lost forever. Clusters are not cleaned, but after the defragmentation is complete, some of them are simply declared unusable (although they may possibly still contain some fragments of files).
Your task is to use a sequence of copy operations to ensure that each file occupies a contiguous area of memory. Each file should occupy a consecutive cluster section, the files must follow one after another from the beginning of the hard disk. After defragmentation all free (unused) clusters should be at the end of the hard disk. After defragmenting files can be placed in an arbitrary order. Clusters of each file should go consecutively from first to last. See explanatory examples in the notes.
Print the sequence of operations leading to the disk defragmentation. Note that you do not have to minimize the number of operations, but it should not exceed 2*n*. | The first line contains two integers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=200) — the number of clusters and the number of files, correspondingly. Next *m* lines contain descriptions of the files. The first number in the line is *n**i* (*n**i*<=≥<=1), the number of clusters occupied by the *i*-th file. Then follow *n**i* numbers *a**i*,<=1, *a**i*,<=2, ..., *a**i*,<=*n**i* (1<=≤<=*a**i*,<=*j*<=≤<=*n*). It is guaranteed that each cluster number occurs not more than once and , that is, there exists at least one unused cluster. Numbers on each line are separated by spaces. | In the first line print a single integer *k* (0<=≤<=*k*<=≤<=2*n*) — the number of operations needed to defragment the disk. Next *k* lines should contain the operations' descriptions as "*i* *j*" (copy the contents of the cluster number *i* to the cluster number *j*). | [
"7 2\n2 1 2\n3 3 4 5\n",
"7 2\n2 1 3\n3 2 4 5\n"
] | [
"0\n",
"3\n2 6\n3 2\n6 3\n"
] | Let's say that a disk consists of 8 clusters and contains two files. The first file occupies two clusters and the second file occupies three clusters. Let's look at examples of correct and incorrect positions of files after defragmentation.
Example 2: each file must occupy a contiguous area of memory.
Example 3: the order of files to each other is not important, at first the second file can be written, and then — the first one.
Example 4: violating the order of file fragments to each other is not allowed.
Example 5: unused clusters should be located at the end, and in this example the unused clusters are 3, 7, 8. | [
{
"input": "7 2\n2 1 2\n3 3 4 5",
"output": "0"
},
{
"input": "7 2\n2 1 3\n3 2 4 5",
"output": "3\n2 6\n3 2\n6 3"
},
{
"input": "2 1\n1 2",
"output": "1\n2 1"
},
{
"input": "3 1\n2 3 1",
"output": "2\n1 2\n3 1"
},
{
"input": "3 2\n1 3\n1 2",
"output": "1\n3 1"... | 248 | 512,000 | 3 | 3,845 | |
952 | 2 + 2 != 4 | [] | null | null | One very experienced problem writer decided to prepare a problem for April Fools Day contest. The task was very simple - given an arithmetic expression, return the result of evaluating this expression. However, looks like there is a bug in the reference solution... | The only line of input data contains the arithmetic expression. The expression will contain between 2 and 10 operands, separated with arithmetic signs plus and/or minus. Each operand will be an integer between 0 and 255, inclusive. | Reproduce the output of the reference solution, including the bug. | [
"8-7+6-5+4-3+2-1-0\n",
"2+2\n",
"112-37\n"
] | [
"4\n",
"-46\n",
"375\n"
] | none | [
{
"input": "8-7+6-5+4-3+2-1-0",
"output": "4"
},
{
"input": "2+2",
"output": "-46"
},
{
"input": "112-37",
"output": "375"
},
{
"input": "255+255+255+255+255+255+255+255+255+255",
"output": "-42450"
},
{
"input": "0-255-255-255-255-255-255-255-255-255",
"outpu... | 0 | 0 | -1 | 3,846 | |
25 | Roads in Berland | [
"graphs",
"shortest paths"
] | C. Roads in Berland | 2 | 256 | There are *n* cities numbered from 1 to *n* in Berland. Some of them are connected by two-way roads. Each road has its own length — an integer number from 1 to 1000. It is known that from each city it is possible to get to any other city by existing roads. Also for each pair of cities it is known the shortest distance between them. Berland Government plans to build *k* new roads. For each of the planned road it is known its length, and what cities it will connect. To control the correctness of the construction of new roads, after the opening of another road Berland government wants to check the sum of the shortest distances between all pairs of cities. Help them — for a given matrix of shortest distances on the old roads and plans of all new roads, find out how the sum of the shortest distances between all pairs of cities changes after construction of each road. | The first line contains integer *n* (2<=≤<=*n*<=≤<=300) — amount of cities in Berland. Then there follow *n* lines with *n* integer numbers each — the matrix of shortest distances. *j*-th integer in the *i*-th row — *d**i*,<=*j*, the shortest distance between cities *i* and *j*. It is guaranteed that *d**i*,<=*i*<==<=0,<=*d**i*,<=*j*<==<=*d**j*,<=*i*, and a given matrix is a matrix of shortest distances for some set of two-way roads with integer lengths from 1 to 1000, such that from each city it is possible to get to any other city using these roads.
Next line contains integer *k* (1<=≤<=*k*<=≤<=300) — amount of planned roads. Following *k* lines contain the description of the planned roads. Each road is described by three space-separated integers *a**i*, *b**i*, *c**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=*n*,<=*a**i*<=≠<=*b**i*,<=1<=≤<=*c**i*<=≤<=1000) — *a**i* and *b**i* — pair of cities, which the road connects, *c**i* — the length of the road. It can be several roads between a pair of cities, but no road connects the city with itself. | Output *k* space-separated integers *q**i* (1<=≤<=*i*<=≤<=*k*). *q**i* should be equal to the sum of shortest distances between all pairs of cities after the construction of roads with indexes from 1 to *i*. Roads are numbered from 1 in the input order. Each pair of cities should be taken into account in the sum exactly once, i. e. we count unordered pairs. | [
"2\n0 5\n5 0\n1\n1 2 3\n",
"3\n0 4 5\n4 0 9\n5 9 0\n2\n2 3 8\n1 2 1\n"
] | [
"3 ",
"17 12 "
] | none | [
{
"input": "2\n0 5\n5 0\n1\n1 2 3",
"output": "3 "
},
{
"input": "3\n0 4 5\n4 0 9\n5 9 0\n2\n2 3 8\n1 2 1",
"output": "17 12 "
},
{
"input": "3\n0 983 173\n983 0 810\n173 810 0\n3\n3 2 567\n2 3 767\n1 2 763",
"output": "1480 1480 1480 "
},
{
"input": "4\n0 537 1064 656\n537 0... | 2,000 | 12,185,600 | 0 | 3,847 |
715 | Create a Maze | [
"constructive algorithms"
] | null | null | ZS the Coder loves mazes. Your job is to create one so that he can play with it. A maze consists of *n*<=×<=*m* rooms, and the rooms are arranged in *n* rows (numbered from the top to the bottom starting from 1) and *m* columns (numbered from the left to the right starting from 1). The room in the *i*-th row and *j*-th column is denoted by (*i*,<=*j*). A player starts in the room (1,<=1) and wants to reach the room (*n*,<=*m*).
Each room has four doors (except for ones at the maze border), one on each of its walls, and two adjacent by the wall rooms shares the same door. Some of the doors are locked, which means it is impossible to pass through the door. For example, if the door connecting (*i*,<=*j*) and (*i*,<=*j*<=+<=1) is locked, then we can't go from (*i*,<=*j*) to (*i*,<=*j*<=+<=1). Also, one can only travel between the rooms downwards (from the room (*i*,<=*j*) to the room (*i*<=+<=1,<=*j*)) or rightwards (from the room (*i*,<=*j*) to the room (*i*,<=*j*<=+<=1)) provided the corresponding door is not locked.
ZS the Coder considers a maze to have difficulty *x* if there is exactly *x* ways of travelling from the room (1,<=1) to the room (*n*,<=*m*). Two ways are considered different if they differ by the sequence of rooms visited while travelling.
Your task is to create a maze such that its difficulty is exactly equal to *T*. In addition, ZS the Coder doesn't like large mazes, so the size of the maze and the number of locked doors are limited. Sounds simple enough, right? | The first and only line of the input contains a single integer *T* (1<=≤<=*T*<=≤<=1018), the difficulty of the required maze. | The first line should contain two integers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=50) — the number of rows and columns of the maze respectively.
The next line should contain a single integer *k* (0<=≤<=*k*<=≤<=300) — the number of locked doors in the maze.
Then, *k* lines describing locked doors should follow. Each of them should contain four integers, *x*1,<=*y*1,<=*x*2,<=*y*2. This means that the door connecting room (*x*1,<=*y*1) and room (*x*2,<=*y*2) is locked. Note that room (*x*2,<=*y*2) should be adjacent either to the right or to the bottom of (*x*1,<=*y*1), i.e. *x*2<=+<=*y*2 should be equal to *x*1<=+<=*y*1<=+<=1. There should not be a locked door that appears twice in the list.
It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them. | [
"3\n",
"4\n"
] | [
"3 2\n0\n",
"4 3\n3\n1 2 2 2\n3 2 3 3\n1 3 2 3"
] | Here are how the sample input and output looks like. The colored arrows denotes all the possible paths while a red cross denotes a locked door.
In the first sample case:
In the second sample case: | [
{
"input": "3",
"output": "4 4\n5\n1 2 2 2\n1 3 2 3\n1 4 2 4\n2 1 2 2\n4 1 4 2"
},
{
"input": "4",
"output": "4 4\n4\n1 2 2 2\n1 3 2 3\n2 1 2 2\n4 1 4 2"
},
{
"input": "576460752303423488",
"output": "48 48\n233\n1 2 2 2\n1 3 2 3\n2 1 2 2\n2 4 2 5\n2 6 3 6\n2 7 3 7\n3 4 3 5\n3 5 4 5\... | 93 | 2,457,600 | 3 | 3,848 | |
294 | Shaass and Bookshelf | [
"dp",
"greedy"
] | null | null | Shaass has *n* books. He wants to make a bookshelf for all his books. He wants the bookshelf's dimensions to be as small as possible. The thickness of the *i*-th book is *t**i* and its pages' width is equal to *w**i*. The thickness of each book is either 1 or 2. All books have the same page heights.
Shaass puts the books on the bookshelf in the following way. First he selects some of the books and put them vertically. Then he puts the rest of the books horizontally above the vertical books. The sum of the widths of the horizontal books must be no more than the total thickness of the vertical books. A sample arrangement of the books is depicted in the figure.
Help Shaass to find the minimum total thickness of the vertical books that we can achieve. | The first line of the input contains an integer *n*, (1<=≤<=*n*<=≤<=100). Each of the next *n* lines contains two integers *t**i* and *w**i* denoting the thickness and width of the *i*-th book correspondingly, (1<=≤<=*t**i*<=≤<=2,<=1<=≤<=*w**i*<=≤<=100). | On the only line of the output print the minimum total thickness of the vertical books that we can achieve. | [
"5\n1 12\n1 3\n2 15\n2 5\n2 1\n",
"3\n1 10\n2 1\n2 4\n"
] | [
"5\n",
"3\n"
] | none | [
{
"input": "5\n1 12\n1 3\n2 15\n2 5\n2 1",
"output": "5"
},
{
"input": "3\n1 10\n2 1\n2 4",
"output": "3"
},
{
"input": "10\n2 10\n2 4\n2 8\n2 3\n2 5\n2 6\n1 2\n1 10\n1 10\n2 5",
"output": "12"
},
{
"input": "1\n2 7",
"output": "2"
},
{
"input": "50\n1 24\n1 16\n1... | 93 | 10,956,800 | 0 | 3,858 | |
896 | Nephren gives a riddle | [
"binary search",
"dfs and similar"
] | null | null |
Nephren is playing a game with little leprechauns.
She gives them an infinite array of strings, *f*0... ∞.
*f*0 is "What are you doing at the end of the world? Are you busy? Will you save us?".
She wants to let more people know about it, so she defines *f**i*<==<= "What are you doing while sending "*f**i*<=-<=1"? Are you busy? Will you send "*f**i*<=-<=1"?" for all *i*<=≥<=1.
For example, *f*1 is
"What are you doing while sending "What are you doing at the end of the world? Are you busy? Will you save us?"? Are you busy? Will you send "What are you doing at the end of the world? Are you busy? Will you save us?"?". Note that the quotes in the very beginning and in the very end are for clarity and are not a part of *f*1.
It can be seen that the characters in *f**i* are letters, question marks, (possibly) quotation marks and spaces.
Nephren will ask the little leprechauns *q* times. Each time she will let them find the *k*-th character of *f**n*. The characters are indexed starting from 1. If *f**n* consists of less than *k* characters, output '.' (without quotes).
Can you answer her queries? | The first line contains one integer *q* (1<=≤<=*q*<=≤<=10) — the number of Nephren's questions.
Each of the next *q* lines describes Nephren's question and contains two integers *n* and *k* (0<=≤<=*n*<=≤<=105,<=1<=≤<=*k*<=≤<=1018). | One line containing *q* characters. The *i*-th character in it should be the answer for the *i*-th query. | [
"3\n1 1\n1 2\n1 111111111111\n",
"5\n0 69\n1 194\n1 139\n0 47\n1 66\n",
"10\n4 1825\n3 75\n3 530\n4 1829\n4 1651\n3 187\n4 584\n4 255\n4 774\n2 474\n"
] | [
"Wh.",
"abdef",
"Areyoubusy"
] | For the first two examples, refer to *f*<sub class="lower-index">0</sub> and *f*<sub class="lower-index">1</sub> given in the legend. | [
{
"input": "3\n1 1\n1 2\n1 111111111111",
"output": "Wh."
