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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
6 | Lizards and Basements 2 | [
"brute force",
"dp"
] | D. Lizards and Basements 2 | 2 | 64 | This is simplified version of the problem used on the original contest. The original problem seems to have too difiicult solution. The constraints for input data have been reduced.
Polycarp likes to play computer role-playing game «Lizards and Basements». At the moment he is playing it as a magician. At one of the last levels he has to fight the line of archers. The only spell with which he can damage them is a fire ball. If Polycarp hits the *i*-th archer with his fire ball (they are numbered from left to right), the archer loses *a* health points. At the same time the spell damages the archers adjacent to the *i*-th (if any) — they lose *b* (1<=≤<=*b*<=<<=*a*<=≤<=10) health points each.
As the extreme archers (i.e. archers numbered 1 and *n*) are very far, the fire ball cannot reach them. Polycarp can hit any other archer with his fire ball.
The amount of health points for each archer is known. An archer will be killed when this amount is less than 0. What is the minimum amount of spells Polycarp can use to kill all the enemies?
Polycarp can throw his fire ball into an archer if the latter is already killed. | The first line of the input contains three integers *n*,<=*a*,<=*b* (3<=≤<=*n*<=≤<=10; 1<=≤<=*b*<=<<=*a*<=≤<=10). The second line contains a sequence of *n* integers — *h*1,<=*h*2,<=...,<=*h**n* (1<=≤<=*h**i*<=≤<=15), where *h**i* is the amount of health points the *i*-th archer has. | In the first line print *t* — the required minimum amount of fire balls.
In the second line print *t* numbers — indexes of the archers that Polycarp should hit to kill all the archers in *t* shots. All these numbers should be between 2 and *n*<=-<=1. Separate numbers with spaces. If there are several solutions, output any of them. Print numbers in any order. | [
"3 2 1\n2 2 2\n",
"4 3 1\n1 4 1 1\n"
] | [
"3\n2 2 2 ",
"4\n2 2 3 3 "
] | none | [
{
"input": "3 2 1\n2 2 2",
"output": "3\n2 2 2 "
},
{
"input": "4 3 1\n1 4 1 1",
"output": "4\n2 2 3 3 "
},
{
"input": "3 5 3\n1 2 1",
"output": "1\n2 "
},
{
"input": "3 5 3\n3 2 2",
"output": "2\n2 2 "
},
{
"input": "3 5 3\n3 2 2",
"output": "2\n2 2 "
},
... | 124 | 0 | 3.969 | 2,399 |
129 | Students and Shoelaces | [
"brute force",
"dfs and similar",
"graphs",
"implementation"
] | null | null | Anna and Maria are in charge of the math club for junior students. When the club gathers together, the students behave badly. They've brought lots of shoe laces to the club and got tied with each other. Specifically, each string ties together two students. Besides, if two students are tied, then the lace connects the first student with the second one as well as the second student with the first one.
To restore order, Anna and Maria do the following. First, for each student Anna finds out what other students he is tied to. If a student is tied to exactly one other student, Anna reprimands him. Then Maria gathers in a single group all the students who have been just reprimanded. She kicks them out from the club. This group of students immediately leaves the club. These students takes with them the laces that used to tie them. Then again for every student Anna finds out how many other students he is tied to and so on. And they do so until Anna can reprimand at least one student.
Determine how many groups of students will be kicked out of the club. | The first line contains two integers *n* and *m* — the initial number of students and laces (). The students are numbered from 1 to *n*, and the laces are numbered from 1 to *m*. Next *m* lines each contain two integers *a* and *b* — the numbers of students tied by the *i*-th lace (1<=≤<=*a*,<=*b*<=≤<=*n*,<=*a*<=≠<=*b*). It is guaranteed that no two students are tied with more than one lace. No lace ties a student to himself. | Print the single number — the number of groups of students that will be kicked out from the club. | [
"3 3\n1 2\n2 3\n3 1\n",
"6 3\n1 2\n2 3\n3 4\n",
"6 5\n1 4\n2 4\n3 4\n5 4\n6 4\n"
] | [
"0\n",
"2\n",
"1\n"
] | In the first sample Anna and Maria won't kick out any group of students — in the initial position every student is tied to two other students and Anna won't be able to reprimand anyone.
In the second sample four students are tied in a chain and two more are running by themselves. First Anna and Maria kick out the two students from both ends of the chain (1 and 4), then — two other students from the chain (2 and 3). At that the students who are running by themselves will stay in the club.
In the third sample Anna and Maria will momentarily kick out all students except for the fourth one and the process stops at that point. The correct answer is one. | [
{
"input": "3 3\n1 2\n2 3\n3 1",
"output": "0"
},
{
"input": "6 3\n1 2\n2 3\n3 4",
"output": "2"
},
{
"input": "6 5\n1 4\n2 4\n3 4\n5 4\n6 4",
"output": "1"
},
{
"input": "100 0",
"output": "0"
},
{
"input": "5 5\n1 2\n2 3\n3 4\n4 5\n5 1",
"output": "0"
},
... | 154 | 0 | -1 | 2,408 | |
722 | Verse Pattern | [
"implementation",
"strings"
] | null | null | You are given a text consisting of *n* lines. Each line contains some space-separated words, consisting of lowercase English letters.
We define a syllable as a string that contains exactly one vowel and any arbitrary number (possibly none) of consonants. In English alphabet following letters are considered to be vowels: 'a', 'e', 'i', 'o', 'u' and 'y'.
Each word of the text that contains at least one vowel can be divided into syllables. Each character should be a part of exactly one syllable. For example, the word "mamma" can be divided into syllables as "ma" and "mma", "mam" and "ma", and "mamm" and "a". Words that consist of only consonants should be ignored.
The verse patterns for the given text is a sequence of *n* integers *p*1,<=*p*2,<=...,<=*p**n*. Text matches the given verse pattern if for each *i* from 1 to *n* one can divide words of the *i*-th line in syllables in such a way that the total number of syllables is equal to *p**i*.
You are given the text and the verse pattern. Check, if the given text matches the given verse pattern. | The first line of the input contains a single integer *n* (1<=≤<=*n*<=≤<=100) — the number of lines in the text.
The second line contains integers *p*1,<=...,<=*p**n* (0<=≤<=*p**i*<=≤<=100) — the verse pattern.
Next *n* lines contain the text itself. Text consists of lowercase English letters and spaces. It's guaranteed that all lines are non-empty, each line starts and ends with a letter and words are separated by exactly one space. The length of each line doesn't exceed 100 characters. | If the given text matches the given verse pattern, then print "YES" (without quotes) in the only line of the output. Otherwise, print "NO" (without quotes). | [
"3\n2 2 3\nintel\ncode\nch allenge\n",
"4\n1 2 3 1\na\nbcdefghi\njklmnopqrstu\nvwxyz\n",
"4\n13 11 15 15\nto be or not to be that is the question\nwhether tis nobler in the mind to suffer\nthe slings and arrows of outrageous fortune\nor to take arms against a sea of troubles\n"
] | [
"YES\n",
"NO\n",
"YES\n"
] | In the first sample, one can split words into syllables in the following way:
Since the word "ch" in the third line doesn't contain vowels, we can ignore it. As the result we get 2 syllabels in first two lines and 3 syllables in the third one. | [
{
"input": "3\n2 2 3\nintel\ncode\nch allenge",
"output": "YES"
},
{
"input": "4\n1 2 3 1\na\nbcdefghi\njklmnopqrstu\nvwxyz",
"output": "NO"
},
{
"input": "4\n13 11 15 15\nto be or not to be that is the question\nwhether tis nobler in the mind to suffer\nthe slings and arrows of outrageo... | 77 | 0 | 3 | 2,410 | |
789 | Anastasia and pebbles | [
"implementation",
"math"
] | null | null | Anastasia loves going for a walk in Central Uzhlyandian Park. But she became uninterested in simple walking, so she began to collect Uzhlyandian pebbles. At first, she decided to collect all the pebbles she could find in the park.
She has only two pockets. She can put at most *k* pebbles in each pocket at the same time. There are *n* different pebble types in the park, and there are *w**i* pebbles of the *i*-th type. Anastasia is very responsible, so she never mixes pebbles of different types in same pocket. However, she can put different kinds of pebbles in different pockets at the same time. Unfortunately, she can't spend all her time collecting pebbles, so she can collect pebbles from the park only once a day.
Help her to find the minimum number of days needed to collect all the pebbles of Uzhlyandian Central Park, taking into consideration that Anastasia can't place pebbles of different types in same pocket. | The first line contains two integers *n* and *k* (1<=≤<=*n*<=≤<=105, 1<=≤<=*k*<=≤<=109) — the number of different pebble types and number of pebbles Anastasia can place in one pocket.
The second line contains *n* integers *w*1,<=*w*2,<=...,<=*w**n* (1<=≤<=*w**i*<=≤<=104) — number of pebbles of each type. | The only line of output contains one integer — the minimum number of days Anastasia needs to collect all the pebbles. | [
"3 2\n2 3 4\n",
"5 4\n3 1 8 9 7\n"
] | [
"3\n",
"5\n"
] | In the first sample case, Anastasia can collect all pebbles of the first type on the first day, of second type — on the second day, and of third type — on the third day.
Optimal sequence of actions in the second sample case:
- In the first day Anastasia collects 8 pebbles of the third type. - In the second day she collects 8 pebbles of the fourth type. - In the third day she collects 3 pebbles of the first type and 1 pebble of the fourth type. - In the fourth day she collects 7 pebbles of the fifth type. - In the fifth day she collects 1 pebble of the second type. | [
{
"input": "3 2\n2 3 4",
"output": "3"
},
{
"input": "5 4\n3 1 8 9 7",
"output": "5"
},
{
"input": "1 22\n1",
"output": "1"
},
{
"input": "3 57\n78 165 54",
"output": "3"
},
{
"input": "5 72\n74 10 146 189 184",
"output": "6"
},
{
"input": "9 13\n132 8... | 46 | 2,355,200 | 0 | 2,420 | |
577 | Modulo Sum | [
"combinatorics",
"data structures",
"dp",
"two pointers"
] | null | null | You are given a sequence of numbers *a*1,<=*a*2,<=...,<=*a**n*, and a number *m*.
Check if it is possible to choose a non-empty subsequence *a**i**j* such that the sum of numbers in this subsequence is divisible by *m*. | The first line contains two numbers, *n* and *m* (1<=≤<=*n*<=≤<=106, 2<=≤<=*m*<=≤<=103) — the size of the original sequence and the number such that sum should be divisible by it.
The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (0<=≤<=*a**i*<=≤<=109). | In the single line print either "YES" (without the quotes) if there exists the sought subsequence, or "NO" (without the quotes), if such subsequence doesn't exist. | [
"3 5\n1 2 3\n",
"1 6\n5\n",
"4 6\n3 1 1 3\n",
"6 6\n5 5 5 5 5 5\n"
] | [
"YES\n",
"NO\n",
"YES\n",
"YES\n"
] | In the first sample test you can choose numbers 2 and 3, the sum of which is divisible by 5.
In the second sample test the single non-empty subsequence of numbers is a single number 5. Number 5 is not divisible by 6, that is, the sought subsequence doesn't exist.
In the third sample test you need to choose two numbers 3 on the ends.
In the fourth sample test you can take the whole subsequence. | [
{
"input": "3 5\n1 2 3",
"output": "YES"
},
{
"input": "1 6\n5",
"output": "NO"
},
{
"input": "4 6\n3 1 1 3",
"output": "YES"
},
{
"input": "6 6\n5 5 5 5 5 5",
"output": "YES"
},
{
"input": "4 5\n1 1 1 1",
"output": "NO"
},
{
"input": "5 5\n1 1 1 1 1",... | 15 | 0 | 0 | 2,422 | |
689 | Mike and Chocolate Thieves | [
"binary search",
"combinatorics",
"math"
] | null | null | Bad news came to Mike's village, some thieves stole a bunch of chocolates from the local factory! Horrible!
Aside from loving sweet things, thieves from this area are known to be very greedy. So after a thief takes his number of chocolates for himself, the next thief will take exactly *k* times more than the previous one. The value of *k* (*k*<=><=1) is a secret integer known only to them. It is also known that each thief's bag can carry at most *n* chocolates (if they intend to take more, the deal is cancelled) and that there were exactly four thieves involved.
Sadly, only the thieves know the value of *n*, but rumours say that the numbers of ways they could have taken the chocolates (for a fixed *n*, but not fixed *k*) is *m*. Two ways are considered different if one of the thieves (they should be numbered in the order they take chocolates) took different number of chocolates in them.
Mike want to track the thieves down, so he wants to know what their bags are and value of *n* will help him in that. Please find the smallest possible value of *n* or tell him that the rumors are false and there is no such *n*. | The single line of input contains the integer *m* (1<=≤<=*m*<=≤<=1015) — the number of ways the thieves might steal the chocolates, as rumours say. | Print the only integer *n* — the maximum amount of chocolates that thieves' bags can carry. If there are more than one *n* satisfying the rumors, print the smallest one.
If there is no such *n* for a false-rumoured *m*, print <=-<=1. | [
"1\n",
"8\n",
"10\n"
] | [
"8\n",
"54\n",
"-1\n"
] | In the first sample case the smallest *n* that leads to exactly one way of stealing chocolates is *n* = 8, whereas the amounts of stealed chocolates are (1, 2, 4, 8) (the number of chocolates stolen by each of the thieves).
In the second sample case the smallest *n* that leads to exactly 8 ways is *n* = 54 with the possibilities: (1, 2, 4, 8), (1, 3, 9, 27), (2, 4, 8, 16), (2, 6, 18, 54), (3, 6, 12, 24), (4, 8, 16, 32), (5, 10, 20, 40), (6, 12, 24, 48).
There is no *n* leading to exactly 10 ways of stealing chocolates in the third sample case. | [
{
"input": "1",
"output": "8"
},
{
"input": "8",
"output": "54"
},
{
"input": "10",
"output": "-1"
},
{
"input": "27",
"output": "152"
},
{
"input": "28206",
"output": "139840"
},
{
"input": "32",
"output": "184"
},
{
"input": "115",
"o... | 1,840 | 1,740,800 | 3 | 2,425 | |
0 | none | [
"none"
] | null | null | Kevin has just recevied his disappointing results on the USA Identification of Cows Olympiad (USAICO) in the form of a binary string of length *n*. Each character of Kevin's string represents Kevin's score on one of the *n* questions of the olympiad—'1' for a correctly identified cow and '0' otherwise.
However, all is not lost. Kevin is a big proponent of alternative thinking and believes that his score, instead of being the sum of his points, should be the length of the longest alternating subsequence of his string. Here, we define an alternating subsequence of a string as a not-necessarily contiguous subsequence where no two consecutive elements are equal. For example, {0,<=1,<=0,<=1}, {1,<=0,<=1}, and {1,<=0,<=1,<=0} are alternating sequences, while {1,<=0,<=0} and {0,<=1,<=0,<=1,<=1} are not.
Kevin, being the sneaky little puffball that he is, is willing to hack into the USAICO databases to improve his score. In order to be subtle, he decides that he will flip exactly one substring—that is, take a contiguous non-empty substring of his score and change all '0's in that substring to '1's and vice versa. After such an operation, Kevin wants to know the length of the longest possible alternating subsequence that his string could have. | The first line contains the number of questions on the olympiad *n* (1<=≤<=*n*<=≤<=100<=000).
The following line contains a binary string of length *n* representing Kevin's results on the USAICO. | Output a single integer, the length of the longest possible alternating subsequence that Kevin can create in his string after flipping a single substring. | [
"8\n10000011\n",
"2\n01\n"
] | [
"5\n",
"2\n"
] | In the first sample, Kevin can flip the bolded substring '10000011' and turn his string into '10011011', which has an alternating subsequence of length 5: '10011011'.