},
{
"input": "5\n0 69\n1 194\n1 139\n0 47\n1 66",
"output": "abdef"
},
{
"input": "10\n4 1825\n3 75\n3 530\n4 1829\n4 1651\n3 187\n4 584\n4 255\n4 774\n2 474",
"output": "Areyoubusy"
},
{
"input": "1\n0 1",
"outpu... | 31 | 102,400 | -1 | 3,859 | |
626 | Simple Skewness | [
"binary search",
"math",
"ternary search"
] | null | null | Define the simple skewness of a collection of numbers to be the collection's mean minus its median. You are given a list of *n* (not necessarily distinct) integers. Find the non-empty subset (with repetition) with the maximum simple skewness.
The mean of a collection is the average of its elements. The median of a collection is its middle element when all of its elements are sorted, or the average of its two middle elements if it has even size. | The first line of the input contains a single integer *n* (1<=≤<=*n*<=≤<=200 000) — the number of elements in the list.
The second line contains *n* integers *x**i* (0<=≤<=*x**i*<=≤<=1<=000<=000) — the *i*th element of the list. | In the first line, print a single integer *k* — the size of the subset.
In the second line, print *k* integers — the elements of the subset in any order.
If there are multiple optimal subsets, print any. | [
"4\n1 2 3 12\n",
"4\n1 1 2 2\n",
"2\n1 2\n"
] | [
"3\n1 2 12 \n",
"3\n1 1 2 \n",
"2\n1 2\n"
] | In the first case, the optimal subset is <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/04cdbd07a0375de9c557422eca077386392a9349.png" style="max-width: 100.0%;max-height: 100.0%;"/>, which has mean 5, median 2, and simple skewness of 5 - 2 = 3.
In the second case, the optimal subset is <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/af49670de7c27def20edf0ec421d9bb17d904c94.png" style="max-width: 100.0%;max-height: 100.0%;"/>. Note that repetition is allowed.
In the last case, any subset has the same median and mean, so all have simple skewness of 0. | [
{
"input": "4\n1 2 3 12",
"output": "3\n1 2 12 "
},
{
"input": "4\n1 1 2 2",
"output": "3\n1 1 2 "
},
{
"input": "2\n1 2",
"output": "2\n1 2"
},
{
"input": "1\n1000000",
"output": "1\n1000000 "
},
{
"input": "20\n999999 999998 999996 999992 999984 999968 999936 99... | 30 | 0 | -1 | 3,874 | |
10 | LCIS | [
"dp"
] | D. LCIS | 1 | 256 | This problem differs from one which was on the online contest.
The sequence *a*1,<=*a*2,<=...,<=*a**n* is called increasing, if *a**i*<=<<=*a**i*<=+<=1 for *i*<=<<=*n*.
The sequence *s*1,<=*s*2,<=...,<=*s**k* is called the subsequence of the sequence *a*1,<=*a*2,<=...,<=*a**n*, if there exist such a set of indexes 1<=≤<=*i*1<=<<=*i*2<=<<=...<=<<=*i**k*<=≤<=*n* that *a**i**j*<==<=*s**j*. In other words, the sequence *s* can be derived from the sequence *a* by crossing out some elements.
You are given two sequences of integer numbers. You are to find their longest common increasing subsequence, i.e. an increasing sequence of maximum length that is the subsequence of both sequences. | The first line contains an integer *n* (1<=≤<=*n*<=≤<=500) — the length of the first sequence. The second line contains *n* space-separated integers from the range [0,<=109] — elements of the first sequence. The third line contains an integer *m* (1<=≤<=*m*<=≤<=500) — the length of the second sequence. The fourth line contains *m* space-separated integers from the range [0,<=109] — elements of the second sequence. | In the first line output *k* — the length of the longest common increasing subsequence. In the second line output the subsequence itself. Separate the elements with a space. If there are several solutions, output any. | [
"7\n2 3 1 6 5 4 6\n4\n1 3 5 6\n",
"5\n1 2 0 2 1\n3\n1 0 1\n"
] | [
"3\n3 5 6 \n",
"2\n0 1 \n"
] | none | [
{
"input": "7\n2 3 1 6 5 4 6\n4\n1 3 5 6",
"output": "3\n3 5 6 "
},
{
"input": "5\n1 2 0 2 1\n3\n1 0 1",
"output": "2\n0 1 "
},
{
"input": "2\n6 10\n3\n6 3 3",
"output": "1\n6 "
},
{
"input": "1\n7\n2\n7 9",
"output": "1\n7 "
},
{
"input": "3\n37 49 24\n3\n33 5 70... | 77 | 204,800 | 0 | 3,880 |
569 | Music | [
"implementation",
"math"
] | null | null | Little Lesha loves listening to music via his smartphone. But the smartphone doesn't have much memory, so Lesha listens to his favorite songs in a well-known social network InTalk.
Unfortunately, internet is not that fast in the city of Ekaterinozavodsk and the song takes a lot of time to download. But Lesha is quite impatient. The song's duration is *T* seconds. Lesha downloads the first *S* seconds of the song and plays it. When the playback reaches the point that has not yet been downloaded, Lesha immediately plays the song from the start (the loaded part of the song stays in his phone, and the download is continued from the same place), and it happens until the song is downloaded completely and Lesha listens to it to the end. For *q* seconds of real time the Internet allows you to download *q*<=-<=1 seconds of the track.
Tell Lesha, for how many times he will start the song, including the very first start. | The single line contains three integers *T*,<=*S*,<=*q* (2<=≤<=*q*<=≤<=104, 1<=≤<=*S*<=<<=*T*<=≤<=105). | Print a single integer — the number of times the song will be restarted. | [
"5 2 2\n",
"5 4 7\n",
"6 2 3\n"
] | [
"2\n",
"1\n",
"1\n"
] | In the first test, the song is played twice faster than it is downloaded, which means that during four first seconds Lesha reaches the moment that has not been downloaded, and starts the song again. After another two seconds, the song is downloaded completely, and thus, Lesha starts the song twice.
In the second test, the song is almost downloaded, and Lesha will start it only once.
In the third sample test the download finishes and Lesha finishes listening at the same moment. Note that song isn't restarted in this case. | [
{
"input": "5 2 2",
"output": "2"
},
{
"input": "5 4 7",
"output": "1"
},
{
"input": "6 2 3",
"output": "1"
},
{
"input": "2 1 2",
"output": "1"
},
{
"input": "2 1 3",
"output": "1"
},
{
"input": "2 1 10000",
"output": "1"
},
{
"input": "12... | 46 | 0 | 0 | 3,885 | |
39 | Company Income Growth | [
"greedy"
] | B. Company Income Growth | 2 | 64 | Petya works as a PR manager for a successful Berland company BerSoft. He needs to prepare a presentation on the company income growth since 2001 (the year of its founding) till now. Petya knows that in 2001 the company income amounted to *a*1 billion bourles, in 2002 — to *a*2 billion, ..., and in the current (2000<=+<=*n*)-th year — *a**n* billion bourles. On the base of the information Petya decided to show in his presentation the linear progress history which is in his opinion perfect. According to a graph Petya has already made, in the first year BerSoft company income must amount to 1 billion bourles, in the second year — 2 billion bourles etc., each following year the income increases by 1 billion bourles. Unfortunately, the real numbers are different from the perfect ones. Among the numbers *a**i* can even occur negative ones that are a sign of the company’s losses in some years. That is why Petya wants to ignore some data, in other words, cross some numbers *a**i* from the sequence and leave only some subsequence that has perfect growth.
Thus Petya has to choose a sequence of years *y*1, *y*2, ..., *y**k*,so that in the year *y*1 the company income amounted to 1 billion bourles, in the year *y*2 — 2 billion bourles etc., in accordance with the perfect growth dynamics. Help him to choose the longest such sequence. | The first line contains an integer *n* (1<=≤<=*n*<=≤<=100). The next line contains *n* integers *a**i* (<=-<=100<=≤<=*a**i*<=≤<=100). The number *a**i* determines the income of BerSoft company in the (2000<=+<=*i*)-th year. The numbers in the line are separated by spaces. | Output *k* — the maximum possible length of a perfect sequence. In the next line output the sequence of years *y*1, *y*2, ..., *y**k*. Separate the numbers by spaces. If the answer is not unique, output any. If no solution exist, output one number 0. | [
"10\n-2 1 1 3 2 3 4 -10 -2 5\n",
"3\n-1 -2 -3\n"
] | [
"5\n2002 2005 2006 2007 2010\n",
"0\n"
] | none | [
{
"input": "10\n-2 1 1 3 2 3 4 -10 -2 5",
"output": "5\n2002 2005 2006 2007 2010 "
},
{
"input": "3\n-1 -2 -3",
"output": "0"
},
{
"input": "1\n0",
"output": "0"
},
{
"input": "1\n0",
"output": "0"
},
{
"input": "2\n-1 1",
"output": "1\n2002 "
},
{
"in... | 156 | 7,065,600 | 3.908357 | 3,889 |
337 | Book of Evil | [
"dfs and similar",
"divide and conquer",
"dp",
"trees"
] | null | null | Paladin Manao caught the trail of the ancient Book of Evil in a swampy area. This area contains *n* settlements numbered from 1 to *n*. Moving through the swamp is very difficult, so people tramped exactly *n*<=-<=1 paths. Each of these paths connects some pair of settlements and is bidirectional. Moreover, it is possible to reach any settlement from any other one by traversing one or several paths.
The distance between two settlements is the minimum number of paths that have to be crossed to get from one settlement to the other one. Manao knows that the Book of Evil has got a damage range *d*. This means that if the Book of Evil is located in some settlement, its damage (for example, emergence of ghosts and werewolves) affects other settlements at distance *d* or less from the settlement where the Book resides.
Manao has heard of *m* settlements affected by the Book of Evil. Their numbers are *p*1,<=*p*2,<=...,<=*p**m*. Note that the Book may be affecting other settlements as well, but this has not been detected yet. Manao wants to determine which settlements may contain the Book. Help him with this difficult task. | The first line contains three space-separated integers *n*, *m* and *d* (1<=≤<=*m*<=≤<=*n*<=≤<=100000; 0<=≤<=*d*<=≤<=*n*<=-<=1). The second line contains *m* distinct space-separated integers *p*1,<=*p*2,<=...,<=*p**m* (1<=≤<=*p**i*<=≤<=*n*). Then *n*<=-<=1 lines follow, each line describes a path made in the area. A path is described by a pair of space-separated integers *a**i* and *b**i* representing the ends of this path. | Print a single number — the number of settlements that may contain the Book of Evil. It is possible that Manao received some controversial information and there is no settlement that may contain the Book. In such case, print 0. | [
"6 2 3\n1 2\n1 5\n2 3\n3 4\n4 5\n5 6\n"
] | [
"3\n"
] | Sample 1. The damage range of the Book of Evil equals 3 and its effects have been noticed in settlements 1 and 2. Thus, it can be in settlements 3, 4 or 5. | [
{
"input": "6 2 3\n1 2\n1 5\n2 3\n3 4\n4 5\n5 6",
"output": "3"
},
{
"input": "2 2 1\n2 1\n1 2",
"output": "2"
},
{
"input": "50 2 5\n9 14\n46 34\n40 35\n44 30\n32 16\n1 38\n48 2\n17 14\n50 25\n6 1\n45 19\n21 15\n22 11\n15 33\n8 28\n2 32\n10 22\n37 3\n43 39\n25 16\n9 19\n16 3\n28 32\n20 ... | 122 | 268,390,400 | 0 | 3,891 | |
592 | The Big Race | [
"math"
] | null | null | Vector Willman and Array Bolt are the two most famous athletes of Byteforces. They are going to compete in a race with a distance of *L* meters today.
Willman and Bolt have exactly the same speed, so when they compete the result is always a tie. That is a problem for the organizers because they want a winner.
While watching previous races the organizers have noticed that Willman can perform only steps of length equal to *w* meters, and Bolt can perform only steps of length equal to *b* meters. Organizers decided to slightly change the rules of the race. Now, at the end of the racetrack there will be an abyss, and the winner will be declared the athlete, who manages to run farther from the starting point of the the racetrack (which is not the subject to change by any of the athletes).
Note that none of the athletes can run infinitely far, as they both will at some moment of time face the point, such that only one step further will cause them to fall in the abyss. In other words, the athlete will not fall into the abyss if the total length of all his steps will be less or equal to the chosen distance *L*.
Since the organizers are very fair, the are going to set the length of the racetrack as an integer chosen randomly and uniformly in range from 1 to *t* (both are included). What is the probability that Willman and Bolt tie again today? | The first line of the input contains three integers *t*, *w* and *b* (1<=≤<=*t*,<=*w*,<=*b*<=≤<=5·1018) — the maximum possible length of the racetrack, the length of Willman's steps and the length of Bolt's steps respectively. | Print the answer to the problem as an irreducible fraction . Follow the format of the samples output.
The fraction (*p* and *q* are integers, and both *p*<=≥<=0 and *q*<=><=0 holds) is called irreducible, if there is no such integer *d*<=><=1, that both *p* and *q* are divisible by *d*. | [
"10 3 2\n",
"7 1 2\n"
] | [
"3/10\n",
"3/7\n"
] | In the first sample Willman and Bolt will tie in case 1, 6 or 7 are chosen as the length of the racetrack. | [
{
"input": "10 3 2",
"output": "3/10"
},
{
"input": "7 1 2",
"output": "3/7"
},
{
"input": "1 1 1",
"output": "1/1"
},
{
"input": "5814 31 7",
"output": "94/2907"
},
{
"input": "94268 813 766",
"output": "765/94268"
},
{
"input": "262610 5583 4717",
... | 46 | 0 | 0 | 3,899 | |
931 | World Cup | [
"constructive algorithms",
"implementation"
] | null | null | The last stage of Football World Cup is played using the play-off system.
There are *n* teams left in this stage, they are enumerated from 1 to *n*. Several rounds are held, in each round the remaining teams are sorted in the order of their ids, then the first in this order plays with the second, the third — with the fourth, the fifth — with the sixth, and so on. It is guaranteed that in each round there is even number of teams. The winner of each game advances to the next round, the loser is eliminated from the tournament, there are no draws. In the last round there is the only game with two remaining teams: the round is called the Final, the winner is called the champion, and the tournament is over.
Arkady wants his two favorite teams to play in the Final. Unfortunately, the team ids are already determined, and it may happen that it is impossible for teams to meet in the Final, because they are to meet in some earlier stage, if they are strong enough. Determine, in which round the teams with ids *a* and *b* can meet. | The only line contains three integers *n*, *a* and *b* (2<=≤<=*n*<=≤<=256, 1<=≤<=*a*,<=*b*<=≤<=*n*) — the total number of teams, and the ids of the teams that Arkady is interested in.
It is guaranteed that *n* is such that in each round an even number of team advance, and that *a* and *b* are not equal. | In the only line print "Final!" (without quotes), if teams *a* and *b* can meet in the Final.
Otherwise, print a single integer — the number of the round in which teams *a* and *b* can meet. The round are enumerated from 1. | [
"4 1 2\n",
"8 2 6\n",
"8 7 5\n"
] | [
"1\n",
"Final!\n",
"2\n"
] | In the first example teams 1 and 2 meet in the first round.
In the second example teams 2 and 6 can only meet in the third round, which is the Final, if they win all their opponents in earlier rounds.
In the third example the teams with ids 7 and 5 can meet in the second round, if they win their opponents in the first round. | [
{
"input": "4 1 2",
"output": "1"
},
{
"input": "8 2 6",
"output": "Final!"
},
{
"input": "8 7 5",
"output": "2"
},
{
"input": "128 30 98",
"output": "Final!"
},
{
"input": "256 128 256",
"output": "Final!"
},
{
"input": "256 2 127",
"output": "7"
... | 61 | 5,632,000 | 0 | 3,904 | |
51 | bHTML Tables Analisys | [
"expression parsing"
] | B. bHTML Tables Analisys | 2 | 256 | In this problem is used an extremely simplified version of HTML table markup. Please use the statement as a formal document and read it carefully.
A string is a bHTML table, if it satisfies the grammar:
Blanks in the grammar are only for purposes of illustration, in the given data there will be no spaces. The bHTML table is very similar to a simple regular HTML table in which meet only the following tags : "table", "tr", "td", all the tags are paired and the table contains at least one row and at least one cell in each row. Have a look at the sample tests as examples of tables.
As can be seen, the tables may be nested. You are given a table (which may contain other(s)). You need to write a program that analyzes all the tables and finds the number of cells in each of them. The tables are not required to be rectangular. | For convenience, input data can be separated into non-empty lines in an arbitrary manner. The input data consist of no more than 10 lines. Combine (concatenate) all the input lines into one, to get a text representation *s* of the specified table. String *s* corresponds to the given grammar (the root element of grammar is TABLE), its length does not exceed 5000. Only lower case letters are used to write tags. There are no spaces in the given string *s*. | Print the sizes of all the tables in the non-decreasing order. | [
"<table><tr><td></td></tr></table>\n",
"<table>\n<tr>\n<td>\n<table><tr><td></td></tr><tr><td></\ntd\n></tr><tr\n><td></td></tr><tr><td></td></tr></table&g... | [
"1 ",
"1 4 ",
"1 1 1 3 "
] | none | [
{
"input": "<table><tr><td></td></tr></table>",
"output": "1 "
},
{
"input": "<table>\n<tr>\n<td>\n<table><tr><td></td></tr><tr><td></\ntd\n></tr><tr\n><td></td></tr><tr><td></td></tr></table>\n</td>\n</tr>\n</table>",
"output": "1 4 "
},
{
"input": "<table><tr><td>\n<table><tr><td>\n<ta... | 62 | 0 | -1 | 3,907 |
845 | Luba And The Ticket | [
"brute force",
"greedy",
"implementation"
] | null | null | Luba has a ticket consisting of 6 digits. In one move she can choose digit in any position and replace it with arbitrary digit. She wants to know the minimum number of digits she needs to replace in order to make the ticket lucky.
The ticket is considered lucky if the sum of first three digits equals to the sum of last three digits. | You are given a string consisting of 6 characters (all characters are digits from 0 to 9) — this string denotes Luba's ticket. The ticket can start with the digit 0. | Print one number — the minimum possible number of digits Luba needs to replace to make the ticket lucky. | [
"000000\n",
"123456\n",
"111000\n"
] | [
"0\n",
"2\n",
"1\n"
] | In the first example the ticket is already lucky, so the answer is 0.
In the second example Luba can replace 4 and 5 with zeroes, and the ticket will become lucky. It's easy to see that at least two replacements are required.
In the third example Luba can replace any zero with 3. It's easy to see that at least one replacement is required. | [
{
"input": "000000",
"output": "0"
},
{
"input": "123456",
"output": "2"
},
{
"input": "111000",
"output": "1"
},
{
"input": "120111",
"output": "0"
},
{
"input": "999999",
"output": "0"
},
{
"input": "199880",
"output": "1"
},
{
"input": "... | 93 | 307,200 | 0 | 3,915 | |
111 | Petya and Rectangle | [] | E. Petya and Rectangle | 5 | 256 | Little Petya loves playing with rectangles. Mom bought Petya a rectangle divided into cells *n*<=×<=*m* in size (containing *n* rows, *m* columns). Petya marked two different cells of the rectangle and now he is solving the following task:
Let's define a simple path between those two cells as a sequence of distinct cells *a*1,<=*a*2,<=...,<=*a**k*, where *a*1 and *a**k* are the two marked cells. Besides, *a**i* and *a**i*<=+<=1 are side-neighboring cells of the path (1<=≤<=*i*<=<<=*k*). Let's denote the path length as number *k* (the sequence length).
Petya's task is to find the longest simple path's length and to print the path. Help him. | The first line contains space-separated integers *n* and *m* (4<=≤<=*n*,<=*m*<=≤<=1000) — the number of rows and the number of columns in the rectangle, correspondingly. The second line contains space-separated integers *x*1 and *y*1 — the coordinates of the first marked cell. The third line contains space-separated integers *x*2 *y*2 — the coordinates of the second marked cell (1<=<<=*x*1,<=*x*2<=<<=*n*,<=1<=<<=*y*1,<=*y*2<=<<=*m*,<=*x*1<=≠<=*x*2,<=*y*1<=≠<=*y*2).
The coordinates of a marked cell are a pair of integers *x* *y*, where *x* represents the row's number and *y* represents the column's number. The rows are numbered from top to bottom with consecutive integers from 1 to *n*. The columns are numbered from the left to the right by consecutive integers from 1 to *m*.
It is guaranteed that the marked cells are not positioned in one row or column. | In the first line print the length of the found path — *k*. In the next lines print *k* pairs of integers, one per line — coordinates of the cells that constitute the found path in the order, in which they follow in the path (the path must go from cell (*x*1,<=*y*1) to cell (*x*2,<=*y*2)). If there are several solutions, print any of them. | [
"4 4\n2 2\n3 3\n"
] | [
"15\n2 2\n1 2\n1 1\n2 1\n3 1\n4 1\n4 2\n4 3\n4 4\n3 4\n2 4\n1 4\n1 3\n2 3\n3 3\n"
] | The statement test is described in the picture: | [] | 92 | 0 | 0 | 3,919 |
208 | Police Station | [
"dp",
"graphs",
"shortest paths"
] | null | null | The Berland road network consists of *n* cities and of *m* bidirectional roads. The cities are numbered from 1 to *n*, where the main capital city has number *n*, and the culture capital — number 1. The road network is set up so that it is possible to reach any city from any other one by the roads. Moving on each road in any direction takes the same time.
All residents of Berland are very lazy people, and so when they want to get from city *v* to city *u*, they always choose one of the shortest paths (no matter which one).
The Berland government wants to make this country's road network safer. For that, it is going to put a police station in one city. The police station has a rather strange property: when a citizen of Berland is driving along the road with a police station at one end of it, the citizen drives more carefully, so all such roads are considered safe. The roads, both ends of which differ from the city with the police station, are dangerous.
Now the government wonders where to put the police station so that the average number of safe roads for all the shortest paths from the cultural capital to the main capital would take the maximum value. | The first input line contains two integers *n* and *m* (2<=≤<=*n*<=≤<=100, ) — the number of cities and the number of roads in Berland, correspondingly. Next *m* lines contain pairs of integers *v**i*, *u**i* (1<=≤<=*v**i*,<=*u**i*<=≤<=*n*, *v**i*<=≠<=*u**i*) — the numbers of cities that are connected by the *i*-th road. The numbers on a line are separated by a space.
It is guaranteed that each pair of cities is connected with no more than one road and that it is possible to get from any city to any other one along Berland roads. | Print the maximum possible value of the average number of safe roads among all shortest paths from the culture capital to the main one. The answer will be considered valid if its absolute or relative inaccuracy does not exceed 10<=-<=6. | [
"4 4\n1 2\n2 4\n1 3\n3 4\n",
"11 14\n1 2\n1 3\n2 4\n3 4\n4 5\n4 6\n5 11\n6 11\n1 8\n8 9\n9 7\n11 7\n1 10\n10 4\n"
] | [
"1.000000000000\n",
"1.714285714286\n"
] | In the first sample you can put a police station in one of the capitals, then each path will have exactly one safe road. If we place the station not in the capital, then the average number of safe roads will also make <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/8f23cc2cd3bef67bde56e16911c7af627da25d4d.png" style="max-width: 100.0%;max-height: 100.0%;"/>.
In the second sample we can obtain the maximum sought value if we put the station in city 4, then 6 paths will have 2 safe roads each, and one path will have 0 safe roads, so the answer will equal <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/d7723df54e28c93b1c3b9d4c68b039b5071092af.png" style="max-width: 100.0%;max-height: 100.0%;"/>. | [] | 60 | 0 | 0 | 3,942 | |
1,004 | Sonya and Exhibition | [
"constructive algorithms",
"greedy",
"implementation",
"math"
] | null | null | Sonya decided to organize an exhibition of flowers. Since the girl likes only roses and lilies, she decided that only these two kinds of flowers should be in this exhibition.
There are $n$ flowers in a row in the exhibition. Sonya can put either a rose or a lily in the $i$-th position. Thus each of $n$ positions should contain exactly one flower: a rose or a lily.
She knows that exactly $m$ people will visit this exhibition. The $i$-th visitor will visit all flowers from $l_i$ to $r_i$ inclusive. The girl knows that each segment has its own beauty that is equal to the product of the number of roses and the number of lilies.
Sonya wants her exhibition to be liked by a lot of people. That is why she wants to put the flowers in such way that the sum of beauties of all segments would be maximum possible. | The first line contains two integers $n$ and $m$ ($1\leq n, m\leq 10^3$) — the number of flowers and visitors respectively.
Each of the next $m$ lines contains two integers $l_i$ and $r_i$ ($1\leq l_i\leq r_i\leq n$), meaning that $i$-th visitor will visit all flowers from $l_i$ to $r_i$ inclusive. | Print the string of $n$ characters. The $i$-th symbol should be «0» if you want to put a rose in the $i$-th position, otherwise «1» if you want to put a lily.
If there are multiple answers, print any. | [
"5 3\n1 3\n2 4\n2 5\n",
"6 3\n5 6\n1 4\n4 6\n"
] | [
"01100",
"110010"
] | In the first example, Sonya can put roses in the first, fourth, and fifth positions, and lilies in the second and third positions;
- in the segment $[1\ldots3]$, there are one rose and two lilies, so the beauty is equal to $1\cdot 2=2$; - in the segment $[2\ldots4]$, there are one rose and two lilies, so the beauty is equal to $1\cdot 2=2$; - in the segment $[2\ldots5]$, there are two roses and two lilies, so the beauty is equal to $2\cdot 2=4$.
The total beauty is equal to $2+2+4=8$.
In the second example, Sonya can put roses in the third, fourth, and sixth positions, and lilies in the first, second, and fifth positions;
- in the segment $[5\ldots6]$, there are one rose and one lily, so the beauty is equal to $1\cdot 1=1$; - in the segment $[1\ldots4]$, there are two roses and two lilies, so the beauty is equal to $2\cdot 2=4$; - in the segment $[4\ldots6]$, there are two roses and one lily, so the beauty is equal to $2\cdot 1=2$.