In the second sample, Kevin can flip the entire string and still have the same score. | [
{
"input": "8\n10000011",
"output": "5"
},
{
"input": "2\n01",
"output": "2"
},
{
"input": "5\n10101",
"output": "5"
},
{
"input": "75\n010101010101010101010101010101010101010101010101010101010101010101010101010",
"output": "75"
},
{
"input": "11\n00000000000",
... | 77 | 204,800 | 0 | 2,430 | |
586 | Alena's Schedule | [
"implementation"
] | null | null | Alena has successfully passed the entrance exams to the university and is now looking forward to start studying.
One two-hour lesson at the Russian university is traditionally called a pair, it lasts for two academic hours (an academic hour is equal to 45 minutes).
The University works in such a way that every day it holds exactly *n* lessons. Depending on the schedule of a particular group of students, on a given day, some pairs may actually contain classes, but some may be empty (such pairs are called breaks).
The official website of the university has already published the schedule for tomorrow for Alena's group. Thus, for each of the *n* pairs she knows if there will be a class at that time or not.
Alena's House is far from the university, so if there are breaks, she doesn't always go home. Alena has time to go home only if the break consists of at least two free pairs in a row, otherwise she waits for the next pair at the university.
Of course, Alena does not want to be sleepy during pairs, so she will sleep as long as possible, and will only come to the first pair that is presented in her schedule. Similarly, if there are no more pairs, then Alena immediately goes home.
Alena appreciates the time spent at home, so she always goes home when it is possible, and returns to the university only at the beginning of the next pair. Help Alena determine for how many pairs she will stay at the university. Note that during some pairs Alena may be at the university waiting for the upcoming pair. | The first line of the input contains a positive integer *n* (1<=≤<=*n*<=≤<=100) — the number of lessons at the university.
The second line contains *n* numbers *a**i* (0<=≤<=*a**i*<=≤<=1). Number *a**i* equals 0, if Alena doesn't have the *i*-th pairs, otherwise it is equal to 1. Numbers *a*1,<=*a*2,<=...,<=*a**n* are separated by spaces. | Print a single number — the number of pairs during which Alena stays at the university. | [
"5\n0 1 0 1 1\n",
"7\n1 0 1 0 0 1 0\n",
"1\n0\n"
] | [
"4\n",
"4\n",
"0\n"
] | In the first sample Alena stays at the university from the second to the fifth pair, inclusive, during the third pair she will be it the university waiting for the next pair.
In the last sample Alena doesn't have a single pair, so she spends all the time at home. | [
{
"input": "5\n0 1 0 1 1",
"output": "4"
},
{
"input": "7\n1 0 1 0 0 1 0",
"output": "4"
},
{
"input": "1\n0",
"output": "0"
},
{
"input": "1\n1",
"output": "1"
},
{
"input": "2\n0 0",
"output": "0"
},
{
"input": "2\n0 1",
"output": "1"
},
{
... | 62 | 204,800 | 0 | 2,431 | |
870 | Maximum splitting | [
"dp",
"greedy",
"math",
"number theory"
] | null | null | You are given several queries. In the *i*-th query you are given a single positive integer *n**i*. You are to represent *n**i* as a sum of maximum possible number of composite summands and print this maximum number, or print -1, if there are no such splittings.
An integer greater than 1 is composite, if it is not prime, i.e. if it has positive divisors not equal to 1 and the integer itself. | The first line contains single integer *q* (1<=≤<=*q*<=≤<=105) — the number of queries.
*q* lines follow. The (*i*<=+<=1)-th line contains single integer *n**i* (1<=≤<=*n**i*<=≤<=109) — the *i*-th query. | For each query print the maximum possible number of summands in a valid splitting to composite summands, or -1, if there are no such splittings. | [
"1\n12\n",
"2\n6\n8\n",
"3\n1\n2\n3\n"
] | [
"3\n",
"1\n2\n",
"-1\n-1\n-1\n"
] | 12 = 4 + 4 + 4 = 4 + 8 = 6 + 6 = 12, but the first splitting has the maximum possible number of summands.
8 = 4 + 4, 6 can't be split into several composite summands.
1, 2, 3 are less than any composite number, so they do not have valid splittings. | [
{
"input": "1\n12",
"output": "3"
},
{
"input": "2\n6\n8",
"output": "1\n2"
},
{
"input": "3\n1\n2\n3",
"output": "-1\n-1\n-1"
},
{
"input": "6\n1\n2\n3\n5\n7\n11",
"output": "-1\n-1\n-1\n-1\n-1\n-1"
},
{
"input": "3\n4\n6\n9",
"output": "1\n1\n1"
},
{
... | 62 | 5,529,600 | 0 | 2,436 | |
185 | Plant | [
"math"
] | null | null | Dwarfs have planted a very interesting plant, which is a triangle directed "upwards". This plant has an amusing feature. After one year a triangle plant directed "upwards" divides into four triangle plants: three of them will point "upwards" and one will point "downwards". After another year, each triangle plant divides into four triangle plants: three of them will be directed in the same direction as the parent plant, and one of them will be directed in the opposite direction. Then each year the process repeats. The figure below illustrates this process.
Help the dwarfs find out how many triangle plants that point "upwards" will be in *n* years. | The first line contains a single integer *n* (0<=≤<=*n*<=≤<=1018) — the number of full years when the plant grew.
Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier. | Print a single integer — the remainder of dividing the number of plants that will point "upwards" in *n* years by 1000000007 (109<=+<=7). | [
"1\n",
"2\n"
] | [
"3\n",
"10\n"
] | The first test sample corresponds to the second triangle on the figure in the statement. The second test sample corresponds to the third one. | [
{
"input": "1",
"output": "3"
},
{
"input": "2",
"output": "10"
},
{
"input": "385599124",
"output": "493875375"
},
{
"input": "989464295",
"output": "31966163"
},
{
"input": "376367012",
"output": "523204186"
},
{
"input": "529357306",
"output": "... | 92 | 0 | 0 | 2,437 | |
382 | Ksenia and Pan Scales | [
"greedy",
"implementation"
] | null | null | Ksenia has ordinary pan scales and several weights of an equal mass. Ksenia has already put some weights on the scales, while other weights are untouched. Ksenia is now wondering whether it is possible to put all the remaining weights on the scales so that the scales were in equilibrium.
The scales is in equilibrium if the total sum of weights on the left pan is equal to the total sum of weights on the right pan. | The first line has a non-empty sequence of characters describing the scales. In this sequence, an uppercase English letter indicates a weight, and the symbol "|" indicates the delimiter (the character occurs in the sequence exactly once). All weights that are recorded in the sequence before the delimiter are initially on the left pan of the scale. All weights that are recorded in the sequence after the delimiter are initially on the right pan of the scale.
The second line contains a non-empty sequence containing uppercase English letters. Each letter indicates a weight which is not used yet.
It is guaranteed that all the English letters in the input data are different. It is guaranteed that the input does not contain any extra characters. | If you cannot put all the weights on the scales so that the scales were in equilibrium, print string "Impossible". Otherwise, print the description of the resulting scales, copy the format of the input.
If there are multiple answers, print any of them. | [
"AC|T\nL\n",
"|ABC\nXYZ\n",
"W|T\nF\n",
"ABC|\nD\n"
] | [
"AC|TL\n",
"XYZ|ABC\n",
"Impossible\n",
"Impossible\n"
] | none | [
{
"input": "AC|T\nL",
"output": "AC|TL"
},
{
"input": "|ABC\nXYZ",
"output": "XYZ|ABC"
},
{
"input": "W|T\nF",
"output": "Impossible"
},
{
"input": "ABC|\nD",
"output": "Impossible"
},
{
"input": "A|BC\nDEF",
"output": "ADF|BCE"
},
{
"input": "|\nABC",... | 93 | 0 | 0 | 2,439 | |
660 | Co-prime Array | [
"greedy",
"implementation",
"math",
"number theory"
] | null | null | You are given an array of *n* elements, you must make it a co-prime array in as few moves as possible.
In each move you can insert any positive integral number you want not greater than 109 in any place in the array.
An array is co-prime if any two adjacent numbers of it are co-prime.
In the number theory, two integers *a* and *b* are said to be co-prime if the only positive integer that divides both of them is 1. | The first line contains integer *n* (1<=≤<=*n*<=≤<=1000) — the number of elements in the given array.
The second line contains *n* integers *a**i* (1<=≤<=*a**i*<=≤<=109) — the elements of the array *a*. | Print integer *k* on the first line — the least number of elements needed to add to the array *a* to make it co-prime.
The second line should contain *n*<=+<=*k* integers *a**j* — the elements of the array *a* after adding *k* elements to it. Note that the new array should be co-prime, so any two adjacent values should be co-prime. Also the new array should be got from the original array *a* by adding *k* elements to it.
If there are multiple answers you can print any one of them. | [
"3\n2 7 28\n"
] | [
"1\n2 7 9 28\n"
] | none | [
{
"input": "3\n2 7 28",
"output": "1\n2 7 1 28"
},
{
"input": "1\n1",
"output": "0\n1"
},
{
"input": "1\n548",
"output": "0\n548"
},
{
"input": "1\n963837006",
"output": "0\n963837006"
},
{
"input": "10\n1 1 1 1 1 1 1 1 1 1",
"output": "0\n1 1 1 1 1 1 1 1 1 1"... | 155 | 3,072,000 | 3 | 2,442 | |
386 | Diverse Substrings | [
"dp",
"strings",
"two pointers"
] | null | null | String diversity is the number of symbols that occur in the string at least once. Diversity of *s* will be denoted by *d*(*s*). For example , *d*("aaa")=1, *d*("abacaba")=3.
Given a string *s*, consisting of lowercase Latin letters. Consider all its substrings. Obviously, any substring diversity is a number from 1 to *d*(*s*). Find statistics about substrings diversity: for each *k* from 1 to *d*(*s*), find how many substrings of *s* has a diversity of exactly *k*. | The input consists of a single line containing *s*. It contains only lowercase Latin letters, the length of *s* is from 1 to 3·105. | Print to the first line the value *d*(*s*). Print sequence *t*1,<=*t*2,<=...,<=*t**d*(*s*) to the following lines, where *t**i* is the number of substrings of *s* having diversity of exactly *i*. | [
"abca\n",
"aabacaabbad\n"
] | [
"3\n4\n3\n3\n",
"4\n14\n19\n28\n5\n"
] | Consider the first example.
We denote by *s*(*i*, *j*) a substring of "abca" with the indices in the segment [*i*, *j*].
- *s*(1, 1) = "a", *d*("a") = 1 - *s*(2, 2) = "b", *d*("b") = 1 - *s*(3, 3) = "c", *d*("c") = 1 - *s*(4, 4) = "a", *d*("a") = 1 - *s*(1, 2) = "ab", *d*("ab") = 2 - *s*(2, 3) = "bc", *d*("bc") = 2 - *s*(3, 4) = "ca", *d*("ca") = 2 - *s*(1, 3) = "abc", *d*("abc") = 3 - *s*(2, 4) = "bca", *d*("bca") = 3 - *s*(1, 4) = "abca", *d*("abca") = 3
Total number of substring with diversity 1 is 4, with diversity 2 equals 3, 3 diversity is 3. | [
{
"input": "abca",
"output": "3\n4\n3\n3"
},
{
"input": "aabacaabbad",
"output": "4\n14\n19\n28\n5"
},
{
"input": "a",
"output": "1\n1"
},
{
"input": "cabaccbcaa",
"output": "3\n12\n13\n30"
},
{
"input": "ccabaccbbb",
"output": "3\n15\n13\n27"
},
{
"in... | 0 | 0 | -1 | 2,444 | |
959 | Mahmoud and Ehab and the message | [
"dsu",
"greedy",
"implementation"
] | null | null | Mahmoud wants to send a message to his friend Ehab. Their language consists of *n* words numbered from 1 to *n*. Some words have the same meaning so there are *k* groups of words such that all the words in some group have the same meaning.
Mahmoud knows that the *i*-th word can be sent with cost *a**i*. For each word in his message, Mahmoud can either replace it with another word of the same meaning or leave it as it is. Can you help Mahmoud determine the minimum cost of sending the message?
The cost of sending the message is the sum of the costs of sending every word in it. | The first line of input contains integers *n*, *k* and *m* (1<=≤<=*k*<=≤<=*n*<=≤<=105,<=1<=≤<=*m*<=≤<=105) — the number of words in their language, the number of groups of words, and the number of words in Mahmoud's message respectively.
The second line contains *n* strings consisting of lowercase English letters of length not exceeding 20 which represent the words. It's guaranteed that the words are distinct.
The third line contains *n* integers *a*1, *a*2, ..., *a**n* (1<=≤<=*a**i*<=≤<=109) where *a**i* is the cost of sending the *i*-th word.
The next *k* lines describe the groups of words of same meaning. The next *k* lines each start with an integer *x* (1<=≤<=*x*<=≤<=*n*) which means that there are *x* words in this group, followed by *x* integers which represent the indices of words in this group. It's guaranteed that each word appears in exactly one group.
The next line contains *m* space-separated words which represent Mahmoud's message. Each of these words appears in the list of language's words. | The only line should contain the minimum cost to send the message after replacing some words (maybe none) with some words of the same meaning. | [
"5 4 4\ni loser am the second\n100 1 1 5 10\n1 1\n1 3\n2 2 5\n1 4\ni am the second\n",
"5 4 4\ni loser am the second\n100 20 1 5 10\n1 1\n1 3\n2 2 5\n1 4\ni am the second\n"
] | [
"107",
"116"
] | In the first sample, Mahmoud should replace the word "second" with the word "loser" because it has less cost so the cost will be 100+1+5+1=107.
In the second sample, Mahmoud shouldn't do any replacement so the cost will be 100+1+5+10=116. | [
{
"input": "5 4 4\ni loser am the second\n100 1 1 5 10\n1 1\n1 3\n2 2 5\n1 4\ni am the second",
"output": "107"
},
{
"input": "5 4 4\ni loser am the second\n100 20 1 5 10\n1 1\n1 3\n2 2 5\n1 4\ni am the second",
"output": "116"
},
{
"input": "1 1 1\na\n1000000000\n1 1\na",
"output": ... | 93 | 2,355,200 | -1 | 2,464 | |
817 | Really Big Numbers | [
"binary search",
"brute force",
"dp",
"math"
] | null | null | Ivan likes to learn different things about numbers, but he is especially interested in really big numbers. Ivan thinks that a positive integer number *x* is really big if the difference between *x* and the sum of its digits (in decimal representation) is not less than *s*. To prove that these numbers may have different special properties, he wants to know how rare (or not rare) they are — in fact, he needs to calculate the quantity of really big numbers that are not greater than *n*.
Ivan tried to do the calculations himself, but soon realized that it's too difficult for him. So he asked you to help him in calculations. | The first (and the only) line contains two integers *n* and *s* (1<=≤<=*n*,<=*s*<=≤<=1018). | Print one integer — the quantity of really big numbers that are not greater than *n*. | [
"12 1\n",
"25 20\n",
"10 9\n"
] | [
"3\n",
"0\n",
"1\n"
] | In the first example numbers 10, 11 and 12 are really big.
In the second example there are no really big numbers that are not greater than 25 (in fact, the first really big number is 30: 30 - 3 ≥ 20).