The total beauty is equal to $1+4+2=7$. | [
{
"input": "5 3\n1 3\n2 4\n2 5",
"output": "01010"
},
{
"input": "6 3\n5 6\n1 4\n4 6",
"output": "010101"
},
{
"input": "10 4\n3 3\n1 6\n9 9\n10 10",
"output": "0101010101"
},
{
"input": "1 1\n1 1",
"output": "0"
},
{
"input": "1000 10\n3 998\n2 1000\n1 999\n2 100... | 108 | 0 | 0 | 3,947 | |
27 | Unordered Subsequence | [
"constructive algorithms",
"greedy"
] | C. Unordered Subsequence | 2 | 256 | The sequence is called ordered if it is non-decreasing or non-increasing. For example, sequnces [3, 1, 1, 0] and [1, 2, 3, 100] are ordered, but the sequence [1, 3, 3, 1] is not. You are given a sequence of numbers. You are to find it's shortest subsequence which is not ordered.
A subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements. | The first line of the input contains one integer *n* (1<=≤<=*n*<=≤<=105). The second line contains *n* space-separated integers — the given sequence. All numbers in this sequence do not exceed 106 by absolute value. | If the given sequence does not contain any unordered subsequences, output 0. Otherwise, output the length *k* of the shortest such subsequence. Then output *k* integers from the range [1..*n*] — indexes of the elements of this subsequence. If there are several solutions, output any of them. | [
"5\n67 499 600 42 23\n",
"3\n1 2 3\n",
"3\n2 3 1\n"
] | [
"3\n1 3 5\n",
"0\n",
"3\n1 2 3\n"
] | none | [
{
"input": "3\n3 1 2",
"output": "3\n1 2 3"
},
{
"input": "1\n-895376",
"output": "0"
},
{
"input": "2\n166442 61629",
"output": "0"
},
{
"input": "3\n-771740 -255752 -300809",
"output": "3\n1 2 3"
},
{
"input": "4\n-227347 -573134 -671045 11011",
"output": "3... | 218 | 0 | -1 | 3,949 |
877 | Ann and Books | [
"data structures",
"flows",
"hashing"
] | null | null | In Ann's favorite book shop are as many as *n* books on math and economics. Books are numbered from 1 to *n*. Each of them contains non-negative number of problems.
Today there is a sale: any subsegment of a segment from *l* to *r* can be bought at a fixed price.
Ann decided that she wants to buy such non-empty subsegment that the sale operates on it and the number of math problems is greater than the number of economics problems exactly by *k*. Note that *k* may be positive, negative or zero.
Unfortunately, Ann is not sure on which segment the sale operates, but she has *q* assumptions. For each of them she wants to know the number of options to buy a subsegment satisfying the condition (because the time she spends on choosing depends on that).
Currently Ann is too busy solving other problems, she asks you for help. For each her assumption determine the number of subsegments of the given segment such that the number of math problems is greaten than the number of economics problems on that subsegment exactly by *k*. | The first line contains two integers *n* and *k* (1<=≤<=*n*<=≤<=100<=000, <=-<=109<=≤<=*k*<=≤<=109) — the number of books and the needed difference between the number of math problems and the number of economics problems.
The second line contains *n* integers *t*1,<=*t*2,<=...,<=*t**n* (1<=≤<=*t**i*<=≤<=2), where *t**i* is 1 if the *i*-th book is on math or 2 if the *i*-th is on economics.
The third line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (0<=≤<=*a**i*<=≤<=109), where *a**i* is the number of problems in the *i*-th book.
The fourth line contains a single integer *q* (1<=≤<=*q*<=≤<=100<=000) — the number of assumptions.
Each of the next *q* lines contains two integers *l**i* and *r**i* (1<=≤<=*l**i*<=≤<=*r**i*<=≤<=*n*) describing the *i*-th Ann's assumption. | Print *q* lines, in the *i*-th of them print the number of subsegments for the *i*-th Ann's assumption. | [
"4 1\n1 1 1 2\n1 1 1 1\n4\n1 2\n1 3\n1 4\n3 4\n",
"4 0\n1 2 1 2\n0 0 0 0\n1\n1 4\n"
] | [
"2\n3\n4\n1\n",
"10\n"
] | In the first sample Ann can buy subsegments [1;1], [2;2], [3;3], [2;4] if they fall into the sales segment, because the number of math problems is greater by 1 on them that the number of economics problems. So we should count for each assumption the number of these subsegments that are subsegments of the given segment.
Segments [1;1] and [2;2] are subsegments of [1;2].
Segments [1;1], [2;2] and [3;3] are subsegments of [1;3].
Segments [1;1], [2;2], [3;3], [2;4] are subsegments of [1;4].
Segment [3;3] is subsegment of [3;4]. | [
{
"input": "4 1\n1 1 1 2\n1 1 1 1\n4\n1 2\n1 3\n1 4\n3 4",
"output": "2\n3\n4\n1"
},
{
"input": "4 0\n1 2 1 2\n0 0 0 0\n1\n1 4",
"output": "10"
},
{
"input": "10 10\n2 1 1 1 1 1 1 1 1 2\n0 10 10 0 0 10 10 10 10 0\n10\n4 10\n3 7\n9 9\n2 9\n10 10\n5 5\n2 2\n6 8\n3 4\n1 3",
"output": "7... | 0 | 0 | -1 | 3,966 | |
90 | Cableway | [
"greedy",
"math"
] | A. Cableway | 2 | 256 | A group of university students wants to get to the top of a mountain to have a picnic there. For that they decided to use a cableway.
A cableway is represented by some cablecars, hanged onto some cable stations by a cable. A cable is scrolled cyclically between the first and the last cable stations (the first of them is located at the bottom of the mountain and the last one is located at the top). As the cable moves, the cablecar attached to it move as well.
The number of cablecars is divisible by three and they are painted three colors: red, green and blue, in such manner that after each red cablecar goes a green one, after each green cablecar goes a blue one and after each blue cablecar goes a red one. Each cablecar can transport no more than two people, the cablecars arrive with the periodicity of one minute (i. e. every minute) and it takes exactly 30 minutes for a cablecar to get to the top.
All students are divided into three groups: *r* of them like to ascend only in the red cablecars, *g* of them prefer only the green ones and *b* of them prefer only the blue ones. A student never gets on a cablecar painted a color that he doesn't like,
The first cablecar to arrive (at the moment of time 0) is painted red. Determine the least time it will take all students to ascend to the mountain top. | The first line contains three integers *r*, *g* and *b* (0<=≤<=*r*,<=*g*,<=*b*<=≤<=100). It is guaranteed that *r*<=+<=*g*<=+<=*b*<=><=0, it means that the group consists of at least one student. | Print a single number — the minimal time the students need for the whole group to ascend to the top of the mountain. | [
"1 3 2\n",
"3 2 1\n"
] | [
"34",
"33"
] | Let's analyze the first sample.
At the moment of time 0 a red cablecar comes and one student from the *r* group get on it and ascends to the top at the moment of time 30.
At the moment of time 1 a green cablecar arrives and two students from the *g* group get on it; they get to the top at the moment of time 31.
At the moment of time 2 comes the blue cablecar and two students from the *b* group get on it. They ascend to the top at the moment of time 32.
At the moment of time 3 a red cablecar arrives but the only student who is left doesn't like red and the cablecar leaves empty.
At the moment of time 4 a green cablecar arrives and one student from the *g* group gets on it. He ascends to top at the moment of time 34.
Thus, all the students are on the top, overall the ascension took exactly 34 minutes. | [
{
"input": "1 3 2",
"output": "34"
},
{
"input": "3 2 1",
"output": "33"
},
{
"input": "3 5 2",
"output": "37"
},
{
"input": "10 10 10",
"output": "44"
},
{
"input": "29 7 24",
"output": "72"
},
{
"input": "28 94 13",
"output": "169"
},
{
"... | 218 | 0 | 3.9455 | 3,971 |
85 | Domino | [
"constructive algorithms",
"implementation"
] | A. Domino | 1 | 256 | We all know the problem about the number of ways one can tile a 2<=×<=*n* field by 1<=×<=2 dominoes. You probably remember that it goes down to Fibonacci numbers. We will talk about some other problem below, there you also are going to deal with tiling a rectangular field with dominoes.
You are given a 4<=×<=*n* rectangular field, that is the field that contains four lines and *n* columns. You have to find for it any tiling by 1<=×<=2 dominoes such that each of the *n*<=-<=1 potential vertical cuts along the grid lines intersects at least one domino, splitting it in two. No two dominoes in the sought tiling should overlap, each square of the field should be covered by exactly one domino. It is allowed to rotate the dominoes, that is, you can use 2<=×<=1 as well as 1<=×<=2 dominoes.
Write a program that finds an arbitrary sought tiling. | The input contains one positive integer *n* (1<=≤<=*n*<=≤<=100) — the number of the field's columns. | If there's no solution, print "-1" (without the quotes). Otherwise, print four lines containing *n* characters each — that's the description of tiling, where each vertical cut intersects at least one domino. You should print the tiling, having painted the field in no more than 26 colors. Each domino should be painted a color. Different dominoes can be painted the same color, but dominoes of the same color should not be side-neighbouring. To indicate colors you should use lowercase Latin letters. Print any of the acceptable ways of tiling. | [
"4\n"
] | [
"yyzz\nbccd\nbxxd\nyyaa\n"
] | none | [
{
"input": "4",
"output": "aacc\nbbdd\nzkkz\nzllz"
},
{
"input": "2",
"output": "aa\nbb\naa\nbb"
},
{
"input": "3",
"output": "aab\nccb\nbaa\nbcc"
},
{
"input": "5",
"output": "aaccz\nbbddz\nzkkmm\nzllnn"
},
{
"input": "1",
"output": "a\na\nb\nb"
},
{
... | 248 | 512,000 | 0 | 3,979 |
31 | Worms Evolution | [
"implementation"
] | A. Worms Evolution | 2 | 256 | Professor Vasechkin is studying evolution of worms. Recently he put forward hypotheses that all worms evolve by division. There are *n* forms of worms. Worms of these forms have lengths *a*1, *a*2, ..., *a**n*. To prove his theory, professor needs to find 3 different forms that the length of the first form is equal to sum of lengths of the other two forms. Help him to do this. | The first line contains integer *n* (3<=≤<=*n*<=≤<=100) — amount of worm's forms. The second line contains *n* space-separated integers *a**i* (1<=≤<=*a**i*<=≤<=1000) — lengths of worms of each form. | Output 3 distinct integers *i* *j* *k* (1<=≤<=*i*,<=*j*,<=*k*<=≤<=*n*) — such indexes of worm's forms that *a**i*<==<=*a**j*<=+<=*a**k*. If there is no such triple, output -1. If there are several solutions, output any of them. It possible that *a**j*<==<=*a**k*. | [
"5\n1 2 3 5 7\n",
"5\n1 8 1 5 1\n"
] | [
"3 2 1\n",
"-1\n"
] | none | [
{
"input": "5\n1 2 3 5 7",
"output": "3 2 1"
},
{
"input": "5\n1 8 1 5 1",
"output": "-1"
},
{
"input": "4\n303 872 764 401",
"output": "-1"
},
{
"input": "6\n86 402 133 524 405 610",
"output": "6 4 1"
},
{
"input": "8\n217 779 418 895 996 473 3 22",
"output":... | 92 | 0 | 3.977 | 3,989 |
400 | Inna and Choose Options | [
"implementation"
] | null | null | There always is something to choose from! And now, instead of "Noughts and Crosses", Inna choose a very unusual upgrade of this game. The rules of the game are given below:
There is one person playing the game. Before the beginning of the game he puts 12 cards in a row on the table. Each card contains a character: "X" or "O". Then the player chooses two positive integers *a* and *b* (*a*·*b*<==<=12), after that he makes a table of size *a*<=×<=*b* from the cards he put on the table as follows: the first *b* cards form the first row of the table, the second *b* cards form the second row of the table and so on, the last *b* cards form the last (number *a*) row of the table. The player wins if some column of the table contain characters "X" on all cards. Otherwise, the player loses.
Inna has already put 12 cards on the table in a row. But unfortunately, she doesn't know what numbers *a* and *b* to choose. Help her win the game: print to her all the possible ways of numbers *a*,<=*b* that she can choose and win. | The first line of the input contains integer *t* (1<=≤<=*t*<=≤<=100). This value shows the number of sets of test data in the input. Next follows the description of each of the *t* tests on a separate line.
The description of each test is a string consisting of 12 characters, each character is either "X", or "O". The *i*-th character of the string shows the character that is written on the *i*-th card from the start. | For each test, print the answer to the test on a single line. The first number in the line must represent the number of distinct ways to choose the pair *a*,<=*b*. Next, print on this line the pairs in the format *a*x*b*. Print the pairs in the order of increasing first parameter (*a*). Separate the pairs in the line by whitespaces. | [
"4\nOXXXOXOOXOOX\nOXOXOXOXOXOX\nXXXXXXXXXXXX\nOOOOOOOOOOOO\n"
] | [
"3 1x12 2x6 4x3\n4 1x12 2x6 3x4 6x2\n6 1x12 2x6 3x4 4x3 6x2 12x1\n0\n"
] | none | [
{
"input": "4\nOXXXOXOOXOOX\nOXOXOXOXOXOX\nXXXXXXXXXXXX\nOOOOOOOOOOOO",
"output": "3 1x12 2x6 4x3\n4 1x12 2x6 3x4 6x2\n6 1x12 2x6 3x4 4x3 6x2 12x1\n0"
},
{
"input": "2\nOOOOOOOOOOOO\nXXXXXXXXXXXX",
"output": "0\n6 1x12 2x6 3x4 4x3 6x2 12x1"
},
{
"input": "13\nXXXXXXXXXXXX\nXXXXXXXXXXXX\n... | 77 | 0 | 3 | 3,992 | |
181 | Number of Triplets | [
"binary search",
"brute force"
] | null | null | You are given *n* points on a plane. All points are different.
Find the number of different groups of three points (*A*,<=*B*,<=*C*) such that point *B* is the middle of segment *AC*.
The groups of three points are considered unordered, that is, if point *B* is the middle of segment *AC*, then groups (*A*,<=*B*,<=*C*) and (*C*,<=*B*,<=*A*) are considered the same. | The first line contains a single integer *n* (3<=≤<=*n*<=≤<=3000) — the number of points.
Next *n* lines contain the points. The *i*-th line contains coordinates of the *i*-th point: two space-separated integers *x**i*,<=*y**i* (<=-<=1000<=≤<=*x**i*,<=*y**i*<=≤<=1000).
It is guaranteed that all given points are different. | Print the single number — the answer to the problem. | [
"3\n1 1\n2 2\n3 3\n",
"3\n0 0\n-1 0\n0 1\n"
] | [
"1\n",
"0\n"
] | none | [
{
"input": "3\n1 1\n2 2\n3 3",
"output": "1"
},
{
"input": "3\n0 0\n-1 0\n0 1",
"output": "0"
},
{
"input": "4\n0 0\n1 0\n2 0\n3 0",
"output": "2"
},
{
"input": "5\n0 -1\n0 -2\n0 -3\n0 -4\n0 -5",
"output": "4"
},
{
"input": "7\n1 1\n-1 -1\n1 0\n0 1\n-1 0\n0 -1\n0 ... | 466 | 16,998,400 | 0 | 3,997 | |
959 | Mahmoud and Ehab and the even-odd game | [
"games",
"math"
] | null | null | Mahmoud and Ehab play a game called the even-odd game. Ehab chooses his favorite integer *n* and then they take turns, starting from Mahmoud. In each player's turn, he has to choose an integer *a* and subtract it from *n* such that:
- 1<=≤<=*a*<=≤<=*n*. - If it's Mahmoud's turn, *a* has to be even, but if it's Ehab's turn, *a* has to be odd.
If the current player can't choose any number satisfying the conditions, he loses. Can you determine the winner if they both play optimally? | The only line contains an integer *n* (1<=≤<=*n*<=≤<=109), the number at the beginning of the game. | Output "Mahmoud" (without quotes) if Mahmoud wins and "Ehab" (without quotes) otherwise. | [
"1\n",
"2\n"
] | [
"Ehab",
"Mahmoud"
] | In the first sample, Mahmoud can't choose any integer *a* initially because there is no positive even integer less than or equal to 1 so Ehab wins.
In the second sample, Mahmoud has to choose *a* = 2 and subtract it from *n*. It's Ehab's turn and *n* = 0. There is no positive odd integer less than or equal to 0 so Mahmoud wins. | [
{
"input": "1",
"output": "Ehab"
},
{
"input": "2",
"output": "Mahmoud"
},
{
"input": "10000",
"output": "Mahmoud"
},
{
"input": "33333",
"output": "Ehab"
},
{
"input": "5",
"output": "Ehab"
},
{
"input": "1000000000",
"output": "Mahmoud"
},
{
... | 0 | 0 | -1 | 4,010 | |
817 | Treasure Hunt | [
"implementation",
"math",
"number theory"
] | null | null | Captain Bill the Hummingbird and his crew recieved an interesting challenge offer. Some stranger gave them a map, potion of teleportation and said that only this potion might help them to reach the treasure.
Bottle with potion has two values *x* and *y* written on it. These values define four moves which can be performed using the potion:
- - - -
Map shows that the position of Captain Bill the Hummingbird is (*x*1,<=*y*1) and the position of the treasure is (*x*2,<=*y*2).
You task is to tell Captain Bill the Hummingbird whether he should accept this challenge or decline. If it is possible for Captain to reach the treasure using the potion then output "YES", otherwise "NO" (without quotes).
The potion can be used infinite amount of times. | The first line contains four integer numbers *x*1,<=*y*1,<=*x*2,<=*y*2 (<=-<=105<=≤<=*x*1,<=*y*1,<=*x*2,<=*y*2<=≤<=105) — positions of Captain Bill the Hummingbird and treasure respectively.
The second line contains two integer numbers *x*,<=*y* (1<=≤<=*x*,<=*y*<=≤<=105) — values on the potion bottle. | Print "YES" if it is possible for Captain to reach the treasure using the potion, otherwise print "NO" (without quotes). | [
"0 0 0 6\n2 3\n",
"1 1 3 6\n1 5\n"
] | [
"YES\n",
"NO\n"
] | In the first example there exists such sequence of moves:
1. <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7c939890fb4ed35688177327dac981bfa9216c00.png" style="max-width: 100.0%;max-height: 100.0%;"/> — the first type of move 1. <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/afbfa42fbac4e0641e7466e3aac74cbbb08ed597.png" style="max-width: 100.0%;max-height: 100.0%;"/> — the third type of move | [
{
"input": "0 0 0 6\n2 3",
"output": "YES"
},
{
"input": "1 1 3 6\n1 5",
"output": "NO"
},
{
"input": "5 4 6 -10\n1 1",
"output": "NO"
},
{
"input": "6 -3 -7 -7\n1 2",
"output": "NO"
},
{
"input": "2 -5 -8 8\n2 1",
"output": "YES"
},
{
"input": "70 -81... | 109 | 307,200 | 3 | 4,028 | |
380 | Sereja and Brackets | [
"data structures",
"schedules"
] | null | null | Sereja has a bracket sequence *s*1,<=*s*2,<=...,<=*s**n*, or, in other words, a string *s* of length *n*, consisting of characters "(" and ")".
Sereja needs to answer *m* queries, each of them is described by two integers *l**i*,<=*r**i* (1<=≤<=*l**i*<=≤<=*r**i*<=≤<=*n*). The answer to the *i*-th query is the length of the maximum correct bracket subsequence of sequence *s**l**i*,<=*s**l**i*<=+<=1,<=...,<=*s**r**i*. Help Sereja answer all queries.
You can find the definitions for a subsequence and a correct bracket sequence in the notes. | The first line contains a sequence of characters *s*1,<=*s*2,<=...,<=*s**n* (1<=≤<=*n*<=≤<=106) without any spaces. Each character is either a "(" or a ")". The second line contains integer *m* (1<=≤<=*m*<=≤<=105) — the number of queries. Each of the next *m* lines contains a pair of integers. The *i*-th line contains integers *l**i*,<=*r**i* (1<=≤<=*l**i*<=≤<=*r**i*<=≤<=*n*) — the description of the *i*-th query. | Print the answer to each question on a single line. Print the answers in the order they go in the input. | [
"())(())(())(\n7\n1 1\n2 3\n1 2\n1 12\n8 12\n5 11\n2 10\n"
] | [
"0\n0\n2\n10\n4\n6\n6\n"
] | A subsequence of length |*x*| of string *s* = *s*<sub class="lower-index">1</sub>*s*<sub class="lower-index">2</sub>... *s*<sub class="lower-index">|*s*|</sub> (where |*s*| is the length of string *s*) is string *x* = *s*<sub class="lower-index">*k*<sub class="lower-index">1</sub></sub>*s*<sub class="lower-index">*k*<sub class="lower-index">2</sub></sub>... *s*<sub class="lower-index">*k*<sub class="lower-index">|*x*|</sub></sub> (1 ≤ *k*<sub class="lower-index">1</sub> < *k*<sub class="lower-index">2</sub> < ... < *k*<sub class="lower-index">|*x*|</sub> ≤ |*s*|).
A correct bracket sequence is a bracket sequence that can be transformed into a correct aryphmetic expression by inserting characters "1" and "+" between the characters of the string. For example, bracket sequences "()()", "(())" are correct (the resulting expressions "(1)+(1)", "((1+1)+1)"), and ")(" and "(" are not.
For the third query required sequence will be «()».
For the fourth query required sequence will be «()(())(())». | [
{
"input": "())(())(())(\n7\n1 1\n2 3\n1 2\n1 12\n8 12\n5 11\n2 10",
"output": "0\n0\n2\n10\n4\n6\n6"
},
{
"input": "(((((()((((((((((()((()(((((\n1\n8 15",
"output": "0"
},
{
"input": "((()((())(((((((((()(()(()(((((((((((((((()(()((((((((((((((()(((((((((((((((((((()(((\n39\n28 56\n39 ... | 1,000 | 139,571,200 | 0 | 4,039 | |
237 | Primes on Interval | [
"binary search",
"number theory",
"two pointers"
] | null | null | You've decided to carry out a survey in the theory of prime numbers. Let us remind you that a prime number is a positive integer that has exactly two distinct positive integer divisors.
Consider positive integers *a*, *a*<=+<=1, ..., *b* (*a*<=≤<=*b*). You want to find the minimum integer *l* (1<=≤<=*l*<=≤<=*b*<=-<=*a*<=+<=1) such that for any integer *x* (*a*<=≤<=*x*<=≤<=*b*<=-<=*l*<=+<=1) among *l* integers *x*, *x*<=+<=1, ..., *x*<=+<=*l*<=-<=1 there are at least *k* prime numbers.
Find and print the required minimum *l*. If no value *l* meets the described limitations, print -1. | A single line contains three space-separated integers *a*,<=*b*,<=*k* (1<=≤<=*a*,<=*b*,<=*k*<=≤<=106; *a*<=≤<=*b*). | In a single line print a single integer — the required minimum *l*. If there's no solution, print -1. | [
"2 4 2\n",
"6 13 1\n",
"1 4 3\n"
] | [
"3\n",
"4\n",
"-1\n"
] | none | [
{
"input": "2 4 2",
"output": "3"
},
{
"input": "6 13 1",
"output": "4"
},
{
"input": "1 4 3",
"output": "-1"
},
{
"input": "5 8 2",
"output": "4"
},
{
"input": "8 10 3",
"output": "-1"
},
{
"input": "1 5 2",
"output": "3"
},
{
"input": "6 ... | 61 | 6,963,200 | 0 | 4,047 | |
548 | Mike and Fun | [
"brute force",
"dp",
"greedy",
"implementation"
] | null | null | Mike and some bears are playing a game just for fun. Mike is the judge. All bears except Mike are standing in an *n*<=×<=*m* grid, there's exactly one bear in each cell. We denote the bear standing in column number *j* of row number *i* by (*i*,<=*j*). Mike's hands are on his ears (since he's the judge) and each bear standing in the grid has hands either on his mouth or his eyes.
They play for *q* rounds. In each round, Mike chooses a bear (*i*,<=*j*) and tells him to change his state i. e. if his hands are on his mouth, then he'll put his hands on his eyes or he'll put his hands on his mouth otherwise. After that, Mike wants to know the score of the bears.
Score of the bears is the maximum over all rows of number of consecutive bears with hands on their eyes in that row.
Since bears are lazy, Mike asked you for help. For each round, tell him the score of these bears after changing the state of a bear selected in that round. | The first line of input contains three integers *n*, *m* and *q* (1<=≤<=*n*,<=*m*<=≤<=500 and 1<=≤<=*q*<=≤<=5000).
The next *n* lines contain the grid description. There are *m* integers separated by spaces in each line. Each of these numbers is either 0 (for mouth) or 1 (for eyes).
The next *q* lines contain the information about the rounds. Each of them contains two integers *i* and *j* (1<=≤<=*i*<=≤<=*n* and 1<=≤<=*j*<=≤<=*m*), the row number and the column number of the bear changing his state. | After each round, print the current score of the bears. | [
"5 4 5\n0 1 1 0\n1 0 0 1\n0 1 1 0\n1 0 0 1\n0 0 0 0\n1 1\n1 4\n1 1\n4 2\n4 3\n"
] | [
"3\n4\n3\n3\n4\n"
] | none | [
{
"input": "5 4 5\n0 1 1 0\n1 0 0 1\n0 1 1 0\n1 0 0 1\n0 0 0 0\n1 1\n1 4\n1 1\n4 2\n4 3",
"output": "3\n4\n3\n3\n4"
},
{
"input": "2 2 10\n1 1\n0 1\n1 1\n2 1\n1 1\n2 2\n1 1\n2 1\n2 2\n2 2\n1 1\n1 1",
"output": "1\n2\n2\n2\n1\n1\n1\n1\n2\n1"
},
{
"input": "2 2 10\n1 1\n0 1\n2 2\n2 2\n1 1\... | 46 | 102,400 | 0 | 4,049 | |
833 | The Meaningless Game | [
"math",
"number theory"
] | null | null | Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number *k* is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by *k*2, and the loser's score is multiplied by *k*. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all *n* games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not. | In the first string, the number of games *n* (1<=≤<=*n*<=≤<=350000) is given.