In the third example 10 is the only really big number (10 - 1 ≥ 9). | [
{
"input": "12 1",
"output": "3"
},
{
"input": "25 20",
"output": "0"
},
{
"input": "10 9",
"output": "1"
},
{
"input": "300 1000",
"output": "0"
},
{
"input": "500 1000",
"output": "0"
},
{
"input": "1000 2000",
"output": "0"
},
{
"input":... | 109 | 0 | 0 | 2,470 | |
435 | Queue on Bus Stop | [
"implementation"
] | null | null | It's that time of the year when the Russians flood their countryside summer cottages (dachas) and the bus stop has a lot of people. People rarely go to the dacha on their own, it's usually a group, so the people stand in queue by groups.
The bus stop queue has *n* groups of people. The *i*-th group from the beginning has *a**i* people. Every 30 minutes an empty bus arrives at the bus stop, it can carry at most *m* people. Naturally, the people from the first group enter the bus first. Then go the people from the second group and so on. Note that the order of groups in the queue never changes. Moreover, if some group cannot fit all of its members into the current bus, it waits for the next bus together with other groups standing after it in the queue.
Your task is to determine how many buses is needed to transport all *n* groups to the dacha countryside. | The first line contains two integers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=100). The next line contains *n* integers: *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=*m*). | Print a single integer — the number of buses that is needed to transport all *n* groups to the dacha countryside. | [
"4 3\n2 3 2 1\n",
"3 4\n1 2 1\n"
] | [
"3\n",
"1\n"
] | none | [
{
"input": "4 3\n2 3 2 1",
"output": "3"
},
{
"input": "3 4\n1 2 1",
"output": "1"
},
{
"input": "1 5\n4",
"output": "1"
},
{
"input": "5 1\n1 1 1 1 1",
"output": "5"
},
{
"input": "6 4\n1 3 2 3 4 1",
"output": "5"
},
{
"input": "6 8\n6 1 1 1 4 5",
... | 124 | 0 | 0 | 2,472 | |
777 | Shell Game | [
"constructive algorithms",
"implementation",
"math"
] | null | null | Bomboslav likes to look out of the window in his room and watch lads outside playing famous shell game. The game is played by two persons: operator and player. Operator takes three similar opaque shells and places a ball beneath one of them. Then he shuffles the shells by swapping some pairs and the player has to guess the current position of the ball.
Bomboslav noticed that guys are not very inventive, so the operator always swaps the left shell with the middle one during odd moves (first, third, fifth, etc.) and always swaps the middle shell with the right one during even moves (second, fourth, etc.).
Let's number shells from 0 to 2 from left to right. Thus the left shell is assigned number 0, the middle shell is 1 and the right shell is 2. Bomboslav has missed the moment when the ball was placed beneath the shell, but he knows that exactly *n* movements were made by the operator and the ball was under shell *x* at the end. Now he wonders, what was the initial position of the ball? | The first line of the input contains an integer *n* (1<=≤<=*n*<=≤<=2·109) — the number of movements made by the operator.
The second line contains a single integer *x* (0<=≤<=*x*<=≤<=2) — the index of the shell where the ball was found after *n* movements. | Print one integer from 0 to 2 — the index of the shell where the ball was initially placed. | [
"4\n2\n",
"1\n1\n"
] | [
"1\n",
"0\n"
] | In the first sample, the ball was initially placed beneath the middle shell and the operator completed four movements.
1. During the first move operator swapped the left shell and the middle shell. The ball is now under the left shell. 1. During the second move operator swapped the middle shell and the right one. The ball is still under the left shell. 1. During the third move operator swapped the left shell and the middle shell again. The ball is again in the middle. 1. Finally, the operators swapped the middle shell and the right shell. The ball is now beneath the right shell. | [
{
"input": "4\n2",
"output": "1"
},
{
"input": "1\n1",
"output": "0"
},
{
"input": "2\n2",
"output": "0"
},
{
"input": "3\n1",
"output": "1"
},
{
"input": "3\n2",
"output": "0"
},
{
"input": "3\n0",
"output": "2"
},
{
"input": "2000000000\n... | 46 | 0 | 3 | 2,476 | |
659 | Tanya and Toys | [
"greedy",
"implementation"
] | null | null | In Berland recently a new collection of toys went on sale. This collection consists of 109 types of toys, numbered with integers from 1 to 109. A toy from the new collection of the *i*-th type costs *i* bourles.
Tania has managed to collect *n* different types of toys *a*1,<=*a*2,<=...,<=*a**n* from the new collection. Today is Tanya's birthday, and her mother decided to spend no more than *m* bourles on the gift to the daughter. Tanya will choose several different types of toys from the new collection as a gift. Of course, she does not want to get a type of toy which she already has.
Tanya wants to have as many distinct types of toys in her collection as possible as the result. The new collection is too diverse, and Tanya is too little, so she asks you to help her in this. | The first line contains two integers *n* (1<=≤<=*n*<=≤<=100<=000) and *m* (1<=≤<=*m*<=≤<=109) — the number of types of toys that Tanya already has and the number of bourles that her mom is willing to spend on buying new toys.
The next line contains *n* distinct integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=109) — the types of toys that Tanya already has. | In the first line print a single integer *k* — the number of different types of toys that Tanya should choose so that the number of different types of toys in her collection is maximum possible. Of course, the total cost of the selected toys should not exceed *m*.
In the second line print *k* distinct space-separated integers *t*1,<=*t*2,<=...,<=*t**k* (1<=≤<=*t**i*<=≤<=109) — the types of toys that Tanya should choose.
If there are multiple answers, you may print any of them. Values of *t**i* can be printed in any order. | [
"3 7\n1 3 4\n",
"4 14\n4 6 12 8\n"
] | [
"2\n2 5 \n",
"4\n7 2 3 1\n"
] | In the first sample mom should buy two toys: one toy of the 2-nd type and one toy of the 5-th type. At any other purchase for 7 bourles (assuming that the toys of types 1, 3 and 4 have already been bought), it is impossible to buy two and more toys. | [
{
"input": "3 7\n1 3 4",
"output": "2\n2 5 "
},
{
"input": "4 14\n4 6 12 8",
"output": "4\n1 2 3 5 "
},
{
"input": "5 6\n97746 64770 31551 96547 65684",
"output": "3\n1 2 3 "
},
{
"input": "10 10\n94125 56116 29758 94024 29289 31663 99794 35076 25328 58656",
"output": "4\... | 326 | 12,902,400 | 3 | 2,483 | |
78 | Archer's Shot | [
"binary search",
"geometry",
"math",
"two pointers"
] | D. Archer's Shot | 2 | 256 | A breakthrough among computer games, "Civilization XIII", is striking in its scale and elaborate details. Let's take a closer look at one of them.
The playing area in the game is split into congruent cells that are regular hexagons. The side of each cell is equal to 1. Each unit occupies exactly one cell of the playing field. The field can be considered infinite.
Let's take a look at the battle unit called an "Archer". Each archer has a parameter "shot range". It's a positive integer that determines the radius of the circle in which the archer can hit a target. The center of the circle coincides with the center of the cell in which the archer stays. A cell is considered to be under the archer’s fire if and only if all points of this cell, including border points are located inside the circle or on its border.
The picture below shows the borders for shot ranges equal to 3, 4 and 5. The archer is depicted as *A*.
Find the number of cells that are under fire for some archer. | The first and only line of input contains a single positive integer *k* — the archer's shot range (1<=≤<=*k*<=≤<=106). | Print the single number, the number of cells that are under fire.
Please do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use the cout stream (also you may use the %I64d specificator). | [
"3\n",
"4\n",
"5\n"
] | [
"7",
"13",
"19"
] | none | [
{
"input": "3",
"output": "7"
},
{
"input": "4",
"output": "13"
},
{
"input": "5",
"output": "19"
},
{
"input": "9",
"output": "85"
},
{
"input": "11",
"output": "121"
},
{
"input": "51",
"output": "3037"
},
{
"input": "101",
"output": ... | 46 | 0 | 0 | 2,485 |
991 | Bus Number | [
"brute force",
"combinatorics",
"math"
] | null | null | This night wasn't easy on Vasya. His favorite team lost, and he didn't find himself victorious either — although he played perfectly, his teammates let him down every time. He had to win at least one more time, but the losestreak only grew longer and longer... It's no wonder he didn't get any sleep this night at all.
In the morning, Vasya was waiting the bus to the university on the bus stop. Vasya's thoughts were hazy and so he couldn't remember the right bus' number quite right and got onto the bus with the number $n$.
In the bus, Vasya thought that he could get the order of the digits in the number of the bus wrong. Futhermore, he could "see" some digits several times, but the digits he saw were definitely in the real number of the bus. For example, if Vasya saw the number 2028, it could mean that the real bus number could be 2028, 8022, 2820 or just 820. However, numbers 80, 22208, 52 definitely couldn't be the number of the bus. Also, real bus number couldn't start with the digit 0, this meaning that, for example, number 082 couldn't be the real bus number too.
Given $n$, determine the total number of possible bus number variants. | The first line contains one integer $n$ ($1 \leq n \leq 10^{18}$) — the number of the bus that was seen by Vasya. It is guaranteed that this number does not start with $0$. | Output a single integer — the amount of possible variants of the real bus number. | [
"97\n",
"2028\n"
] | [
"2\n",
"13\n"
] | In the first sample, only variants $97$ and $79$ are possible.
In the second sample, the variants (in the increasing order) are the following: $208$, $280$, $802$, $820$, $2028$, $2082$, $2208$, $2280$, $2802$, $2820$, $8022$, $8202$, $8220$. | [
{
"input": "97",
"output": "2"
},
{
"input": "2028",
"output": "13"
},
{
"input": "1",
"output": "1"
},
{
"input": "10",
"output": "1"
},
{
"input": "168",
"output": "6"
},
{
"input": "999999",
"output": "6"
},
{
"input": "98765432002345678... | 156 | 1,536,000 | 3 | 2,493 | |
938 | Constructing Tests | [
"binary search",
"brute force",
"constructive algorithms"
] | null | null | Let's denote a *m*-free matrix as a binary (that is, consisting of only 1's and 0's) matrix such that every square submatrix of size *m*<=×<=*m* of this matrix contains at least one zero.
Consider the following problem:
You are given two integers *n* and *m*. You have to construct an *m*-free square matrix of size *n*<=×<=*n* such that the number of 1's in this matrix is maximum possible. Print the maximum possible number of 1's in such matrix.
You don't have to solve this problem. Instead, you have to construct a few tests for it.
You will be given *t* numbers *x*1, *x*2, ..., *x**t*. For every , find two integers *n**i* and *m**i* (*n**i*<=≥<=*m**i*) such that the answer for the aforementioned problem is exactly *x**i* if we set *n*<==<=*n**i* and *m*<==<=*m**i*. | The first line contains one integer *t* (1<=≤<=*t*<=≤<=100) — the number of tests you have to construct.
Then *t* lines follow, *i*-th line containing one integer *x**i* (0<=≤<=*x**i*<=≤<=109).
Note that in hacks you have to set *t*<==<=1. | For each test you have to construct, output two positive numbers *n**i* and *m**i* (1<=≤<=*m**i*<=≤<=*n**i*<=≤<=109) such that the maximum number of 1's in a *m**i*-free *n**i*<=×<=*n**i* matrix is exactly *x**i*. If there are multiple solutions, you may output any of them; and if this is impossible to construct a test, output a single integer <=-<=1. | [
"3\n21\n0\n1\n"
] | [
"5 2\n1 1\n-1\n"
] | none | [
{
"input": "3\n21\n0\n1",
"output": "5 2\n1 1\n-1"
},
{
"input": "1\n420441920",
"output": "-1"
},
{
"input": "1\n4",
"output": "-1"
},
{
"input": "1\n297540",
"output": "546 22"
},
{
"input": "1\n9",
"output": "-1"
},
{
"input": "1\n144",
"output"... | 46 | 0 | 0 | 2,500 | |
180 | Mathematical Analysis Rocks! | [
"constructive algorithms",
"implementation",
"math"
] | null | null | Students of group 199 have written their lectures dismally. Now an exam on Mathematical Analysis is approaching and something has to be done asap (that is, quickly). Let's number the students of the group from 1 to *n*. Each student *i* (1<=≤<=*i*<=≤<=*n*) has a best friend *p*[*i*] (1<=≤<=*p*[*i*]<=≤<=*n*). In fact, each student is a best friend of exactly one student. In other words, all *p*[*i*] are different. It is possible that the group also has some really "special individuals" for who *i*<==<=*p*[*i*].
Each student wrote exactly one notebook of lecture notes. We know that the students agreed to act by the following algorithm:
- on the first day of revising each student studies his own Mathematical Analysis notes, - in the morning of each following day each student gives the notebook to his best friend and takes a notebook from the student who calls him the best friend.
Thus, on the second day the student *p*[*i*] (1<=≤<=*i*<=≤<=*n*) studies the *i*-th student's notes, on the third day the notes go to student *p*[*p*[*i*]] and so on. Due to some characteristics of the boys' friendship (see paragraph 1), each day each student has exactly one notebook to study.
You are given two sequences that describe the situation on the third and fourth days of revising:
- *a*1,<=*a*2,<=...,<=*a**n*, where *a**i* means the student who gets the *i*-th student's notebook on the third day of revising; - *b*1,<=*b*2,<=...,<=*b**n*, where *b**i* means the student who gets the *i*-th student's notebook on the fourth day of revising.
You do not know array *p*, that is you do not know who is the best friend to who. Write a program that finds *p* by the given sequences *a* and *b*. | The first line contains integer *n* (1<=≤<=*n*<=≤<=105) — the number of students in the group. The second line contains sequence of different integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=*n*). The third line contains the sequence of different integers *b*1,<=*b*2,<=...,<=*b**n* (1<=≤<=*b**i*<=≤<=*n*). | Print sequence *n* of different integers *p*[1],<=*p*[2],<=...,<=*p*[*n*] (1<=≤<=*p*[*i*]<=≤<=*n*). It is guaranteed that the solution exists and that it is unique. | [
"4\n2 1 4 3\n3 4 2 1\n",
"5\n5 2 3 1 4\n1 3 2 4 5\n",
"2\n1 2\n2 1\n"
] | [
"4 3 1 2 ",
"4 3 2 5 1 ",
"2 1 "
] | none | [
{
"input": "4\n2 1 4 3\n3 4 2 1",
"output": "4 3 1 2 "
},
{
"input": "5\n5 2 3 1 4\n1 3 2 4 5",
"output": "4 3 2 5 1 "
},
{
"input": "2\n1 2\n2 1",
"output": "2 1 "
},
{
"input": "1\n1\n1",
"output": "1 "
},
{
"input": "2\n1 2\n1 2",
"output": "1 2 "
},
{
... | 654 | 22,118,400 | 3 | 2,506 | |
597 | Subsequences | [
"data structures",
"dp"
] | null | null | For the given sequence with *n* different elements find the number of increasing subsequences with *k*<=+<=1 elements. It is guaranteed that the answer is not greater than 8·1018. | First line contain two integer values *n* and *k* (1<=≤<=*n*<=≤<=105,<=0<=≤<=*k*<=≤<=10) — the length of sequence and the number of elements in increasing subsequences.
Next *n* lines contains one integer *a**i* (1<=≤<=*a**i*<=≤<=*n*) each — elements of sequence. All values *a**i* are different. | Print one integer — the answer to the problem. | [
"5 2\n1\n2\n3\n5\n4\n"
] | [
"7\n"
] | none | [
{
"input": "5 2\n1\n2\n3\n5\n4",
"output": "7"
},
{
"input": "1 0\n1",
"output": "1"
},
{
"input": "2 1\n1\n2",
"output": "1"
},
{
"input": "2 1\n2\n1",
"output": "0"
},
{
"input": "3 2\n1\n2\n3",
"output": "1"
},
{
"input": "3 1\n1\n3\n2",
"output... | 31 | 0 | 0 | 2,508 | |
740 | Alyona and flowers | [
"constructive algorithms"
] | null | null | Little Alyona is celebrating Happy Birthday! Her mother has an array of *n* flowers. Each flower has some mood, the mood of *i*-th flower is *a**i*. The mood can be positive, zero or negative.