Each game is represented by a pair of scores *a*, *b* (1<=≤<=*a*,<=*b*<=≤<=109) – the results of Slastyona and Pushok, correspondingly. | For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower). | [
"6\n2 4\n75 45\n8 8\n16 16\n247 994\n1000000000 1000000\n"
] | [
"Yes\nYes\nYes\nNo\nNo\nYes\n"
] | First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3. | [
{
"input": "6\n2 4\n75 45\n8 8\n16 16\n247 994\n1000000000 1000000",
"output": "Yes\nYes\nYes\nNo\nNo\nYes"
},
{
"input": "3\n1 1\n8 27\n1000 1331",
"output": "Yes\nNo\nNo"
},
{
"input": "1\n12004 18012002",
"output": "Yes"
},
{
"input": "1\n3331 11095561",
"output": "Yes... | 1,000 | 0 | 0 | 4,052 | |
596 | Wilbur and Points | [
"combinatorics",
"greedy",
"sortings"
] | null | null | Wilbur is playing with a set of *n* points on the coordinate plane. All points have non-negative integer coordinates. Moreover, if some point (*x*, *y*) belongs to the set, then all points (*x*', *y*'), such that 0<=≤<=*x*'<=≤<=*x* and 0<=≤<=*y*'<=≤<=*y* also belong to this set.
Now Wilbur wants to number the points in the set he has, that is assign them distinct integer numbers from 1 to *n*. In order to make the numbering aesthetically pleasing, Wilbur imposes the condition that if some point (*x*, *y*) gets number *i*, then all (*x*',*y*') from the set, such that *x*'<=≥<=*x* and *y*'<=≥<=*y* must be assigned a number not less than *i*. For example, for a set of four points (0, 0), (0, 1), (1, 0) and (1, 1), there are two aesthetically pleasing numberings. One is 1, 2, 3, 4 and another one is 1, 3, 2, 4.
Wilbur's friend comes along and challenges Wilbur. For any point he defines it's special value as *s*(*x*,<=*y*)<==<=*y*<=-<=*x*. Now he gives Wilbur some *w*1, *w*2,..., *w**n*, and asks him to find an aesthetically pleasing numbering of the points in the set, such that the point that gets number *i* has it's special value equal to *w**i*, that is *s*(*x**i*,<=*y**i*)<==<=*y**i*<=-<=*x**i*<==<=*w**i*.
Now Wilbur asks you to help him with this challenge. | The first line of the input consists of a single integer *n* (1<=≤<=*n*<=≤<=100<=000) — the number of points in the set Wilbur is playing with.
Next follow *n* lines with points descriptions. Each line contains two integers *x* and *y* (0<=≤<=*x*,<=*y*<=≤<=100<=000), that give one point in Wilbur's set. It's guaranteed that all points are distinct. Also, it is guaranteed that if some point (*x*, *y*) is present in the input, then all points (*x*', *y*'), such that 0<=≤<=*x*'<=≤<=*x* and 0<=≤<=*y*'<=≤<=*y*, are also present in the input.
The last line of the input contains *n* integers. The *i*-th of them is *w**i* (<=-<=100<=000<=≤<=*w**i*<=≤<=100<=000) — the required special value of the point that gets number *i* in any aesthetically pleasing numbering. | If there exists an aesthetically pleasant numbering of points in the set, such that *s*(*x**i*,<=*y**i*)<==<=*y**i*<=-<=*x**i*<==<=*w**i*, then print "YES" on the first line of the output. Otherwise, print "NO".
If a solution exists, proceed output with *n* lines. On the *i*-th of these lines print the point of the set that gets number *i*. If there are multiple solutions, print any of them. | [
"5\n2 0\n0 0\n1 0\n1 1\n0 1\n0 -1 -2 1 0\n",
"3\n1 0\n0 0\n2 0\n0 1 2\n"
] | [
"YES\n0 0\n1 0\n2 0\n0 1\n1 1\n",
"NO\n"
] | In the first sample, point (2, 0) gets number 3, point (0, 0) gets number one, point (1, 0) gets number 2, point (1, 1) gets number 5 and point (0, 1) gets number 4. One can easily check that this numbering is aesthetically pleasing and *y*<sub class="lower-index">*i*</sub> - *x*<sub class="lower-index">*i*</sub> = *w*<sub class="lower-index">*i*</sub>.
In the second sample, the special values of the points in the set are 0, - 1, and - 2 while the sequence that the friend gives to Wilbur is 0, 1, 2. Therefore, the answer does not exist. | [
{
"input": "5\n2 0\n0 0\n1 0\n1 1\n0 1\n0 -1 -2 1 0",
"output": "YES\n0 0\n1 0\n2 0\n0 1\n1 1"
},
{
"input": "3\n1 0\n0 0\n2 0\n0 1 2",
"output": "NO"
},
{
"input": "9\n0 0\n1 0\n2 0\n0 1\n1 1\n2 1\n1 2\n2 2\n0 2\n0 0 0 -1 -1 -2 1 1 2",
"output": "NO"
},
{
"input": "18\n0 0\n... | 46 | 0 | 0 | 4,054 | |
0 | none | [
"none"
] | null | null | На координатной прямой сидит *n* собачек, *i*-я собачка находится в точке *x**i*. Кроме того, на прямой есть *m* мисок с едой, для каждой известна её координата на прямой *u**j* и время *t**j*, через которое еда в миске остынет и станет невкусной. Это значит, что если собачка прибежит к миске в момент времени, строго больший *t**j*, то еда уже остынет, и собачка кушать её не станет.
Считая, что каждая собачка бежит со скоростью 1, найдите максимальное количество собачек, которые смогут покушать. Считайте, что собачки побегут к тем мискам, на которые вы им укажете. Из одной миски не могут кушать две или более собачки.
Собачки могут обгонять друг друга, то есть, если одна из них остановится покушать, другая может пройти мимо неё, чтобы попасть к другой миске. | В первой строке находится пара целых чисел *n* и *m* (1<=≤<=*n*,<=*m*<=≤<=200<=000) — количество собачек и мисок соответственно.
Во второй строке находятся *n* целых чисел *x**i* (<=-<=109<=≤<=*x**i*<=≤<=109) — координата *i*-й собачки.
В следующих *m* строках находятся пары целых чисел *u**j* и *t**j* (<=-<=109<=≤<=*u**j*<=≤<=109, 1<=≤<=*t**j*<=≤<=109) — координата *j*-й миски и время, когда остынет еда в ней, соответственно.
Гарантируется, что никакие две собачки не находятся в одной точке. Никакие две миски также не могут находиться в одной точке. | Выведите одно целое число *a* — максимальное количество собачек, которые смогут покушать. | [
"5 4\n-2 0 4 8 13\n-1 1\n4 3\n6 3\n11 2\n",
"3 3\n-1 3 7\n1 1\n4 1\n7 1\n",
"4 4\n20 1 10 30\n1 1\n2 5\n22 2\n40 10\n"
] | [
"4\n",
"2\n",
"3\n"
] | В первом примере первая собачка побежит направо к первой миске, третья собачка сразу начнёт есть из второй миски, четвёртая собачка побежит влево к третьей миске, а пятая собачка побежит влево к четвёртой миске. | [] | 2,000 | 25,907,200 | 0 | 4,089 | |
847 | University Classes | [
"implementation"
] | null | null | There are *n* student groups at the university. During the study day, each group can take no more than 7 classes. Seven time slots numbered from 1 to 7 are allocated for the classes.
The schedule on Monday is known for each group, i. e. time slots when group will have classes are known.
Your task is to determine the minimum number of rooms needed to hold classes for all groups on Monday. Note that one room can hold at most one group class in a single time slot. | The first line contains a single integer *n* (1<=≤<=*n*<=≤<=1000) — the number of groups.
Each of the following *n* lines contains a sequence consisting of 7 zeroes and ones — the schedule of classes on Monday for a group. If the symbol in a position equals to 1 then the group has class in the corresponding time slot. In the other case, the group has no class in the corresponding time slot. | Print minimum number of rooms needed to hold all groups classes on Monday. | [
"2\n0101010\n1010101\n",
"3\n0101011\n0011001\n0110111\n"
] | [
"1\n",
"3\n"
] | In the first example one room is enough. It will be occupied in each of the seven time slot by the first group or by the second group.
In the second example three rooms is enough, because in the seventh time slot all three groups have classes. | [
{
"input": "2\n0101010\n1010101",
"output": "1"
},
{
"input": "3\n0101011\n0011001\n0110111",
"output": "3"
},
{
"input": "1\n0111000",
"output": "1"
},
{
"input": "1\n0000000",
"output": "0"
},
{
"input": "1\n1111111",
"output": "1"
},
{
"input": "2\n... | 109 | 3,481,600 | 3 | 4,090 | |
124 | Permutations | [
"brute force",
"combinatorics",
"implementation"
] | null | null | You are given *n* *k*-digit integers. You have to rearrange the digits in the integers so that the difference between the largest and the smallest number was minimum. Digits should be rearranged by the same rule in all integers. | The first line contains integers *n* and *k* — the number and digit capacity of numbers correspondingly (1<=≤<=*n*,<=*k*<=≤<=8). Next *n* lines contain *k*-digit positive integers. Leading zeroes are allowed both in the initial integers and the integers resulting from the rearranging of digits. | Print a single number: the minimally possible difference between the largest and the smallest number after the digits are rearranged in all integers by the same rule. | [
"6 4\n5237\n2753\n7523\n5723\n5327\n2537\n",
"3 3\n010\n909\n012\n",
"7 5\n50808\n36603\n37198\n44911\n29994\n42543\n50156\n"
] | [
"2700\n",
"3\n",
"20522\n"
] | In the first sample, if we rearrange the digits in numbers as (3,1,4,2), then the 2-nd and the 4-th numbers will equal 5237 and 2537 correspondingly (they will be maximum and minimum for such order of digits).
In the second sample, if we swap the second digits and the first ones, we get integers 100, 99 and 102. | [
{
"input": "6 4\n5237\n2753\n7523\n5723\n5327\n2537",
"output": "2700"
},
{
"input": "3 3\n010\n909\n012",
"output": "3"
},
{
"input": "7 5\n50808\n36603\n37198\n44911\n29994\n42543\n50156",
"output": "20522"
},
{
"input": "5 5\n61374\n74304\n41924\n46010\n09118",
"output... | 122 | 2,867,200 | -1 | 4,106 | |
704 | Ant Man | [
"dp",
"graphs",
"greedy"
] | null | null | Scott Lang is at war with Darren Cross. There are *n* chairs in a hall where they are, numbered with 1,<=2,<=...,<=*n* from left to right. The *i*-th chair is located at coordinate *x**i*. Scott is on chair number *s* and Cross is on chair number *e*. Scott can jump to all other chairs (not only neighboring chairs). He wants to start at his position (chair number *s*), visit each chair exactly once and end up on chair number *e* with Cross.
As we all know, Scott can shrink or grow big (grow big only to his normal size), so at any moment of time he can be either small or large (normal). The thing is, he can only shrink or grow big while being on a chair (not in the air while jumping to another chair). Jumping takes time, but shrinking and growing big takes no time. Jumping from chair number *i* to chair number *j* takes |*x**i*<=-<=*x**j*| seconds. Also, jumping off a chair and landing on a chair takes extra amount of time.
If Scott wants to jump to a chair on his left, he can only be small, and if he wants to jump to a chair on his right he should be large.
Jumping off the *i*-th chair takes:
- *c**i* extra seconds if he's small. - *d**i* extra seconds otherwise (he's large).
Also, landing on *i*-th chair takes:
- *b**i* extra seconds if he's small. - *a**i* extra seconds otherwise (he's large).
In simpler words, jumping from *i*-th chair to *j*-th chair takes exactly:
- |*x**i*<=-<=*x**j*|<=+<=*c**i*<=+<=*b**j* seconds if *j*<=<<=*i*. - |*x**i*<=-<=*x**j*|<=+<=*d**i*<=+<=*a**j* seconds otherwise (*j*<=><=*i*).
Given values of *x*, *a*, *b*, *c*, *d* find the minimum time Scott can get to Cross, assuming he wants to visit each chair exactly once. | The first line of the input contains three integers *n*,<=*s* and *e* (2<=≤<=*n*<=≤<=5000,<=1<=≤<=*s*,<=*e*<=≤<=*n*,<=*s*<=≠<=*e*) — the total number of chairs, starting and ending positions of Scott.
The second line contains *n* integers *x*1,<=*x*2,<=...,<=*x**n* (1<=≤<=*x*1<=<<=*x*2<=<<=...<=<<=*x**n*<=≤<=109).
The third line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a*1,<=*a*2,<=...,<=*a**n*<=≤<=109).
The fourth line contains *n* integers *b*1,<=*b*2,<=...,<=*b**n* (1<=≤<=*b*1,<=*b*2,<=...,<=*b**n*<=≤<=109).
The fifth line contains *n* integers *c*1,<=*c*2,<=...,<=*c**n* (1<=≤<=*c*1,<=*c*2,<=...,<=*c**n*<=≤<=109).