Let's define a subarray as a segment of consecutive flowers. The mother suggested some set of subarrays. Alyona wants to choose several of the subarrays suggested by her mother. After that, each of the flowers will add to the girl's happiness its mood multiplied by the number of chosen subarrays the flower is in.
For example, consider the case when the mother has 5 flowers, and their moods are equal to 1,<=<=-<=2,<=1,<=3,<=<=-<=4. Suppose the mother suggested subarrays (1,<=<=-<=2), (3,<=<=-<=4), (1,<=3), (1,<=<=-<=2,<=1,<=3). Then if the girl chooses the third and the fourth subarrays then:
- the first flower adds 1·1<==<=1 to the girl's happiness, because he is in one of chosen subarrays, - the second flower adds (<=-<=2)·1<==<=<=-<=2, because he is in one of chosen subarrays, - the third flower adds 1·2<==<=2, because he is in two of chosen subarrays, - the fourth flower adds 3·2<==<=6, because he is in two of chosen subarrays, - the fifth flower adds (<=-<=4)·0<==<=0, because he is in no chosen subarrays.
Thus, in total 1<=+<=(<=-<=2)<=+<=2<=+<=6<=+<=0<==<=7 is added to the girl's happiness. Alyona wants to choose such subarrays from those suggested by the mother that the value added to her happiness would be as large as possible. Help her do this!
Alyona can choose any number of the subarrays, even 0 or all suggested by her mother. | The first line contains two integers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=100) — the number of flowers and the number of subarrays suggested by the mother.
The second line contains the flowers moods — *n* integers *a*1,<=*a*2,<=...,<=*a**n* (<=-<=100<=≤<=*a**i*<=≤<=100).
The next *m* lines contain the description of the subarrays suggested by the mother. The *i*-th of these lines contain two integers *l**i* and *r**i* (1<=≤<=*l**i*<=≤<=*r**i*<=≤<=*n*) denoting the subarray *a*[*l**i*],<=*a*[*l**i*<=+<=1],<=...,<=*a*[*r**i*].
Each subarray can encounter more than once. | Print single integer — the maximum possible value added to the Alyona's happiness. | [
"5 4\n1 -2 1 3 -4\n1 2\n4 5\n3 4\n1 4\n",
"4 3\n1 2 3 4\n1 3\n2 4\n1 1\n",
"2 2\n-1 -2\n1 1\n1 2\n"
] | [
"7\n",
"16\n",
"0\n"
] | The first example is the situation described in the statements.
In the second example Alyona should choose all subarrays.
The third example has answer 0 because Alyona can choose none of the subarrays. | [
{
"input": "5 4\n1 -2 1 3 -4\n1 2\n4 5\n3 4\n1 4",
"output": "7"
},
{
"input": "4 3\n1 2 3 4\n1 3\n2 4\n1 1",
"output": "16"
},
{
"input": "2 2\n-1 -2\n1 1\n1 2",
"output": "0"
},
{
"input": "5 6\n1 1 1 -1 0\n2 4\n1 3\n4 5\n1 5\n1 4\n4 5",
"output": "8"
},
{
"inpu... | 62 | 6,963,200 | 3 | 2,509 | |
5 | Longest Regular Bracket Sequence | [
"constructive algorithms",
"data structures",
"dp",
"greedy",
"sortings",
"strings"
] | C. Longest Regular Bracket Sequence | 2 | 256 | This is yet another problem dealing with regular bracket sequences.
We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well. | The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106. | Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1". | [
")((())))(()())\n",
"))(\n"
] | [
"6 2\n",
"0 1\n"
] | none | [
{
"input": ")((())))(()())",
"output": "6 2"
},
{
"input": "))(",
"output": "0 1"
},
{
"input": "()(())()",
"output": "8 1"
},
{
"input": "((((()(((",
"output": "2 1"
},
{
"input": "))))()())))",
"output": "4 1"
},
{
"input": "(()())()(())()()())())()(... | 92 | 0 | 0 | 2,515 |
62 | A Student's Dream | [
"greedy",
"math"
] | A. A Student's Dream | 2 | 256 | Statistics claims that students sleep no more than three hours a day. But even in the world of their dreams, while they are snoring peacefully, the sense of impending doom is still upon them.
A poor student is dreaming that he is sitting the mathematical analysis exam. And he is examined by the most formidable professor of all times, a three times Soviet Union Hero, a Noble Prize laureate in student expulsion, venerable Petr Palych.
The poor student couldn't answer a single question. Thus, instead of a large spacious office he is going to apply for a job to thorium mines. But wait a minute! Petr Palych decided to give the student the last chance! Yes, that is possible only in dreams.
So the professor began: "Once a Venusian girl and a Marsian boy met on the Earth and decided to take a walk holding hands. But the problem is the girl has *a**l* fingers on her left hand and *a**r* fingers on the right one. The boy correspondingly has *b**l* and *b**r* fingers. They can only feel comfortable when holding hands, when no pair of the girl's fingers will touch each other. That is, they are comfortable when between any two girl's fingers there is a boy's finger. And in addition, no three fingers of the boy should touch each other. Determine if they can hold hands so that the both were comfortable."
The boy any the girl don't care who goes to the left and who goes to the right. The difference is only that if the boy goes to the left of the girl, he will take her left hand with his right one, and if he goes to the right of the girl, then it is vice versa. | The first line contains two positive integers not exceeding 100. They are the number of fingers on the Venusian girl's left and right hand correspondingly. The second line contains two integers not exceeding 100. They are the number of fingers on the Marsian boy's left and right hands correspondingly. | Print YES or NO, that is, the answer to Petr Palych's question. | [
"5 1\n10 5\n",
"4 5\n3 3\n",
"1 2\n11 6\n"
] | [
"YES",
"YES",
"NO"
] | The boy and the girl don't really care who goes to the left. | [
{
"input": "5 1\n10 5",
"output": "YES"
},
{
"input": "4 5\n3 3",
"output": "YES"
},
{
"input": "1 2\n11 6",
"output": "NO"
},
{
"input": "1 1\n1 1",
"output": "YES"
},
{
"input": "2 2\n1 1",
"output": "YES"
},
{
"input": "3 3\n1 1",
"output": "NO"... | 124 | 6,758,400 | 3.956411 | 2,523 |
599 | Day at the Beach | [
"sortings"
] | null | null | One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were *n* castles built by friends. Castles are numbered from 1 to *n*, and the height of the *i*-th castle is equal to *h**i*. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition *h**i*<=≤<=*h**i*<=+<=1 holds for all *i* from 1 to *n*<=-<=1.
Squidward suggested the following process of sorting castles:
- Castles are split into blocks — groups of consecutive castles. Therefore the block from *i* to *j* will include castles *i*,<=*i*<=+<=1,<=...,<=*j*. A block may consist of a single castle. - The partitioning is chosen in such a way that every castle is a part of exactly one block. - Each block is sorted independently from other blocks, that is the sequence *h**i*,<=*h**i*<=+<=1,<=...,<=*h**j* becomes sorted. - The partitioning should satisfy the condition that after each block is sorted, the sequence *h**i* becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements. | The first line of the input contains a single integer *n* (1<=≤<=*n*<=≤<=100<=000) — the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains *n* integers *h**i* (1<=≤<=*h**i*<=≤<=109). The *i*-th of these integers corresponds to the height of the *i*-th castle. | Print the maximum possible number of blocks in a valid partitioning. | [
"3\n1 2 3\n",
"4\n2 1 3 2\n"
] | [
"3\n",
"2\n"
] | In the first sample the partitioning looks like that: [1][2][3].
In the second sample the partitioning is: [2, 1][3, 2] | [
{
"input": "3\n1 2 3",
"output": "3"
},
{
"input": "4\n2 1 3 2",
"output": "2"
},
{
"input": "17\n1 45 22 39 28 23 23 100 500 778 777 778 1001 1002 1005 1003 1005",
"output": "10"
},
{
"input": "101\n1 50 170 148 214 153 132 234 181 188 180 225 226 200 197 122 181 168 87 220 ... | 46 | 0 | 0 | 2,530 | |
10 | Cinema Cashier | [
"dp",
"implementation"
] | B. Cinema Cashier | 1 | 256 | All cinema halls in Berland are rectangles with *K* rows of *K* seats each, and *K* is an odd number. Rows and seats are numbered from 1 to *K*. For safety reasons people, who come to the box office to buy tickets, are not allowed to choose seats themselves. Formerly the choice was made by a cashier, but now this is the responsibility of a special seating program. It was found out that the large majority of Berland's inhabitants go to the cinema in order to watch a movie, that's why they want to sit as close to the hall center as possible. Moreover, a company of *M* people, who come to watch a movie, want necessarily to occupy *M* successive seats in one row. Let's formulate the algorithm, according to which the program chooses seats and sells tickets. As the request for *M* seats comes, the program should determine the row number *x* and the segment [*y**l*,<=*y**r*] of the seats numbers in this row, where *y**r*<=-<=*y**l*<=+<=1<==<=*M*. From all such possible variants as a final result the program should choose the one with the minimum function value of total seats remoteness from the center. Say, — the row and the seat numbers of the most "central" seat. Then the function value of seats remoteness from the hall center is . If the amount of minimum function values is more than one, the program should choose the one that is closer to the screen (i.e. the row number *x* is lower). If the variants are still multiple, it should choose the one with the minimum *y**l*. If you did not get yet, your task is to simulate the work of this program. | The first line contains two integers *N* and *K* (1<=≤<=*N*<=≤<=1000,<=1<=≤<=*K*<=≤<=99) — the amount of requests and the hall size respectively. The second line contains *N* space-separated integers *M**i* from the range [1,<=*K*] — requests to the program. | Output *N* lines. In the *i*-th line output «-1» (without quotes), if it is impossible to find *M**i* successive seats in one row, otherwise output three numbers *x*,<=*y**l*,<=*y**r*. Separate the numbers with a space. | [
"2 1\n1 1\n",
"4 3\n1 2 3 1\n"
] | [
"1 1 1\n-1\n",
"2 2 2\n1 1 2\n3 1 3\n2 1 1\n"
] | none | [
{
"input": "2 1\n1 1",
"output": "1 1 1\n-1"
},
{
"input": "4 3\n1 2 3 1",
"output": "2 2 2\n1 1 2\n3 1 3\n2 1 1"
},
{
"input": "1 3\n1",
"output": "2 2 2"
},
{
"input": "2 3\n3 3",
"output": "2 1 3\n1 1 3"
},
{
"input": "3 3\n3 2 3",
"output": "2 1 3\n1 1 2\n... | 109 | 20,172,800 | 0 | 2,532 |
107 | Dorm Water Supply | [
"dfs and similar",
"graphs"
] | A. Dorm Water Supply | 1 | 256 | The German University in Cairo (GUC) dorm houses are numbered from 1 to *n*. Underground water pipes connect these houses together. Each pipe has certain direction (water can flow only in this direction and not vice versa), and diameter (which characterizes the maximal amount of water it can handle).
For each house, there is at most one pipe going into it and at most one pipe going out of it. With the new semester starting, GUC student and dorm resident, Lulu, wants to install tanks and taps at the dorms. For every house with an outgoing water pipe and without an incoming water pipe, Lulu should install a water tank at that house. For every house with an incoming water pipe and without an outgoing water pipe, Lulu should install a water tap at that house. Each tank house will convey water to all houses that have a sequence of pipes from the tank to it. Accordingly, each tap house will receive water originating from some tank house.
In order to avoid pipes from bursting one week later (like what happened last semester), Lulu also has to consider the diameter of the pipes. The amount of water each tank conveys should not exceed the diameter of the pipes connecting a tank to its corresponding tap. Lulu wants to find the maximal amount of water that can be safely conveyed from each tank to its corresponding tap. | The first line contains two space-separated integers *n* and *p* (1<=≤<=*n*<=≤<=1000,<=0<=≤<=*p*<=≤<=*n*) — the number of houses and the number of pipes correspondingly.
Then *p* lines follow — the description of *p* pipes. The *i*-th line contains three integers *a**i* *b**i* *d**i*, indicating a pipe of diameter *d**i* going from house *a**i* to house *b**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=*n*,<=*a**i*<=≠<=*b**i*,<=1<=≤<=*d**i*<=≤<=106).
It is guaranteed that for each house there is at most one pipe going into it and at most one pipe going out of it. | Print integer *t* in the first line — the number of tank-tap pairs of houses.
For the next *t* lines, print 3 integers per line, separated by spaces: *tank**i*, *tap**i*, and *diameter**i*, where *tank**i*<=≠<=*tap**i* (1<=≤<=*i*<=≤<=*t*). Here *tank**i* and *tap**i* are indexes of tank and tap houses respectively, and *diameter**i* is the maximum amount of water that can be conveyed. All the *t* lines should be ordered (increasingly) by *tank**i*. | [
"3 2\n1 2 10\n2 3 20\n",
"3 3\n1 2 20\n2 3 10\n3 1 5\n",
"4 2\n1 2 60\n3 4 50\n"
] | [
"1\n1 3 10\n",
"0\n",
"2\n1 2 60\n3 4 50\n"
] | none | [
{
"input": "3 2\n1 2 10\n2 3 20",
"output": "1\n1 3 10"
},
{
"input": "3 3\n1 2 20\n2 3 10\n3 1 5",
"output": "0"
},
{
"input": "4 2\n1 2 60\n3 4 50",
"output": "2\n1 2 60\n3 4 50"
},
{
"input": "10 10\n10 3 70\n1 9 98\n9 10 67\n5 2 78\n8 6 71\n4 8 95\n7 1 10\n2 5 73\n6 7 94\... | 109 | 0 | 0 | 2,533 |
913 | Christmas Spruce | [
"implementation",
"trees"
] | null | null | Consider a rooted tree. A rooted tree has one special vertex called the root. All edges are directed from the root. Vertex *u* is called a child of vertex *v* and vertex *v* is called a parent of vertex *u* if there exists a directed edge from *v* to *u*. A vertex is called a leaf if it doesn't have children and has a parent.
Let's call a rooted tree a spruce if its every non-leaf vertex has at least 3 leaf children. You are given a rooted tree, check whether it's a spruce.
The definition of a rooted tree can be found [here](https://goo.gl/1dqvzz). | The first line contains one integer *n* — the number of vertices in the tree (3<=≤<=*n*<=≤<=1<=000). Each of the next *n*<=-<=1 lines contains one integer *p**i* (1<=≤<=*i*<=≤<=*n*<=-<=1) — the index of the parent of the *i*<=+<=1-th vertex (1<=≤<=*p**i*<=≤<=*i*).
Vertex 1 is the root. It's guaranteed that the root has at least 2 children. | Print "Yes" if the tree is a spruce and "No" otherwise. | [
"4\n1\n1\n1\n",
"7\n1\n1\n1\n2\n2\n2\n",
"8\n1\n1\n1\n1\n3\n3\n3\n"
] | [
"Yes\n",
"No\n",
"Yes\n"
] | The first example:
<img class="tex-graphics" src="https://espresso.codeforces.com/8dd976913226df83d535dfa66193f5525f8471bc.png" style="max-width: 100.0%;max-height: 100.0%;"/>
The second example:
<img class="tex-graphics" src="https://espresso.codeforces.com/44dad5804f5290a2e026c9c41a15151562df8682.png" style="max-width: 100.0%;max-height: 100.0%;"/>
It is not a spruce, because the non-leaf vertex 1 has only 2 leaf children.