The sixth line contains *n* integers *d*1,<=*d*2,<=...,<=*d**n* (1<=≤<=*d*1,<=*d*2,<=...,<=*d**n*<=≤<=109). | Print the minimum amount of time Scott needs to get to the Cross while visiting each chair exactly once. | [
"7 4 3\n8 11 12 16 17 18 20\n17 16 20 2 20 5 13\n17 8 8 16 12 15 13\n12 4 16 4 15 7 6\n8 14 2 11 17 12 8\n"
] | [
"139\n"
] | In the sample testcase, an optimal solution would be <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5bbd3e094ffa5a72e263dfaec7aeaff795bc22a3.png" style="max-width: 100.0%;max-height: 100.0%;"/>. Spent time would be 17 + 24 + 23 + 20 + 33 + 22 = 139. | [
{
"input": "7 4 3\n8 11 12 16 17 18 20\n17 16 20 2 20 5 13\n17 8 8 16 12 15 13\n12 4 16 4 15 7 6\n8 14 2 11 17 12 8",
"output": "139"
},
{
"input": "2 1 2\n75475634 804928248\n476927808 284875072\n503158867 627937890\n322595515 786026685\n645468307 669240390",
"output": "1659795993"
},
{
... | 46 | 512,000 | 0 | 4,107 | |
523 | Rotate, Flip and Zoom | [
"*special",
"implementation"
] | null | null | Polycarp is writing the prototype of a graphic editor. He has already made up his mind that the basic image transformations in his editor will be: rotate the image 90 degrees clockwise, flip the image horizontally (symmetry relative to the vertical line, that is, the right part of the image moves to the left, and vice versa) and zooming on the image. He is sure that that there is a large number of transformations that can be expressed through these three.
He has recently stopped implementing all three transformations for monochrome images. To test this feature, he asked you to write a code that will consecutively perform three actions with a monochrome image: first it will rotate the image 90 degrees clockwise, then it will flip the image horizontally and finally, it will zoom in twice on the image (that is, it will double all the linear sizes).
Implement this feature to help Polycarp test his editor. | The first line contains two integers, *w* and *h* (1<=≤<=*w*,<=*h*<=≤<=100) — the width and height of an image in pixels. The picture is given in *h* lines, each line contains *w* characters — each character encodes the color of the corresponding pixel of the image. The line consists only of characters "." and "*", as the image is monochrome. | Print 2*w* lines, each containing 2*h* characters — the result of consecutive implementing of the three transformations, described above. | [
"3 2\n.*.\n.*.\n",
"9 20\n**.......\n****.....\n******...\n*******..\n..******.\n....****.\n......***\n*.....***\n*********\n*********\n*********\n*********\n....**...\n...****..\n..******.\n.********\n****..***\n***...***\n**.....**\n*.......*\n"
] | [
"....\n....\n****\n****\n....\n....\n",
"********......**********........********\n********......**********........********\n********........********......********..\n********........********......********..\n..********......********....********....\n..********......********....********....\n..********......*****... | none | [
{
"input": "3 2\n.*.\n.*.",
"output": "....\n....\n****\n****\n....\n...."
},
{
"input": "9 20\n**.......\n****.....\n******...\n*******..\n..******.\n....****.\n......***\n*.....***\n*********\n*********\n*********\n*********\n....**...\n...****..\n..******.\n.********\n****..***\n***...***\n**....... | 62 | 102,400 | 3 | 4,108 | |
929 | Прокат велосипедов | [
"*special",
"greedy",
"implementation"
] | null | null | Как известно, в теплую погоду многие жители крупных городов пользуются сервисами городского велопроката. Вот и Аркадий сегодня будет добираться от школы до дома, используя городские велосипеды.
Школа и дом находятся на одной прямой улице, кроме того, на той же улице есть *n* точек, где можно взять велосипед в прокат или сдать его. Первый велопрокат находится в точке *x*1 километров вдоль улицы, второй — в точке *x*2 и так далее, *n*-й велопрокат находится в точке *x**n*. Школа Аркадия находится в точке *x*1 (то есть там же, где и первый велопрокат), а дом — в точке *x**n* (то есть там же, где и *n*-й велопрокат). Известно, что *x**i*<=<<=*x**i*<=+<=1 для всех 1<=≤<=*i*<=<<=*n*.
Согласно правилам пользования велопроката, Аркадий может брать велосипед в прокат только на ограниченное время, после этого он должен обязательно вернуть его в одной из точек велопроката, однако, он тут же может взять новый велосипед, и отсчет времени пойдет заново. Аркадий может брать не более одного велосипеда в прокат одновременно. Если Аркадий решает взять велосипед в какой-то точке проката, то он сдаёт тот велосипед, на котором он до него доехал, берёт ровно один новый велосипед и продолжает на нём своё движение.
За отведенное время, независимо от выбранного велосипеда, Аркадий успевает проехать не больше *k* километров вдоль улицы.
Определите, сможет ли Аркадий доехать на велосипедах от школы до дома, и если да, то какое минимальное число раз ему необходимо будет взять велосипед в прокат, включая первый велосипед? Учтите, что Аркадий не намерен сегодня ходить пешком. | В первой строке следуют два целых числа *n* и *k* (2<=≤<=*n*<=≤<=1<=000, 1<=≤<=*k*<=≤<=100<=000) — количество велопрокатов и максимальное расстояние, которое Аркадий может проехать на одном велосипеде.
В следующей строке следует последовательность целых чисел *x*1,<=*x*2,<=...,<=*x**n* (0<=≤<=*x*1<=<<=*x*2<=<<=...<=<<=*x**n*<=≤<=100<=000) — координаты точек, в которых находятся велопрокаты. Гарантируется, что координаты велопрокатов заданы в порядке возрастания. | Если Аркадий не сможет добраться от школы до дома только на велосипедах, выведите -1. В противном случае, выведите минимальное количество велосипедов, которые Аркадию нужно взять в точках проката. | [
"4 4\n3 6 8 10\n",
"2 9\n10 20\n",
"12 3\n4 6 7 9 10 11 13 15 17 18 20 21\n"
] | [
"2\n",
"-1\n",
"6\n"
] | В первом примере Аркадий должен взять первый велосипед в первом велопрокате и доехать на нём до второго велопроката. Во втором велопрокате он должен взять новый велосипед, на котором он сможет добраться до четвертого велопроката, рядом с которым и находится его дом. Поэтому Аркадию нужно всего два велосипеда, чтобы добраться от школы до дома.
Во втором примере всего два велопроката, расстояние между которыми 10. Но максимальное расстояние, которое можно проехать на одном велосипеде, равно 9. Поэтому Аркадий не сможет добраться от школы до дома только на велосипедах. | [
{
"input": "4 4\n3 6 8 10",
"output": "2"
},
{
"input": "2 9\n10 20",
"output": "-1"
},
{
"input": "12 3\n4 6 7 9 10 11 13 15 17 18 20 21",
"output": "6"
},
{
"input": "2 1\n11164 11165",
"output": "1"
},
{
"input": "3 7\n45823 45825 45829",
"output": "1"
},... | 62 | 5,632,000 | 3 | 4,119 | |
895 | String Mark | [
"combinatorics",
"math",
"strings"
] | null | null | At the Byteland State University marks are strings of the same length. Mark *x* is considered better than *y* if string *y* is lexicographically smaller than *x*.
Recently at the BSU was an important test work on which Vasya recived the mark *a*. It is very hard for the teacher to remember the exact mark of every student, but he knows the mark *b*, such that every student recieved mark strictly smaller than *b*.
Vasya isn't satisfied with his mark so he decided to improve it. He can swap characters in the string corresponding to his mark as many times as he like. Now he want to know only the number of different ways to improve his mark so that his teacher didn't notice something suspicious.
More formally: you are given two strings *a*, *b* of the same length and you need to figure out the number of different strings *c* such that:
1) *c* can be obtained from *a* by swapping some characters, in other words *c* is a permutation of *a*.
2) String *a* is lexicographically smaller than *c*.
3) String *c* is lexicographically smaller than *b*.
For two strings *x* and *y* of the same length it is true that *x* is lexicographically smaller than *y* if there exists such *i*, that *x*1<==<=*y*1,<=*x*2<==<=*y*2,<=...,<=*x**i*<=-<=1<==<=*y**i*<=-<=1,<=*x**i*<=<<=*y**i*.
Since the answer can be very large, you need to find answer modulo 109<=+<=7. | First line contains string *a*, second line contains string *b*. Strings *a*,<=*b* consist of lowercase English letters. Their lengths are equal and don't exceed 106.
It is guaranteed that *a* is lexicographically smaller than *b*. | Print one integer — the number of different strings satisfying the condition of the problem modulo 109<=+<=7. | [
"abc\nddd\n",
"abcdef\nabcdeg\n",
"abacaba\nubuduba\n"
] | [
"5\n",
"0\n",
"64\n"
] | In first sample from string *abc* can be obtained strings *acb*, *bac*, *bca*, *cab*, *cba*, all of them are larger than *abc*, but smaller than *ddd*. So the answer is 5.
In second sample any string obtained from *abcdef* is larger than *abcdeg*. So the answer is 0. | [
{
"input": "abc\nddd",
"output": "5"
},
{
"input": "abcdef\nabcdeg",
"output": "0"
},
{
"input": "abacaba\nubuduba",
"output": "64"
},
{
"input": "aac\nbbb",
"output": "1"
},
{
"input": "aaaccc\nbbbbbb",
"output": "9"
},
{
"input": "aaaaaa\nzzzzzz",
... | 4,000 | 43,315,200 | 0 | 4,127 | |
207 | The Beaver's Problem - 3 | [] | null | null | The Smart Beaver from ABBYY came up with another splendid problem for the ABBYY Cup participants! This time the Beaver invites the contest participants to check out a problem on sorting documents by their subjects. Let's describe the problem:
You've got some training set of documents. For each document you know its subject. The subject in this problem is an integer from 1 to 3. Each of these numbers has a physical meaning. For instance, all documents with subject 3 are about trade.
You can download the training set of documents at the following link: http://download4.abbyy.com/a2/X2RZ2ZWXBG5VYWAL61H76ZQM/train.zip. The archive contains three directories with names "1", "2", "3". Directory named "1" contains documents on the 1-st subject, directory "2" contains documents on the 2-nd subject, and directory "3" contains documents on the 3-rd subject. Each document corresponds to exactly one file from some directory.
All documents have the following format: the first line contains the document identifier, the second line contains the name of the document, all subsequent lines contain the text of the document. The document identifier is used to make installing the problem more convenient and has no useful information for the participants.
You need to write a program that should indicate the subject for a given document. It is guaranteed that all documents given as input to your program correspond to one of the three subjects of the training set. | The first line contains integer *id* (0<=≤<=*id*<=≤<=106) — the document identifier. The second line contains the name of the document. The third and the subsequent lines contain the text of the document. It is guaranteed that the size of any given document will not exceed 10 kilobytes.
The tests for this problem are divided into 10 groups. Documents of groups 1 and 2 are taken from the training set, but their identifiers will not match the identifiers specified in the training set. Groups from the 3-rd to the 10-th are roughly sorted by the author in ascending order of difficulty (these groups contain documents which aren't present in the training set). | Print an integer from 1 to 3, inclusive — the number of the subject the given document corresponds to. | [] | [] | none | [
{
"input": "2000\nJAPAN FEBRUARY MONEY SUPPLY RISES 8.8 PCT\nTOKYO, March 17 - Japan's broadly defined money supply\naverage of M-2 plus certificate of deposits (CDs) rose a\npreliminary 8.8 pct in February from a year earlier, compared\nwith an 8.6 pct rise in January, the Bank of Japan said.\nThe seasonally a... | 31 | 0 | 0 | 4,146 | |
535 | Tavas and Nafas | [
"brute force",
"implementation"
] | null | null | Today Tavas got his test result as an integer score and he wants to share it with his girlfriend, Nafas.
His phone operating system is Tavdroid, and its keyboard doesn't have any digits! He wants to share his score with Nafas via text, so he has no choice but to send this number using words.
He ate coffee mix without water again, so right now he's really messed up and can't think.
Your task is to help him by telling him what to type. | The first and only line of input contains an integer *s* (0<=≤<=*s*<=≤<=99), Tavas's score. | In the first and only line of output, print a single string consisting only from English lowercase letters and hyphens ('-'). Do not use spaces. | [
"6\n",
"99\n",
"20\n"
] | [
"six\n",
"ninety-nine\n",
"twenty\n"
] | You can find all you need to know about English numerals in [http://en.wikipedia.org/wiki/English_numerals](https://en.wikipedia.org/wiki/English_numerals) . | [
{
"input": "6",
"output": "six"
},
{
"input": "99",
"output": "ninety-nine"
},
{
"input": "20",
"output": "twenty"
},
{
"input": "10",
"output": "ten"
},
{
"input": "15",
"output": "fifteen"
},
{
"input": "27",
"output": "twenty-seven"
},
{
... | 124 | 307,200 | 3 | 4,167 | |
464 | The Classic Problem | [
"data structures",
"graphs",
"shortest paths"
] | null | null | You are given a weighted undirected graph on *n* vertices and *m* edges. Find the shortest path from vertex *s* to vertex *t* or else state that such path doesn't exist. | The first line of the input contains two space-separated integers — *n* and *m* (1<=≤<=*n*<=≤<=105; 0<=≤<=*m*<=≤<=105).
Next *m* lines contain the description of the graph edges. The *i*-th line contains three space-separated integers — *u**i*, *v**i*, *x**i* (1<=≤<=*u**i*,<=*v**i*<=≤<=*n*; 0<=≤<=*x**i*<=≤<=105). That means that vertices with numbers *u**i* and *v**i* are connected by edge of length 2*x**i* (2 to the power of *x**i*).
The last line contains two space-separated integers — the numbers of vertices *s* and *t*.
The vertices are numbered from 1 to *n*. The graph contains no multiple edges and self-loops. | In the first line print the remainder after dividing the length of the shortest path by 1000000007 (109<=+<=7) if the path exists, and -1 if the path doesn't exist.
If the path exists print in the second line integer *k* — the number of vertices in the shortest path from vertex *s* to vertex *t*; in the third line print *k* space-separated integers — the vertices of the shortest path in the visiting order. The first vertex should be vertex *s*, the last vertex should be vertex *t*. If there are multiple shortest paths, print any of them. | [
"4 4\n1 4 2\n1 2 0\n2 3 0\n3 4 0\n1 4\n",
"4 3\n1 2 4\n2 3 5\n3 4 6\n1 4\n",
"4 2\n1 2 0\n3 4 1\n1 4\n"
] | [
"3\n4\n1 2 3 4 \n",
"112\n4\n1 2 3 4 \n",
"-1\n"
] | A path from vertex *s* to vertex *t* is a sequence *v*<sub class="lower-index">0</sub>, ..., *v*<sub class="lower-index">*k*</sub>, such that *v*<sub class="lower-index">0</sub> = *s*, *v*<sub class="lower-index">*k*</sub> = *t*, and for any *i* from 0 to *k* - 1 vertices *v*<sub class="lower-index">*i*</sub> and *v*<sub class="lower-index">*i* + 1</sub> are connected by an edge.
The length of the path is the sum of weights of edges between *v*<sub class="lower-index">*i*</sub> and *v*<sub class="lower-index">*i* + 1</sub> for all *i* from 0 to *k* - 1.
The shortest path from *s* to *t* is the path which length is minimum among all possible paths from *s* to *t*. | [] | 5,000 | 3,584,000 | 0 | 4,168 | |
686 | Little Robber Girl's Zoo | [
"constructive algorithms",
"implementation",
"sortings"
] | null | null | Little Robber Girl likes to scare animals in her zoo for fun. She decided to arrange the animals in a row in the order of non-decreasing height. However, the animals were so scared that they couldn't stay in the right places.
The robber girl was angry at first, but then she decided to arrange the animals herself. She repeatedly names numbers *l* and *r* such that *r*<=-<=*l*<=+<=1 is even. After that animals that occupy positions between *l* and *r* inclusively are rearranged as follows: the animal at position *l* swaps places with the animal at position *l*<=+<=1, the animal *l*<=+<=2 swaps with the animal *l*<=+<=3, ..., finally, the animal at position *r*<=-<=1 swaps with the animal *r*.
Help the robber girl to arrange the animals in the order of non-decreasing height. You should name at most 20<=000 segments, since otherwise the robber girl will become bored and will start scaring the animals again. | The first line contains a single integer *n* (1<=≤<=*n*<=≤<=100) — number of animals in the robber girl's zoo.
The second line contains *n* space-separated integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=109), where *a**i* is the height of the animal occupying the *i*-th place. | Print the sequence of operations that will rearrange the animals by non-decreasing height.
The output should contain several lines, *i*-th of the lines should contain two space-separated integers *l**i* and *r**i* (1<=≤<=*l**i*<=<<=*r**i*<=≤<=*n*) — descriptions of segments the robber girl should name. The segments should be described in the order the operations are performed.
The number of operations should not exceed 20<=000.
If the animals are arranged correctly from the start, you are allowed to output nothing. | [
"4\n2 1 4 3\n",
"7\n36 28 57 39 66 69 68\n",
"5\n1 2 1 2 1\n"
] | [
"1 4\n",
"1 4\n6 7\n",
"2 5\n3 4\n1 4\n1 4\n"
] | Note that you don't have to minimize the number of operations. Any solution that performs at most 20 000 operations is allowed. | [
{
"input": "4\n2 1 4 3",
"output": "1 2\n3 4"
},
{
"input": "7\n36 28 57 39 66 69 68",
"output": "1 2\n3 4\n6 7"
},
{
"input": "5\n1 2 1 2 1",
"output": "2 3\n4 5\n3 4"
},
{
"input": "78\n7 3 8 8 9 8 10 9 12 11 16 14 17 17 18 18 20 20 25 22 27 26 29 27 35 35 36 36 37 37 38 38... | 140 | 4,300,800 | 3 | 4,173 | |
761 | Dasha and friends | [
"brute force",
"implementation",
"math"
] | null | null | Running with barriers on the circle track is very popular in the country where Dasha lives, so no wonder that on her way to classes she saw the following situation:
The track is the circle with length *L*, in distinct points of which there are *n* barriers. Athlete always run the track in counterclockwise direction if you look on him from above. All barriers are located at integer distance from each other along the track.
Her friends the parrot Kefa and the leopard Sasha participated in competitions and each of them ran one lap. Each of the friends started from some integral point on the track. Both friends wrote the distance from their start along the track to each of the *n* barriers. Thus, each of them wrote *n* integers in the ascending order, each of them was between 0 and *L*<=-<=1, inclusively.
There are several tracks in the country, all of them have same length and same number of barriers, but the positions of the barriers can differ among different tracks. Now Dasha is interested if it is possible that Kefa and Sasha ran the same track or they participated on different tracks.
Write the program which will check that Kefa's and Sasha's tracks coincide (it means that one can be obtained from the other by changing the start position). Note that they always run the track in one direction — counterclockwise, if you look on a track from above. | The first line contains two integers *n* and *L* (1<=≤<=*n*<=≤<=50, *n*<=≤<=*L*<=≤<=100) — the number of barriers on a track and its length.
The second line contains *n* distinct integers in the ascending order — the distance from Kefa's start to each barrier in the order of its appearance. All integers are in the range from 0 to *L*<=-<=1 inclusively.
The second line contains *n* distinct integers in the ascending order — the distance from Sasha's start to each barrier in the order of its overcoming. All integers are in the range from 0 to *L*<=-<=1 inclusively. | Print "YES" (without quotes), if Kefa and Sasha ran the coinciding tracks (it means that the position of all barriers coincides, if they start running from the same points on the track). Otherwise print "NO" (without quotes). | [
"3 8\n2 4 6\n1 5 7\n",
"4 9\n2 3 5 8\n0 1 3 6\n",
"2 4\n1 3\n1 2\n"
] | [
"YES\n",
"YES\n",
"NO\n"
] | The first test is analyzed in the statement. | [
{
"input": "3 8\n2 4 6\n1 5 7",
"output": "YES"
},
{
"input": "4 9\n2 3 5 8\n0 1 3 6",
"output": "YES"
},
{
"input": "2 4\n1 3\n1 2",
"output": "NO"
},
{
"input": "5 9\n0 2 5 6 7\n1 3 6 7 8",
"output": "YES"
},
{
"input": "5 60\n7 26 27 40 59\n14 22 41 42 55",
... | 46 | 4,608,000 | 0 | 4,181 | |
253 | Text Editor | [
"data structures",
"dfs and similar",
"graphs",
"greedy",
"shortest paths"
] | null | null | Vasya is pressing the keys on the keyboard reluctantly, squeezing out his ideas on the classical epos depicted in Homer's Odysseus... How can he explain to his literature teacher that he isn't going to become a writer? In fact, he is going to become a programmer. So, he would take great pleasure in writing a program, but none — in writing a composition.
As Vasya was fishing for a sentence in the dark pond of his imagination, he suddenly wondered: what is the least number of times he should push a key to shift the cursor from one position to another one?
Let's describe his question more formally: to type a text, Vasya is using the text editor. He has already written *n* lines, the *i*-th line contains *a**i* characters (including spaces). If some line contains *k* characters, then this line overall contains (*k*<=+<=1) positions where the cursor can stand: before some character or after all characters (at the end of the line). Thus, the cursor's position is determined by a pair of integers (*r*,<=*c*), where *r* is the number of the line and *c* is the cursor's position in the line (the positions are indexed starting from one from the beginning of the line).
Vasya doesn't use the mouse to move the cursor. He uses keys "Up", "Down", "Right" and "Left". When he pushes each of these keys, the cursor shifts in the needed direction. Let's assume that before the corresponding key is pressed, the cursor was located in the position (*r*,<=*c*), then Vasya pushed key:
- "Up": if the cursor was located in the first line (*r*<==<=1), then it does not move. Otherwise, it moves to the previous line (with number *r*<=-<=1), to the same position. At that, if the previous line was short, that is, the cursor couldn't occupy position *c* there, the cursor moves to the last position of the line with number *r*<=-<=1;- "Down": if the cursor was located in the last line (*r*<==<=*n*), then it does not move. Otherwise, it moves to the next line (with number *r*<=+<=1), to the same position. At that, if the next line was short, that is, the cursor couldn't occupy position *c* there, the cursor moves to the last position of the line with number *r*<=+<=1;- "Right": if the cursor can move to the right in this line (*c*<=<<=*a**r*<=+<=1), then it moves to the right (to position *c*<=+<=1). Otherwise, it is located at the end of the line and doesn't move anywhere when Vasya presses the "Right" key;- "Left": if the cursor can move to the left in this line (*c*<=><=1), then it moves to the left (to position *c*<=-<=1). Otherwise, it is located at the beginning of the line and doesn't move anywhere when Vasya presses the "Left" key.
You've got the number of lines in the text file and the number of characters, written in each line of this file. Find the least number of times Vasya should push the keys, described above, to shift the cursor from position (*r*1,<=*c*1) to position (*r*2,<=*c*2). | The first line of the input contains an integer *n* (1<=≤<=*n*<=≤<=100) — the number of lines in the file. The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (0<=≤<=*a**i*<=≤<=105), separated by single spaces. The third line contains four integers *r*1,<=*c*1,<=*r*2,<=*c*2 (1<=≤<=*r*1,<=*r*2<=≤<=*n*,<=1<=≤<=*c*1<=≤<=*a**r*1<=+<=1,<=1<=≤<=*c*2<=≤<=*a**r*2<=+<=1). | Print a single integer — the minimum number of times Vasya should push a key to move the cursor from position (*r*1,<=*c*1) to position (*r*2,<=*c*2). | [
"4\n2 1 6 4\n3 4 4 2\n",
"4\n10 5 6 4\n1 11 4 2\n",
"3\n10 1 10\n1 10 1 1\n"
] | [
"3\n",
"6\n",
"3\n"
] | In the first sample the editor contains four lines. Let's represent the cursor's possible positions in the line as numbers. Letter *s* represents the cursor's initial position, letter *t* represents the last one. Then all possible positions of the cursor in the text editor are described by the following table.
123
12
123s567
1t345
One of the possible answers in the given sample is: "Left", "Down", "Left". | [
{
"input": "4\n2 1 6 4\n3 4 4 2",
"output": "3"
},
{
"input": "4\n10 5 6 4\n1 11 4 2",
"output": "6"
},
{
"input": "3\n10 1 10\n1 10 1 1",
"output": "3"
},
{
"input": "4\n2 1 6 4\n4 2 3 5",
"output": "4"
},
{
"input": "3\n20 3 20\n1 20 1 1",
"output": "5"
},... | 186 | 409,600 | 0 | 4,182 | |
234 | Lefthanders and Righthanders | [
"implementation"
] | null | null | One fine October day a mathematics teacher Vasily Petrov went to a class and saw there *n* pupils who sat at the desks, two people at each desk. Vasily quickly realized that number *n* is even. Like all true mathematicians, Vasily has all students numbered from 1 to *n*.
But Vasily Petrov did not like the way the children were seated at the desks. According to him, the students whose numbers differ by 1, can not sit together, as they talk to each other all the time, distract others and misbehave.
On the other hand, if a righthanded student sits at the left end of the desk and a lefthanded student sits at the right end of the desk, they hit elbows all the time and distract each other. In other cases, the students who sit at the same desk, do not interfere with each other.
Vasily knows very well which students are lefthanders and which ones are righthanders, and he asks you to come up with any order that meets these two uncomplicated conditions (students do not talk to each other and do not bump their elbows). It is guaranteed that the input is such that at least one way to seat the students always exists. | The first input line contains a single even integer *n* (4<=≤<=*n*<=≤<=100) — the number of students in the class. The second line contains exactly *n* capital English letters "L" and "R". If the *i*-th letter at the second line equals "L", then the student number *i* is a lefthander, otherwise he is a righthander. | Print integer pairs, one pair per line. In the *i*-th line print the numbers of students that will sit at the *i*-th desk. The first number in the pair stands for the student who is sitting to the left, and the second number stands for the student who is sitting to the right. Separate the numbers in the pairs by spaces. If there are multiple solutions, print any of them. | [
"6\nLLRLLL\n",
"4\nRRLL\n"
] | [
"1 4\n2 5\n6 3\n",
"3 1\n4 2\n"
] | none | [
{
"input": "6\nLLRLLL",
"output": "1 4\n2 5\n6 3"
},
{
"input": "4\nRRLL",
"output": "3 1\n4 2"
},
{
"input": "4\nLLRR",
"output": "1 3\n2 4"
},
{
"input": "6\nRLLRRL",
"output": "1 4\n2 5\n3 6"
},
{
"input": "8\nLRLRLLLR",
"output": "1 5\n6 2\n3 7\n4 8"
},
... | 46 | 6,656,000 | -1 | 4,186 |
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