The third example:
<img class="tex-graphics" src="https://espresso.codeforces.com/cf84a9e1585707f4ab06eff8eb1120a49b5e1ef7.png" style="max-width: 100.0%;max-height: 100.0%;"/> | [
{
"input": "4\n1\n1\n1",
"output": "Yes"
},
{
"input": "7\n1\n1\n1\n2\n2\n2",
"output": "No"
},
{
"input": "8\n1\n1\n1\n1\n3\n3\n3",
"output": "Yes"
},
{
"input": "3\n1\n1",
"output": "No"
},
{
"input": "13\n1\n2\n2\n2\n1\n6\n6\n6\n1\n10\n10\n10",
"output": "N... | 92 | 1,433,600 | 0 | 2,536 | |
391 | Genetic Engineering | [
"implementation",
"two pointers"
] | null | null | You will receive 3 points for solving this problem.
Manao is designing the genetic code for a new type of algae to efficiently produce fuel. Specifically, Manao is focusing on a stretch of DNA that encodes one protein. The stretch of DNA is represented by a string containing only the characters 'A', 'T', 'G' and 'C'.
Manao has determined that if the stretch of DNA contains a maximal sequence of consecutive identical nucleotides that is of even length, then the protein will be nonfunctional. For example, consider a protein described by DNA string "GTTAAAG". It contains four maximal sequences of consecutive identical nucleotides: "G", "TT", "AAA", and "G". The protein is nonfunctional because sequence "TT" has even length.
Manao is trying to obtain a functional protein from the protein he currently has. Manao can insert additional nucleotides into the DNA stretch. Each additional nucleotide is a character from the set {'A', 'T', 'G', 'C'}. Manao wants to determine the minimum number of insertions necessary to make the DNA encode a functional protein. | The input consists of a single line, containing a string *s* of length *n* (1<=≤<=*n*<=≤<=100). Each character of *s* will be from the set {'A', 'T', 'G', 'C'}.
This problem doesn't have subproblems. You will get 3 points for the correct submission. | The program should print on one line a single integer representing the minimum number of 'A', 'T', 'G', 'C' characters that are required to be inserted into the input string in order to make all runs of identical characters have odd length. | [
"GTTAAAG\n",
"AACCAACCAAAAC\n"
] | [
"1\n",
"5\n"
] | In the first example, it is sufficient to insert a single nucleotide of any type between the two 'T's in the sequence to restore the functionality of the protein. | [
{
"input": "GTTAAAG",
"output": "1"
},
{
"input": "AACCAACCAAAAC",
"output": "5"
},
{
"input": "GTGAATTTCC",
"output": "2"
},
{
"input": "CAGGGGGCCGCCCATGAAAAAAACCCGGCCCCTTGGGAAAACTTGGGTTA",
"output": "7"
},
{
"input": "CCCTTCACCCGGATCCAAATCCCTTAGAAATAATCCCCGACGGC... | 93 | 21,401,600 | 3 | 2,537 | |
476 | Dreamoon and Sums | [
"math"
] | null | null | Dreamoon loves summing up something for no reason. One day he obtains two integers *a* and *b* occasionally. He wants to calculate the sum of all nice integers. Positive integer *x* is called nice if and , where *k* is some integer number in range [1,<=*a*].
By we denote the quotient of integer division of *x* and *y*. By we denote the remainder of integer division of *x* and *y*. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1<=000<=000<=007 (109<=+<=7). Can you compute it faster than Dreamoon? | The single line of the input contains two integers *a*, *b* (1<=≤<=*a*,<=*b*<=≤<=107). | Print a single integer representing the answer modulo 1<=000<=000<=007 (109<=+<=7). | [
"1 1\n",
"2 2\n"
] | [
"0\n",
"8\n"
] | For the first sample, there are no nice integers because <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/03b1dc6bae5180f8a2d8eb85789e8b393e585970.png" style="max-width: 100.0%;max-height: 100.0%;"/> is always zero.
For the second sample, the set of nice integers is {3, 5}. | [
{
"input": "1 1",
"output": "0"
},
{
"input": "2 2",
"output": "8"
},
{
"input": "4 1",
"output": "0"
},
{
"input": "4 2",
"output": "24"
},
{
"input": "4 3",
"output": "102"
},
{
"input": "4 4",
"output": "264"
},
{
"input": "3 4",
"ou... | 1,500 | 0 | 0 | 2,551 | |
817 | Makes And The Product | [
"combinatorics",
"implementation",
"math",
"sortings"
] | null | null | After returning from the army Makes received a gift — an array *a* consisting of *n* positive integer numbers. He hadn't been solving problems for a long time, so he became interested to answer a particular question: how many triples of indices (*i*,<= *j*,<= *k*) (*i*<=<<=*j*<=<<=*k*), such that *a**i*·*a**j*·*a**k* is minimum possible, are there in the array? Help him with it! | The first line of input contains a positive integer number *n* (3<=≤<=*n*<=≤<=105) — the number of elements in array *a*. The second line contains *n* positive integer numbers *a**i* (1<=≤<=*a**i*<=≤<=109) — the elements of a given array. | Print one number — the quantity of triples (*i*,<= *j*,<= *k*) such that *i*,<= *j* and *k* are pairwise distinct and *a**i*·*a**j*·*a**k* is minimum possible. | [
"4\n1 1 1 1\n",
"5\n1 3 2 3 4\n",
"6\n1 3 3 1 3 2\n"
] | [
"4\n",
"2\n",
"1\n"
] | In the first example Makes always chooses three ones out of four, and the number of ways to choose them is 4.
In the second example a triple of numbers (1, 2, 3) is chosen (numbers, not indices). Since there are two ways to choose an element 3, then the answer is 2.
In the third example a triple of numbers (1, 1, 2) is chosen, and there's only one way to choose indices. | [
{
"input": "4\n1 1 1 1",
"output": "4"
},
{
"input": "5\n1 3 2 3 4",
"output": "2"
},
{
"input": "6\n1 3 3 1 3 2",
"output": "1"
},
{
"input": "3\n1000000000 1000000000 1000000000",
"output": "1"
},
{
"input": "4\n1 1 2 2",
"output": "2"
},
{
"input": ... | 249 | 15,974,400 | 3 | 2,553 | |
31 | TV Game | [
"dp"
] | E. TV Game | 2 | 256 | There is a new TV game on BerTV. In this game two players get a number *A* consisting of 2*n* digits. Before each turn players determine who will make the next move. Each player should make exactly *n* moves. On it's turn *i*-th player takes the leftmost digit of *A* and appends it to his or her number *S**i*. After that this leftmost digit is erased from *A*. Initially the numbers of both players (*S*1 and *S*2) are «empty». Leading zeroes in numbers *A*,<=*S*1,<=*S*2 are allowed. In the end of the game the first player gets *S*1 dollars, and the second gets *S*2 dollars.
One day Homer and Marge came to play the game. They managed to know the number *A* beforehand. They want to find such sequence of their moves that both of them makes exactly *n* moves and which maximizes their total prize. Help them. | The first line contains integer *n* (1<=≤<=*n*<=≤<=18). The second line contains integer *A* consisting of exactly 2*n* digits. This number can have leading zeroes. | Output the line of 2*n* characters «H» and «M» — the sequence of moves of Homer and Marge, which gives them maximum possible total prize. Each player must make exactly *n* moves. If there are several solutions, output any of them. | [
"2\n1234\n",
"2\n9911\n"
] | [
"HHMM",
"HMHM"
] | none | [
{
"input": "2\n1234",
"output": "HHMM"
},
{
"input": "2\n9911",
"output": "HMHM"
},
{
"input": "2\n0153",
"output": "HHMM"
},
{
"input": "3\n614615",
"output": "HHHMMM"
},
{
"input": "4\n21305374",
"output": "HHHHMMMM"
},
{
"input": "4\n00013213",
... | 60 | 0 | 0 | 2,557 |
960 | Check the string | [
"implementation"
] | null | null | A has a string consisting of some number of lowercase English letters 'a'. He gives it to his friend B who appends some number of letters 'b' to the end of this string. Since both A and B like the characters 'a' and 'b', they have made sure that at this point, at least one 'a' and one 'b' exist in the string.
B now gives this string to C and he appends some number of letters 'c' to the end of the string. However, since C is a good friend of A and B, the number of letters 'c' he appends is equal to the number of 'a' or to the number of 'b' in the string. It is also possible that the number of letters 'c' equals both to the number of letters 'a' and to the number of letters 'b' at the same time.
You have a string in your hands, and you want to check if it is possible to obtain the string in this way or not. If it is possible to obtain the string, print "YES", otherwise print "NO" (without the quotes). | The first and only line consists of a string $S$ ($ 1 \le |S| \le 5\,000 $). It is guaranteed that the string will only consist of the lowercase English letters 'a', 'b', 'c'. | Print "YES" or "NO", according to the condition. | [
"aaabccc\n",
"bbacc\n",
"aabc\n"
] | [
"YES\n",
"NO\n",
"YES\n"
] | Consider first example: the number of 'c' is equal to the number of 'a'.
Consider second example: although the number of 'c' is equal to the number of the 'b', the order is not correct.
Consider third example: the number of 'c' is equal to the number of 'b'. | [
{
"input": "aaabccc",
"output": "YES"
},
{
"input": "bbacc",
"output": "NO"
},
{
"input": "aabc",
"output": "YES"
},
{
"input": "aabbcc",
"output": "YES"
},
{
"input": "aaacccbb",
"output": "NO"
},
{
"input": "abc",
"output": "YES"
},
{
"in... | 78 | 7,065,600 | 0 | 2,559 | |
246 | Colorful Graph | [
"brute force",
"dfs and similar",
"graphs"
] | null | null | You've got an undirected graph, consisting of *n* vertices and *m* edges. We will consider the graph's vertices numbered with integers from 1 to *n*. Each vertex of the graph has a color. The color of the *i*-th vertex is an integer *c**i*.
Let's consider all vertices of the graph, that are painted some color *k*. Let's denote a set of such as *V*(*k*). Let's denote the value of the neighbouring color diversity for color *k* as the cardinality of the set *Q*(*k*)<==<={*c**u* :<= *c**u*<=≠<=*k* and there is vertex *v* belonging to set *V*(*k*) such that nodes *v* and *u* are connected by an edge of the graph}.
Your task is to find such color *k*, which makes the cardinality of set *Q*(*k*) maximum. In other words, you want to find the color that has the most diverse neighbours. Please note, that you want to find such color *k*, that the graph has at least one vertex with such color. | The first line contains two space-separated integers *n*,<=*m* (1<=≤<=*n*,<=*m*<=≤<=105) — the number of vertices end edges of the graph, correspondingly. The second line contains a sequence of integers *c*1,<=*c*2,<=...,<=*c**n* (1<=≤<=*c**i*<=≤<=105) — the colors of the graph vertices. The numbers on the line are separated by spaces.
Next *m* lines contain the description of the edges: the *i*-th line contains two space-separated integers *a**i*,<=*b**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=*n*; *a**i*<=≠<=*b**i*) — the numbers of the vertices, connected by the *i*-th edge.
It is guaranteed that the given graph has no self-loops or multiple edges. | Print the number of the color which has the set of neighbours with the maximum cardinality. It there are multiple optimal colors, print the color with the minimum number. Please note, that you want to find such color, that the graph has at least one vertex with such color. | [
"6 6\n1 1 2 3 5 8\n1 2\n3 2\n1 4\n4 3\n4 5\n4 6\n",
"5 6\n4 2 5 2 4\n1 2\n2 3\n3 1\n5 3\n5 4\n3 4\n"
] | [
"3\n",
"2\n"
] | none | [
{
"input": "6 6\n1 1 2 3 5 8\n1 2\n3 2\n1 4\n4 3\n4 5\n4 6",
"output": "3"
},
{
"input": "5 6\n4 2 5 2 4\n1 2\n2 3\n3 1\n5 3\n5 4\n3 4",
"output": "2"
},
{
"input": "3 1\n13 13 4\n1 2",
"output": "4"
},
{
"input": "2 1\n500 300\n1 2",
"output": "300"
},
{
"input":... | 156 | 3,481,600 | 0 | 2,567 | |
837 | Round Subset | [
"dp",
"math"
] | null | null | Let's call the roundness of the number the number of zeros to which it ends.
You have an array of *n* numbers. You need to choose a subset of exactly *k* numbers so that the roundness of the product of the selected numbers will be maximum possible. | The first line contains two integer numbers *n* and *k* (1<=≤<=*n*<=≤<=200,<=1<=≤<=*k*<=≤<=*n*).
The second line contains *n* space-separated integer numbers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=1018). | Print maximal roundness of product of the chosen subset of length *k*. | [
"3 2\n50 4 20\n",
"5 3\n15 16 3 25 9\n",
"3 3\n9 77 13\n"
] | [
"3\n",
"3\n",
"0\n"
] | In the first example there are 3 subsets of 2 numbers. [50, 4] has product 200 with roundness 2, [4, 20] — product 80, roundness 1, [50, 20] — product 1000, roundness 3.
In the second example subset [15, 16, 25] has product 6000, roundness 3.
In the third example all subsets has product with roundness 0. | [
{
"input": "3 2\n50 4 20",
"output": "3"
},
{
"input": "5 3\n15 16 3 25 9",
"output": "3"
},
{
"input": "3 3\n9 77 13",
"output": "0"
},
{
"input": "1 1\n200000000",
"output": "8"
},
{
"input": "1 1\n3",
"output": "0"
},
{
"input": "3 1\n10000000000000... | 2,000 | 13,312,000 | 0 | 2,568 | |
921 | Labyrinth-1 | [] | null | null | You have a robot in a two-dimensional labyrinth which consists of *N*<=×<=*M* cells. Some pairs of cells adjacent by side are separated by a wall or a door. The labyrinth itself is separated from the outside with walls around it. Some labyrinth cells are the exits. In order to leave the labyrinth the robot should reach any exit. There are keys in some cells. Any key can open any door but after the door is opened the key stays in the lock. Thus every key can be used only once. There are no labyrinth cells that contain both a key and an exit. Also there can not be both a wall and a door between the pair of adjacent cells.
Your need to write a program in *abc* language (see the language description below) that will lead the robot to one of the exits. Lets numerate the labyrinth rows from 0 to *N*<=-<=1 top to bottom and the columns – from 0 to *M*<=-<=1 left to right.
In *abc* language the following primary commands are available:
- move-DIR – move to the adjacent cell in the direction. *down* increases the number of the row by 1, *right* increases the number of the column by 1. In case there’s a wall or a closed door in this direction, nothing’s happening. - open-DIR – open the door between the current cell and the adjacent one in *DIR* direction. In case there isn’t any door in this direction or it’s already been opened or the robot doesn’t have a key, nothing’s happening.- take – take the key in the current cell. In case there isn’t any key or the robot has already picked it up, nothing’s happening. The robot is able to carry any number of keys.- terminate – terminate the program. This command is not obligatory to use. In case it’s absent the command is added at the end of the program automatically.
Also, there are the following control commands in *abc* language:
- for-N OPS end – repeat the sequence of the *OPS* commands *N* times, 0<=<<=*N*<=≤<=100000. Each loop counter check counts as a command fulfilled by the robot. - if-ok OPS1 else OPS2 endif – carries out the sequence of the *OPS*1 commands, if the previous command of moving, taking the key or opening the door was successful, otherwise the sequence of the *OPS*2 commands is being carried out. Should there be no previous command run, the sequence *OPS*1 will be carried out. If-ok check counts as a command fulfilled by the robot. - break – stops the current *for* loop. - continue – finishes the current *for* loop iterations.
Note that the control and the primary commands can be fit into each other arbitrarily.
The robot will fulfill your commands sequentially until it exits the labyrinth, or it runs out of the commands, or the *terminate* command is run, or the quantity of the fulfilled commands exceeds the bound number 5·106.
In *abc* language each command is a separate word and should be separated from other commands with at least one space symbol.
You should write a program that prints the sequence of commands leading the robot out of the labyrinth. Of course, as you are a good programmer, you should optimize these sequence.
The number of the non-space symbols in the sequence should not exceed 107. If you succeed in finding the way out of the labyrinth *i* you’ll be granted the number of points equal to:
- *W**i* – labyrinth’s weight, some fixed constant. - *G**i* – number of robots moves. - *O**i* – number of fulfilled commands. Note that this number includes commands like *take* executed in the cells with no key, as well as opening commands applied to the already opened doors. - *L**i* – sequence length in symbols, excluding space symbols and line breaks. - *Q*<==<=10·*N*·*M*.
In case your sequence doesn’t lead the robot to the exit you’ll be granted 0 points. Your programs result will be the sum of all *S**i*. You should maximize this total sum.
All labyrinths will be known and available to you. You can download the archive with labyrinths by any of the given links, password to extract files is aimtechiscool:
1. [https://drive.google.com/file/d/1dkIBfW_Gy6c3FJtXjMXZPMsGKRyn3pzp](https://drive.google.com/file/d/1dkIBfW_Gy6c3FJtXjMXZPMsGKRyn3pzp) 1. [https://www.dropbox.com/s/77jrplnjgmviiwt/aimmaze.zip?dl=0](https://www.dropbox.com/s/77jrplnjgmviiwt/aimmaze.zip?dl=0) 1. [https://yadi.sk/d/JNXDLeH63RzaCi](https://yadi.sk/d/JNXDLeH63RzaCi)
In order to make local testing of your programs more convenient, the program calculating your results (checker) and the labyrinth visualizer will be available. This program is written in *python*3 programming language, that’s why you’re going to need *python*3 interpreter, as well as *pillow* library, which you can install with the following command pip3 install pillow. *pip*3 is a utility program for *python*3 package (library) installation. It will be installed automatically with the *python*3 interpreter.
Example command to run checker and visualizer: python3 aimmaze.py maze.in robot.abc --image maze.png. The checker can be run separately of visualization: python3 aimmaze.py maze.in robot.abc. Flag --output-log will let you see the information of robots each step: python3 aimmaze.py maze.in robot.abc --output-log. Note *python*3 can be installed as *python* on your computer.
To adjust image settings, you can edit constants at the beginning of the program *aimmaze*.*py*. | The first line contains integers *i*,<= *W*,<= *N*,<= *M*,<= *x*0,<= *y*0,<= *C*,<= *D*,<= *K*,<= *E*.
- 1<=≤<=*i*<=≤<=14 – labyrinth’s number, which is needed for a checking program. - 1<=≤<=*W*<=≤<=1018 – labyrinth’s weight, which is needed for a checking program. - 2<=≤<=*N*,<=*M*<=≤<=1000 – labyrinth’s height and width. - 0<=≤<=*x*0<=≤<=*N*<=-<=1,<= 0<=≤<=*y*0<=≤<=*M*<=-<=1 – robot’s starting position (*x*0,<=*y*0). - 0<=≤<=*C*<=≤<=2·*NM* – number of walls. - 0<=≤<=*D*<=≤<=105 – number of doors. - 0<=≤<=*K*<=≤<=105 – number of keys. - 1<=≤<=*E*<=≤<=1000 – number of exits.
The *x* coordinate corresponds to the row number, *y* – to the column number. (0,<=0) cell is located on the left-up corner, so that *down* direction increases the *x* coordinate, while *right* direction increases the *y* coordinate.
Each of the next *C* lines contains 4 integers each *x*1,<=*y*1,<=*x*2,<=*y*2 – the coordinates of cells with a wall between them in a zero based indexing. It is guaranteed that |*x*1<=-<=*x*2|<=+<=|*y*1<=-<=*y*2|<==<=1,<= 0<=≤<=*x*1,<=*x*2<=≤<=*N*<=-<=1,<= 0<=≤<=*y*1,<=*y*2<=≤<=*M*<=-<=1. Also there are always walls around the labyrinth’s borders, which are not given in the labyrinths description.
Each of the next *D* lines contains door description in the same format as walls description. It is guaranteed that doors and walls don’t overlap.
Each of the next *K* rows contains a pair of integer which are the key coordinates in a zero based indexing.
Each of the next *E* rows contains a pair of integer which are the exit coordinates in a zero based indexing.
It is guaranteed that the robots starting position as well as keys and exits are located in pairwise different cells. | Print a program in *abc* language which passes the given labyrinth. Commands have to be separated by at least one space symbol. You can use arbitrary formatting for the program. | [
"1 1 30 30 1 1 1 1 1 1\n1 1 1 2\n2 2 2 3\n1 4\n9 0\n"
] | [
"for-1111\n take\n open-up\n open-left\n open-right\n open-down\n move-left\n if-ok\n for-11\n move-left\n take\n open-up\n open-left\n open-right\n open-down\n end\n else\n move-right\n if-ok\n for-11\n move-right\n take\n open-up\n open-left\n open-right\n open-down\... | none | [] | 31 | 5,632,000 | 2 | 2,577 | |
379 | New Year Ratings Change | [
"greedy",
"sortings"
] | null | null | One very well-known internet resource site (let's call it X) has come up with a New Year adventure. Specifically, they decided to give ratings to all visitors.
There are *n* users on the site, for each user we know the rating value he wants to get as a New Year Present. We know that user *i* wants to get at least *a**i* rating units as a present.
The X site is administered by very creative and thrifty people. On the one hand, they want to give distinct ratings and on the other hand, the total sum of the ratings in the present must be as small as possible.
Help site X cope with the challenging task of rating distribution. Find the optimal distribution. | The first line contains integer *n* (1<=≤<=*n*<=≤<=3·105) — the number of users on the site. The next line contains integer sequence *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=109). | Print a sequence of integers *b*1,<=*b*2,<=...,<=*b**n*. Number *b**i* means that user *i* gets *b**i* of rating as a present. The printed sequence must meet the problem conditions.
If there are multiple optimal solutions, print any of them. | [
"3\n5 1 1\n",
"1\n1000000000\n"
] | [
"5 1 2\n",
"1000000000\n"
] | none | [
{
"input": "3\n5 1 1",
"output": "5 1 2"
},
{
"input": "1\n1000000000",
"output": "1000000000"
},
{
"input": "10\n1 1 1 1 1 1 1 1 1 1",
"output": "1 2 3 4 5 6 7 8 9 10"
},
{
"input": "10\n1 10 1 10 1 1 7 8 6 7",
"output": "1 10 2 11 3 4 7 9 6 8"
},
{
"input": "10\... | 1,000 | 29,593,600 | 0 | 2,583 | |
754 | Lesha and array splitting | [
"constructive algorithms",
"greedy",
"implementation"
] | null | null | One spring day on his way to university Lesha found an array *A*. Lesha likes to split arrays into several parts. This time Lesha decided to split the array *A* into several, possibly one, new arrays so that the sum of elements in each of the new arrays is not zero. One more condition is that if we place the new arrays one after another they will form the old array *A*.
Lesha is tired now so he asked you to split the array. Help Lesha! | The first line contains single integer *n* (1<=≤<=*n*<=≤<=100) — the number of elements in the array *A*.
The next line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (<=-<=103<=≤<=*a**i*<=≤<=103) — the elements of the array *A*. | If it is not possible to split the array *A* and satisfy all the constraints, print single line containing "NO" (without quotes).
Otherwise in the first line print "YES" (without quotes). In the next line print single integer *k* — the number of new arrays. In each of the next *k* lines print two integers *l**i* and *r**i* which denote the subarray *A*[*l**i*... *r**i*] of the initial array *A* being the *i*-th new array. Integers *l**i*, *r**i* should satisfy the following conditions:
- *l*1<==<=1 - *r**k*<==<=*n* - *r**i*<=+<=1<==<=*l**i*<=+<=1 for each 1<=≤<=*i*<=<<=*k*.
If there are multiple answers, print any of them. | [
"3\n1 2 -3\n",
"8\n9 -12 3 4 -4 -10 7 3\n",
"1\n0\n",
"4\n1 2 3 -5\n"
] | [
"YES\n2\n1 2\n3 3\n",
"YES\n2\n1 2\n3 8\n",
"NO\n",
"YES\n4\n1 1\n2 2\n3 3\n4 4\n"
] | none | [
{
"input": "3\n1 2 -3",
"output": "YES\n3\n1 1\n2 2\n3 3"
},
{
"input": "8\n9 -12 3 4 -4 -10 7 3",
"output": "YES\n8\n1 1\n2 2\n3 3\n4 4\n5 5\n6 6\n7 7\n8 8"
},
{
"input": "1\n0",
"output": "NO"
},
{
"input": "4\n1 2 3 -5",
"output": "YES\n4\n1 1\n2 2\n3 3\n4 4"
},
{
... | 46 | 0 | 0 | 2,584 | |
743 | Vladik and fractions | [
"brute force",
"constructive algorithms",
"math",
"number theory"
] | null | null | Vladik and Chloe decided to determine who of them is better at math. Vladik claimed that for any positive integer *n* he can represent fraction as a sum of three distinct positive fractions in form .
Help Vladik with that, i.e for a given *n* find three distinct positive integers *x*, *y* and *z* such that . Because Chloe can't check Vladik's answer if the numbers are large, he asks you to print numbers not exceeding 109.
If there is no such answer, print -1. | The single line contains single integer *n* (1<=≤<=*n*<=≤<=104). | If the answer exists, print 3 distinct numbers *x*, *y* and *z* (1<=≤<=*x*,<=*y*,<=*z*<=≤<=109, *x*<=≠<=*y*, *x*<=≠<=*z*, *y*<=≠<=*z*). Otherwise print -1.
If there are multiple answers, print any of them. | [
"3\n",
"7\n"
] | [
"2 7 42\n",
"7 8 56\n"
] | none | [
{
"input": "3",
"output": "2 7 42"
},
{
"input": "7",
"output": "7 8 56"
},
{
"input": "2",
"output": "2 3 6"
},
{
"input": "5",
"output": "5 6 30"
},
{
"input": "4",
"output": "4 5 20"
},
{
"input": "7",
"output": "7 8 56"
},
{
"input": "8... | 46 | 0 | 0 | 2,589 | |
22 | Second Order Statistics | [
"brute force"
] | A. Second Order Statistics | 2 | 256 | Once Bob needed to find the second order statistics of a sequence of integer numbers. Lets choose each number from the sequence exactly once and sort them. The value on the second position is the second order statistics of the given sequence. In other words it is the smallest element strictly greater than the minimum. Help Bob solve this problem. | The first input line contains integer *n* (1<=≤<=*n*<=≤<=100) — amount of numbers in the sequence. The second line contains *n* space-separated integer numbers — elements of the sequence. These numbers don't exceed 100 in absolute value. | If the given sequence has the second order statistics, output this order statistics, otherwise output NO. | [
"4\n1 2 2 -4\n",
"5\n1 2 3 1 1\n"
] | [
"1\n",
"2\n"
] | none | [
{
"input": "4\n1 2 2 -4",
"output": "1"
},
{
"input": "5\n1 2 3 1 1",
"output": "2"
},
{
"input": "1\n28",
"output": "NO"
},
{
"input": "2\n-28 12",
"output": "12"
},
{
"input": "3\n-83 40 -80",
"output": "-80"
},
{
"input": "8\n93 77 -92 26 21 -48 53 ... | 186 | 0 | 3.9535 | 2,592 |
120 | Spiders | [
"dp",
"greedy",
"trees"
] | null | null | One day mum asked Petya to sort his toys and get rid of some of them. Petya found a whole box of toy spiders. They were quite dear to him and the boy didn't want to throw them away. Petya conjured a cunning plan: he will glue all the spiders together and attach them to the ceiling. Besides, Petya knows that the lower the spiders will hang, the more mum is going to like it and then she won't throw his favourite toys away. Help Petya carry out the plan.
A spider consists of *k* beads tied together by *k*<=-<=1 threads. Each thread connects two different beads, at that any pair of beads that make up a spider is either directly connected by a thread, or is connected via some chain of threads and beads.
Petya may glue spiders together directly gluing their beads. The length of each thread equals 1. The sizes of the beads can be neglected. That's why we can consider that gluing spiders happens by identifying some of the beads (see the picture). Besides, the construction resulting from the gluing process should also represent a spider, that is, it should have the given features.
After Petya glues all spiders together, he measures the length of the resulting toy. The distance between a pair of beads is identified as the total length of the threads that connect these two beads. The length of the resulting construction is the largest distance between all pairs of beads. Petya wants to make the spider whose length is as much as possible.
The picture two shows two spiders from the second sample. We can glue to the bead number 2 of the first spider the bead number 1 of the second spider. The threads in the spiders that form the sequence of threads of maximum lengths are highlighted on the picture. | The first input file line contains one integer *n* (1<=≤<=*n*<=≤<=100) — the number of spiders. Next *n* lines contain the descriptions of each spider: integer *n**i* (2<=≤<=*n**i*<=≤<=100) — the number of beads, then *n**i*<=-<=1 pairs of numbers denoting the numbers of the beads connected by threads. The beads that make up each spider are numbered from 1 to *n**i*. | Print a single number — the length of the required construction. | [
"1\n3 1 2 2 3\n",
"2\n3 1 2 1 3\n4 1 2 2 3 2 4\n",
"2\n5 1 2 2 3 3 4 3 5\n7 3 4 1 2 2 4 4 6 2 7 6 5\n"
] | [
"2\n",
"4\n",
"7\n"
] | none | [
{
"input": "1\n3 1 2 2 3",
"output": "2"
},
{
"input": "2\n3 1 2 1 3\n4 1 2 2 3 2 4",
"output": "4"
},
{
"input": "2\n5 1 2 2 3 3 4 3 5\n7 3 4 1 2 2 4 4 6 2 7 6 5",
"output": "7"
},
{
"input": "3\n3 1 2 2 3\n5 2 5 5 3 3 4 5 1\n9 6 5 5 9 4 8 4 7 2 1 2 6 2 4 6 3",
"output":... | 404 | 3,891,200 | 3 | 2,597 | |
372 | Counting Kangaroos is Fun | [
"binary search",
"greedy",
"sortings",
"two pointers"
] | null | null | There are *n* kangaroos with pockets. Each kangaroo has a size (integer number). A kangaroo can go into another kangaroo's pocket if and only if the size of kangaroo who hold the kangaroo is at least twice as large as the size of kangaroo who is held.
Each kangaroo can hold at most one kangaroo, and the kangaroo who is held by another kangaroo cannot hold any kangaroos.
The kangaroo who is held by another kangaroo cannot be visible from outside. Please, find a plan of holding kangaroos with the minimal number of kangaroos who is visible. | The first line contains a single integer — *n* (1<=≤<=*n*<=≤<=5·105). Each of the next *n* lines contains an integer *s**i* — the size of the *i*-th kangaroo (1<=≤<=*s**i*<=≤<=105). | Output a single integer — the optimal number of visible kangaroos. | [
"8\n2\n5\n7\n6\n9\n8\n4\n2\n",
"8\n9\n1\n6\n2\n6\n5\n8\n3\n"
] | [
"5\n",
"5\n"
] | none | [
{
"input": "8\n2\n5\n7\n6\n9\n8\n4\n2",
"output": "5"
},
{
"input": "8\n9\n1\n6\n2\n6\n5\n8\n3",
"output": "5"
},
{
"input": "12\n3\n99\n24\n46\n75\n63\n57\n55\n10\n62\n34\n52",
"output": "7"
},
{
"input": "12\n55\n75\n1\n98\n63\n64\n9\n39\n82\n18\n47\n9",
"output": "6"
... | 46 | 3,993,600 | -1 | 2,599 | |
284 | Cows and Poker Game | [
"brute force",
"implementation"
] | null | null | There are *n* cows playing poker at a table. For the current betting phase, each player's status is either "ALLIN", "IN", or "FOLDED", and does not change throughout the phase. To increase the suspense, a player whose current status is not "FOLDED" may show his/her hand to the table. However, so as not to affect any betting decisions, he/she may only do so if all other players have a status of either "ALLIN" or "FOLDED". The player's own status may be either "ALLIN" or "IN".
Find the number of cows that can currently show their hands without affecting any betting decisions. | The first line contains a single integer, *n* (2<=≤<=*n*<=≤<=2·105). The second line contains *n* characters, each either "A", "I", or "F". The *i*-th character is "A" if the *i*-th player's status is "ALLIN", "I" if the *i*-th player's status is "IN", or "F" if the *i*-th player's status is "FOLDED". | The first line should contain a single integer denoting the number of players that can currently show their hands. | [
"6\nAFFAAA\n",
"3\nAFI\n"
] | [
"4\n",
"1\n"
] | In the first sample, cows 1, 4, 5, and 6 can show their hands. In the second sample, only cow 3 can show her hand. | [
{
"input": "6\nAFFAAA",
"output": "4"
},
{
"input": "3\nAFI",
"output": "1"
},
{
"input": "3\nFFF",
"output": "0"
},
{
"input": "3\nFIF",
"output": "1"
},
{
"input": "3\nAAA",
"output": "3"
},
{
"input": "3\nIII",
"output": "0"
},
{
"input"... | 154 | 0 | 0 | 2,604 | |
346 | Alice and Bob | [
"games",
"math",
"number theory"
] | null | null | It is so boring in the summer holiday, isn't it? So Alice and Bob have invented a new game to play. The rules are as follows. First, they get a set of *n* distinct integers. And then they take turns to make the following moves. During each move, either Alice or Bob (the player whose turn is the current) can choose two distinct integers *x* and *y* from the set, such that the set doesn't contain their absolute difference |*x*<=-<=*y*|. Then this player adds integer |*x*<=-<=*y*| to the set (so, the size of the set increases by one).
If the current player has no valid move, he (or she) loses the game. The question is who will finally win the game if both players play optimally. Remember that Alice always moves first. | The first line contains an integer *n* (2<=≤<=*n*<=≤<=100) — the initial number of elements in the set. The second line contains *n* distinct space-separated integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=109) — the elements of the set. | Print a single line with the winner's name. If Alice wins print "Alice", otherwise print "Bob" (without quotes). | [
"2\n2 3\n",
"2\n5 3\n",
"3\n5 6 7\n"
] | [
"Alice\n",
"Alice\n",
"Bob\n"
] | Consider the first test sample. Alice moves first, and the only move she can do is to choose 2 and 3, then to add 1 to the set. Next Bob moves, there is no valid move anymore, so the winner is Alice. | [
{
"input": "2\n2 3",
"output": "Alice"
},
{
"input": "2\n5 3",
"output": "Alice"
},
{
"input": "3\n5 6 7",
"output": "Bob"
},
{
"input": "10\n72 96 24 66 6 18 12 30 60 48",
"output": "Bob"
},
{
"input": "10\n78 66 6 60 18 84 36 96 72 48",
"output": "Bob"
},
... | 218 | 6,656,000 | 3 | 2,608 | |
538 | Tourist's Notes | [
"binary search",
"brute force",
"greedy",
"implementation",
"math"
] | null | null | A tourist hiked along the mountain range. The hike lasted for *n* days, during each day the tourist noted height above the sea level. On the *i*-th day height was equal to some integer *h**i*. The tourist pick smooth enough route for his hike, meaning that the between any two consecutive days height changes by at most 1, i.e. for all *i*'s from 1 to *n*<=-<=1 the inequality |*h**i*<=-<=*h**i*<=+<=1|<=≤<=1 holds.
At the end of the route the tourist rafted down a mountain river and some notes in the journal were washed away. Moreover, the numbers in the notes could have been distorted. Now the tourist wonders what could be the maximum height during his hike. Help him restore the maximum possible value of the maximum height throughout the hike or determine that the notes were so much distorted that they do not represent any possible height values that meet limits |*h**i*<=-<=*h**i*<=+<=1|<=≤<=1. | The first line contains two space-separated numbers, *n* and *m* (1<=≤<=*n*<=≤<=108, 1<=≤<=*m*<=≤<=105) — the number of days of the hike and the number of notes left in the journal.
Next *m* lines contain two space-separated integers *d**i* and *h**d**i* (1<=≤<=*d**i*<=≤<=*n*, 0<=≤<=*h**d**i*<=≤<=108) — the number of the day when the *i*-th note was made and height on the *d**i*-th day. It is guaranteed that the notes are given in the chronological order, i.e. for all *i* from 1 to *m*<=-<=1 the following condition holds: *d**i*<=<<=*d**i*<=+<=1. | If the notes aren't contradictory, print a single integer — the maximum possible height value throughout the whole route.
If the notes do not correspond to any set of heights, print a single word 'IMPOSSIBLE' (without the quotes). | [
"8 2\n2 0\n7 0\n",
"8 3\n2 0\n7 0\n8 3\n"
] | [
"2\n",
"IMPOSSIBLE\n"
] | For the first sample, an example of a correct height sequence with a maximum of 2: (0, 0, 1, 2, 1, 1, 0, 1).
In the second sample the inequality between *h*<sub class="lower-index">7</sub> and *h*<sub class="lower-index">8</sub> does not hold, thus the information is inconsistent. | [
{
"input": "8 2\n2 0\n7 0",
"output": "2"
},
{
"input": "8 3\n2 0\n7 0\n8 3",
"output": "IMPOSSIBLE"
},
{
"input": "10 10\n1 0\n2 0\n3 0\n4 0\n5 1\n6 2\n7 3\n8 2\n9 3\n10 4",
"output": "4"
},
{
"input": "50 10\n1 42\n7 36\n16 40\n21 40\n26 39\n30 41\n32 41\n36 40\n44 37\n50 4... | 920 | 9,420,800 | 3 | 2,618 | |
552 | Vanya and Triangles | [
"brute force",
"combinatorics",
"data structures",
"geometry",
"math",
"sortings"
] | null | null | Vanya got bored and he painted *n* distinct points on the plane. After that he connected all the points pairwise and saw that as a result many triangles were formed with vertices in the painted points. He asks you to count the number of the formed triangles with the non-zero area. | The first line contains integer *n* (1<=≤<=*n*<=≤<=2000) — the number of the points painted on the plane.
Next *n* lines contain two integers each *x**i*,<=*y**i* (<=-<=100<=≤<=*x**i*,<=*y**i*<=≤<=100) — the coordinates of the *i*-th point. It is guaranteed that no two given points coincide. | In the first line print an integer — the number of triangles with the non-zero area among the painted points. | [
"4\n0 0\n1 1\n2 0\n2 2\n",
"3\n0 0\n1 1\n2 0\n",
"1\n1 1\n"
] | [
"3\n",
"1\n",
"0\n"
] | Note to the first sample test. There are 3 triangles formed: (0, 0) - (1, 1) - (2, 0); (0, 0) - (2, 2) - (2, 0); (1, 1) - (2, 2) - (2, 0).
Note to the second sample test. There is 1 triangle formed: (0, 0) - (1, 1) - (2, 0).
Note to the third sample test. A single point doesn't form a single triangle. | [
{
"input": "4\n0 0\n1 1\n2 0\n2 2",
"output": "3"
},
{
"input": "3\n0 0\n1 1\n2 0",
"output": "1"
},
{
"input": "1\n1 1",
"output": "0"
},
{
"input": "5\n0 0\n1 1\n2 2\n3 3\n4 4",
"output": "0"
},
{
"input": "5\n0 0\n1 1\n2 3\n3 6\n4 10",
"output": "10"
},
... | 4,000 | 60,211,200 | 0 | 2,629 | |
409 | Magnum Opus | [
"*special"
] | null | null | Salve, mi amice.
Et tu quidem de lapis philosophorum. Barba non facit philosophum. Labor omnia vincit. Non potest creatio ex nihilo. Necesse est partibus.
Rp:
I Aqua Fortis
I Aqua Regia
II Amalgama
VII Minium
IV Vitriol
Misce in vitro et æstus, et nil admirari. Festina lente, et nulla tenaci invia est via.
Fac et spera,
Vale,
Nicolas Flamel | The first line of input contains several space-separated integers *a**i* (0<=≤<=*a**i*<=≤<=100). | Print a single integer. | [
"2 4 6 8 10\n"
] | [
"1\n"
] | none | [
{
"input": "2 4 6 8 10",
"output": "1"
},
{
"input": "50 27 17 31 89",
"output": "4"
},
{
"input": "50 87 29 81 21",
"output": "5"
},
{
"input": "74 21 36 68 80",
"output": "9"
},
{
"input": "75 82 48 95 12",
"output": "3"
},
{
"input": "41 85 14 43 23... | 30 | 0 | 0 | 2,636 | |
608 | Hamming Distance Sum | [
"combinatorics",
"strings"
] | null | null | Genos needs your help. He was asked to solve the following programming problem by Saitama:
The length of some string *s* is denoted |*s*|. The Hamming distance between two strings *s* and *t* of equal length is defined as , where *s**i* is the *i*-th character of *s* and *t**i* is the *i*-th character of *t*. For example, the Hamming distance between string "0011" and string "0110" is |0<=-<=0|<=+<=|0<=-<=1|<=+<=|1<=-<=1|<=+<=|1<=-<=0|<==<=0<=+<=1<=+<=0<=+<=1<==<=2.
Given two binary strings *a* and *b*, find the sum of the Hamming distances between *a* and all contiguous substrings of *b* of length |*a*|. | The first line of the input contains binary string *a* (1<=≤<=|*a*|<=≤<=200<=000).
The second line of the input contains binary string *b* (|*a*|<=≤<=|*b*|<=≤<=200<=000).
Both strings are guaranteed to consist of characters '0' and '1' only. | Print a single integer — the sum of Hamming distances between *a* and all contiguous substrings of *b* of length |*a*|. | [
"01\n00111\n",
"0011\n0110\n"
] | [
"3\n",
"2\n"
] | For the first sample case, there are four contiguous substrings of *b* of length |*a*|: "00", "01", "11", and "11". The distance between "01" and "00" is |0 - 0| + |1 - 0| = 1. The distance between "01" and "01" is |0 - 0| + |1 - 1| = 0. The distance between "01" and "11" is |0 - 1| + |1 - 1| = 1. Last distance counts twice, as there are two occurrences of string "11". The sum of these edit distances is 1 + 0 + 1 + 1 = 3.
The second sample case is described in the statement. | [
{
"input": "01\n00111",
"output": "3"
},
{
"input": "0011\n0110",
"output": "2"
},
{
"input": "0\n0",
"output": "0"
},
{
"input": "1\n0",
"output": "1"
},
{
"input": "0\n1",
"output": "1"
},
{
"input": "1\n1",
"output": "0"
},
{
"input": "1... | 2,000 | 921,600 | 0 | 2,648 | |
76 | Points | [
"implementation",
"math"
] | E. Points | 1 | 256 | You are given *N* points on a plane. Write a program which will find the sum of squares of distances between all pairs of points. | The first line of input contains one integer number *N* (1<=≤<=*N*<=≤<=100<=000) — the number of points. Each of the following *N* lines contain two integer numbers *X* and *Y* (<=-<=10<=000<=≤<=*X*,<=*Y*<=≤<=10<=000) — the coordinates of points. Two or more points may coincide. | The only line of output should contain the required sum of squares of distances between all pairs of points. | [
"4\n1 1\n-1 -1\n1 -1\n-1 1\n"
] | [
"32\n"
] | none | [
{
"input": "4\n1 1\n-1 -1\n1 -1\n-1 1",
"output": "32"
},
{
"input": "1\n6 3",
"output": "0"
},
{
"input": "30\n-7 -12\n-2 5\n14 8\n9 17\n15 -18\n20 6\n20 8\n-13 12\n-4 -20\n-11 -16\n-6 16\n1 -9\n5 -12\n13 -17\n11 5\n8 -9\n-13 5\n19 -13\n-19 -8\n-14 10\n10 3\n-16 -8\n-17 16\n-14 -15\n5 1... | 528 | 0 | 3.736 | 2,655 |
997 | Convert to Ones | [
"brute force",
"greedy",
"implementation",
"math"
] | null | null | You've got a string $a_1, a_2, \dots, a_n$, consisting of zeros and ones.
Let's call a sequence of consecutive elements $a_i, a_{i<=+<=1}, \ldots,<=a_j$ ($1\leq<=i\leq<=j\leq<=n$) a substring of string $a$.
You can apply the following operations any number of times:
- Choose some substring of string $a$ (for example, you can choose entire string) and reverse it, paying $x$ coins for it (for example, «0101101» $\to$ «0111001»); - Choose some substring of string $a$ (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying $y$ coins for it (for example, «0101101» $\to$ «0110001»).
You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.
What is the minimum number of coins you need to spend to get a string consisting only of ones? | The first line of input contains integers $n$, $x$ and $y$ ($1<=\leq<=n<=\leq<=300\,000, 0 \leq x, y \leq 10^9$) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).
The second line contains the string $a$ of length $n$, consisting of zeros and ones. | Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print $0$, if you do not need to perform any operations. | [
"5 1 10\n01000\n",
"5 10 1\n01000\n",
"7 2 3\n1111111\n"
] | [
"11\n",
"2\n",
"0\n"
] | In the first sample, at first you need to reverse substring $[1 \dots 2]$, and then you need to invert substring $[2 \dots 5]$.
Then the string was changed as follows:
«01000» $\to$ «10000» $\to$ «11111».
The total cost of operations is $1 + 10 = 11$.
In the second sample, at first you need to invert substring $[1 \dots 1]$, and then you need to invert substring $[3 \dots 5]$.
Then the string was changed as follows:
«01000» $\to$ «11000» $\to$ «11111».
The overall cost is $1 + 1 = 2$.
In the third example, string already consists only of ones, so the answer is $0$. | [
{
"input": "5 1 10\n01000",
"output": "11"
},
{
"input": "5 10 1\n01000",
"output": "2"
},
{
"input": "7 2 3\n1111111",
"output": "0"
},
{
"input": "1 60754033 959739508\n0",
"output": "959739508"
},
{
"input": "1 431963980 493041212\n1",
"output": "0"
},
... | 124 | 1,433,600 | 3 | 2,661 | |
813 | The Golden Age | [
"brute force",
"math"
] | null | null | Unlucky year in Berland is such a year that its number *n* can be represented as *n*<==<=*x**a*<=+<=*y**b*, where *a* and *b* are non-negative integer numbers.
For example, if *x*<==<=2 and *y*<==<=3 then the years 4 and 17 are unlucky (4<==<=20<=+<=31, 17<==<=23<=+<=32<==<=24<=+<=30) and year 18 isn't unlucky as there is no such representation for it.
Such interval of years that there are no unlucky years in it is called The Golden Age.
You should write a program which will find maximum length of The Golden Age which starts no earlier than the year *l* and ends no later than the year *r*. If all years in the interval [*l*,<=*r*] are unlucky then the answer is 0. | The first line contains four integer numbers *x*, *y*, *l* and *r* (2<=≤<=*x*,<=*y*<=≤<=1018, 1<=≤<=*l*<=≤<=*r*<=≤<=1018). | Print the maximum length of The Golden Age within the interval [*l*,<=*r*].
If all years in the interval [*l*,<=*r*] are unlucky then print 0. | [
"2 3 1 10\n",
"3 5 10 22\n",
"2 3 3 5\n"
] | [
"1\n",
"8\n",
"0\n"
] | In the first example the unlucky years are 2, 3, 4, 5, 7, 9 and 10. So maximum length of The Golden Age is achived in the intervals [1, 1], [6, 6] and [8, 8].
In the second example the longest Golden Age is the interval [15, 22]. | [
{
"input": "2 3 1 10",
"output": "1"
},
{
"input": "3 5 10 22",
"output": "8"
},
{
"input": "2 3 3 5",
"output": "0"
},
{
"input": "2 2 1 10",
"output": "1"
},
{
"input": "2 2 1 1000000",
"output": "213568"
},
{
"input": "2 2 1 1000000000000000000",
... | 62 | 307,200 | 0 | 2,670 | |
876 | Trip For Meal | [
"math"
] | null | null | Winnie-the-Pooh likes honey very much! That is why he decided to visit his friends. Winnie has got three best friends: Rabbit, Owl and Eeyore, each of them lives in his own house. There are winding paths between each pair of houses. The length of a path between Rabbit's and Owl's houses is *a* meters, between Rabbit's and Eeyore's house is *b* meters, between Owl's and Eeyore's house is *c* meters.
For enjoying his life and singing merry songs Winnie-the-Pooh should have a meal *n* times a day. Now he is in the Rabbit's house and has a meal for the first time. Each time when in the friend's house where Winnie is now the supply of honey is about to end, Winnie leaves that house. If Winnie has not had a meal the required amount of times, he comes out from the house and goes to someone else of his two friends. For this he chooses one of two adjacent paths, arrives to the house on the other end and visits his friend. You may assume that when Winnie is eating in one of his friend's house, the supply of honey in other friend's houses recover (most probably, they go to the supply store).
Winnie-the-Pooh does not like physical activity. He wants to have a meal *n* times, traveling minimum possible distance. Help him to find this distance. | First line contains an integer *n* (1<=≤<=*n*<=≤<=100) — number of visits.
Second line contains an integer *a* (1<=≤<=*a*<=≤<=100) — distance between Rabbit's and Owl's houses.
Third line contains an integer *b* (1<=≤<=*b*<=≤<=100) — distance between Rabbit's and Eeyore's houses.
Fourth line contains an integer *c* (1<=≤<=*c*<=≤<=100) — distance between Owl's and Eeyore's houses. | Output one number — minimum distance in meters Winnie must go through to have a meal *n* times. | [
"3\n2\n3\n1\n",
"1\n2\n3\n5\n"
] | [
"3\n",
"0\n"
] | In the first test case the optimal path for Winnie is the following: first have a meal in Rabbit's house, then in Owl's house, then in Eeyore's house. Thus he will pass the distance 2 + 1 = 3.
In the second test case Winnie has a meal in Rabbit's house and that is for him. So he doesn't have to walk anywhere at all. | [
{
"input": "3\n2\n3\n1",
"output": "3"
},
{
"input": "1\n2\n3\n5",
"output": "0"
},
{
"input": "10\n1\n8\n3",
"output": "9"
},
{
"input": "7\n10\n5\n6",
"output": "30"
},
{
"input": "9\n9\n7\n5",
"output": "42"
},
{
"input": "9\n37\n85\n76",
"outpu... | 77 | 0 | 3 | 2,673 | |
465 | Inbox (100500) | [
"implementation"
] | null | null | Over time, Alexey's mail box got littered with too many letters. Some of them are read, while others are unread.
Alexey's mail program can either show a list of all letters or show the content of a single letter. As soon as the program shows the content of an unread letter, it becomes read letter (if the program shows the content of a read letter nothing happens). In one click he can do any of the following operations:
- Move from the list of letters to the content of any single letter.- Return to the list of letters from single letter viewing mode.- In single letter viewing mode, move to the next or to the previous letter in the list. You cannot move from the first letter to the previous one or from the last letter to the next one.
The program cannot delete the letters from the list or rearrange them.
Alexey wants to read all the unread letters and go watch football. Now he is viewing the list of all letters and for each letter he can see if it is read or unread. What minimum number of operations does Alexey need to perform to read all unread letters? | The first line contains a single integer *n* (1<=≤<=*n*<=≤<=1000) — the number of letters in the mailbox.
The second line contains *n* space-separated integers (zeros and ones) — the state of the letter list. The *i*-th number equals either 1, if the *i*-th number is unread, or 0, if the *i*-th letter is read. | Print a single number — the minimum number of operations needed to make all the letters read. | [
"5\n0 1 0 1 0\n",
"5\n1 1 0 0 1\n",
"2\n0 0\n"
] | [
"3\n",
"4\n",
"0\n"
] | In the first sample Alexey needs three operations to cope with the task: open the second letter, move to the third one, move to the fourth one.
In the second sample the action plan: open the first letter, move to the second letter, return to the list, open the fifth letter.
In the third sample all letters are already read. | [
{
"input": "5\n0 1 0 1 0",
"output": "3"
},
{
"input": "5\n1 1 0 0 1",
"output": "4"
},
{
"input": "2\n0 0",
"output": "0"
},
{
"input": "9\n1 0 1 0 1 0 1 0 1",
"output": "9"
},
{
"input": "5\n1 1 1 1 1",
"output": "5"
},
{
"input": "14\n0 0 1 1 1 0 1 ... | 62 | 307,200 | 0 | 2,685 | |
898 | Proper Nutrition | [
"brute force",
"implementation",
"number theory"
] | null | null | Vasya has *n* burles. One bottle of Ber-Cola costs *a* burles and one Bars bar costs *b* burles. He can buy any non-negative integer number of bottles of Ber-Cola and any non-negative integer number of Bars bars.
Find out if it's possible to buy some amount of bottles of Ber-Cola and Bars bars and spend exactly *n* burles.
In other words, you should find two non-negative integers *x* and *y* such that Vasya can buy *x* bottles of Ber-Cola and *y* Bars bars and *x*·*a*<=+<=*y*·*b*<==<=*n* or tell that it's impossible. | First line contains single integer *n* (1<=≤<=*n*<=≤<=10<=000<=000) — amount of money, that Vasya has.
Second line contains single integer *a* (1<=≤<=*a*<=≤<=10<=000<=000) — cost of one bottle of Ber-Cola.
Third line contains single integer *b* (1<=≤<=*b*<=≤<=10<=000<=000) — cost of one Bars bar. | If Vasya can't buy Bars and Ber-Cola in such a way to spend exactly *n* burles print «NO» (without quotes).
Otherwise in first line print «YES» (without quotes). In second line print two non-negative integers *x* and *y* — number of bottles of Ber-Cola and number of Bars bars Vasya should buy in order to spend exactly *n* burles, i.e. *x*·*a*<=+<=*y*·*b*<==<=*n*. If there are multiple answers print any of them.
Any of numbers *x* and *y* can be equal 0. | [
"7\n2\n3\n",
"100\n25\n10\n",
"15\n4\n8\n",
"9960594\n2551\n2557\n"
] | [
"YES\n2 1\n",
"YES\n0 10\n",
"NO\n",
"YES\n1951 1949\n"
] | In first example Vasya can buy two bottles of Ber-Cola and one Bars bar. He will spend exactly 2·2 + 1·3 = 7 burles.
In second example Vasya can spend exactly *n* burles multiple ways:
- buy two bottles of Ber-Cola and five Bars bars; - buy four bottles of Ber-Cola and don't buy Bars bars; - don't buy Ber-Cola and buy 10 Bars bars.
In third example it's impossible to but Ber-Cola and Bars bars in order to spend exactly *n* burles. | [
{
"input": "7\n2\n3",
"output": "YES\n2 1"
},
{
"input": "100\n25\n10",
"output": "YES\n0 10"
},
{
"input": "15\n4\n8",
"output": "NO"
},
{
"input": "9960594\n2551\n2557",
"output": "YES\n1951 1949"
},
{
"input": "10000000\n1\n1",
"output": "YES\n0 10000000"
... | 139 | 1,228,800 | 3 | 2,692 | |
922 | Cave Painting | [
"brute force",
"number theory"
] | null | null | Imp is watching a documentary about cave painting.
Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number *n* by all integers *i* from 1 to *k*. Unfortunately, there are too many integers to analyze for Imp.
Imp wants you to check whether all these remainders are distinct. Formally, he wants to check, if all , 1<=≤<=*i*<=≤<=*k*, are distinct, i. e. there is no such pair (*i*,<=*j*) that:
- 1<=≤<=*i*<=<<=*j*<=≤<=*k*, - , where is the remainder of division *x* by *y*. | The only line contains two integers *n*, *k* (1<=≤<=*n*,<=*k*<=≤<=1018). | Print "Yes", if all the remainders are distinct, and "No" otherwise.
You can print each letter in arbitrary case (lower or upper). | [
"4 4\n",
"5 3\n"
] | [
"No\n",
"Yes\n"
] | In the first sample remainders modulo 1 and 4 coincide. | [
{
"input": "4 4",
"output": "No"
},
{
"input": "5 3",
"output": "Yes"
},
{
"input": "1 1",
"output": "Yes"
},
{
"input": "744 18",
"output": "No"
},
{
"input": "47879 10",
"output": "Yes"
},
{
"input": "1000000000000000000 1000000000000000000",
"ou... | 124 | 512,000 | 0 | 2,693 | |
765 | Neverending competitions | [
"implementation",
"math"
] | null | null | There are literally dozens of snooker competitions held each year, and team Jinotega tries to attend them all (for some reason they prefer name "snookah")! When a competition takes place somewhere far from their hometown, Ivan, Artsem and Konstantin take a flight to the contest and back.
Jinotega's best friends, team Base have found a list of their itinerary receipts with information about departure and arrival airports. Now they wonder, where is Jinotega now: at home or at some competition far away? They know that:
- this list contains all Jinotega's flights in this year (in arbitrary order), - Jinotega has only flown from his hometown to a snooker contest and back, - after each competition Jinotega flies back home (though they may attend a competition in one place several times), - and finally, at the beginning of the year Jinotega was at home.
Please help them to determine Jinotega's location! | In the first line of input there is a single integer *n*: the number of Jinotega's flights (1<=≤<=*n*<=≤<=100). In the second line there is a string of 3 capital Latin letters: the name of Jinotega's home airport. In the next *n* lines there is flight information, one flight per line, in form "XXX->YYY", where "XXX" is the name of departure airport "YYY" is the name of arrival airport. Exactly one of these airports is Jinotega's home airport.
It is guaranteed that flights information is consistent with the knowledge of Jinotega's friends, which is described in the main part of the statement. | If Jinotega is now at home, print "home" (without quotes), otherwise print "contest". | [
"4\nSVO\nSVO->CDG\nLHR->SVO\nSVO->LHR\nCDG->SVO\n",
"3\nSVO\nSVO->HKT\nHKT->SVO\nSVO->RAP\n"
] | [
"home\n",
"contest\n"
] | In the first sample Jinotega might first fly from SVO to CDG and back, and then from SVO to LHR and back, so now they should be at home. In the second sample Jinotega must now be at RAP because a flight from RAP back to SVO is not on the list. | [
{
"input": "4\nSVO\nSVO->CDG\nLHR->SVO\nSVO->LHR\nCDG->SVO",
"output": "home"
},
{
"input": "3\nSVO\nSVO->HKT\nHKT->SVO\nSVO->RAP",
"output": "contest"
},
{
"input": "1\nESJ\nESJ->TSJ",
"output": "contest"
},
{
"input": "2\nXMR\nFAJ->XMR\nXMR->FAJ",
"output": "home"
},
... | 62 | 0 | 3 | 2,695 | |
999 | Reversing Encryption | [
"implementation"
] | null | null | A string $s$ of length $n$ can be encrypted by the following algorithm:
- iterate over all divisors of $n$ in decreasing order (i.e. from $n$ to $1$), - for each divisor $d$, reverse the substring $s[1 \dots d]$ (i.e. the substring which starts at position $1$ and ends at position $d$).
For example, the above algorithm applied to the string $s$="codeforces" leads to the following changes: "codeforces" $\to$ "secrofedoc" $\to$ "orcesfedoc" $\to$ "rocesfedoc" $\to$ "rocesfedoc" (obviously, the last reverse operation doesn't change the string because $d=1$).
You are given the encrypted string $t$. Your task is to decrypt this string, i.e., to find a string $s$ such that the above algorithm results in string $t$. It can be proven that this string $s$ always exists and is unique. | The first line of input consists of a single integer $n$ ($1 \le n \le 100$) — the length of the string $t$. The second line of input consists of the string $t$. The length of $t$ is $n$, and it consists only of lowercase Latin letters. | Print a string $s$ such that the above algorithm results in $t$. | [
"10\nrocesfedoc\n",
"16\nplmaetwoxesisiht\n",
"1\nz\n"
] | [
"codeforces\n",
"thisisexampletwo\n",
"z\n"
] | The first example is described in the problem statement. | [
{
"input": "10\nrocesfedoc",
"output": "codeforces"
},
{
"input": "16\nplmaetwoxesisiht",
"output": "thisisexampletwo"
},
{
"input": "1\nz",
"output": "z"
},
{
"input": "2\nir",
"output": "ri"
},
{
"input": "3\nilj",
"output": "jli"
},
{
"input": "4\nj... | 30 | 0 | 0 | 2,696 | |
46 | T-shirts from Sponsor | [
"implementation"
] | B. T-shirts from Sponsor | 2 | 256 | One day a well-known sponsor of a well-known contest decided to give every participant of the contest a T-shirt as a present. A natural problem occurred: on the one hand, it is not clear how many T-shirts of what sizes should be ordered, and on the other hand, one doesn't want to order too many T-shirts (and we do not exactly paper the walls with the oversupply). After considerable brain racking and some pre-estimating, the sponsor representatives ordered a certain number of T-shirts of sizes S, M, L, XL and XXL. The T-shirts turned out to bring good luck, that's why on the contest day there built up a line of *K* participants willing to get one. Every contestant is characterized by his/her desired T-shirt size (so it happens that for all the participants it is also one of the sizes S, M, L, XL and XXL). The participants come up to get a T-shirt one by one and try to choose the most suitable one, choosing it like this. If there is still a T-shirt of the optimal size left, that he/she takes it without further ado. Otherwise the contestant would prefer to choose a T-shirt with the size as close to the optimal one as possible (the distance between neighboring sizes is considered equal to one). If the variant of choice is not unique, the contestant will take a T-shirt of a bigger size (in case he/she grows more). For example, for a person whose optimal size is L the preference list looks like this: L, XL, M, XXL, S. Using the data on how many T-shirts of every size had been ordered by the organizers, on the size of contestants in the line determine who got a T-shirt of what size. | The first line contains five non-negative integers *N**S*,<=*N**M*,<=*N**L*,<=*N**XL*,<=*N**XXL* not exceeding 1000 which represent the number of T-shirts of the corresponding sizes. The second line contains an integer *K* (1<=≤<=*K*<=≤<=1000) which represents the number of participants. The next *K* lines contain the optimal T-shirt sizes for the contestants. The sizes are given in the order in which the participants stand in the line. It is guaranteed that *N**S*<=+<=*N**M*<=+<=*N**L*<=+<=*N**XL*<=+<=*N**XXL*<=≥<=*K*. | For each contestant, print a line containing the size of the T-shirt he/she got. | [
"1 0 2 0 1\n3\nXL\nXXL\nM\n"
] | [
"XXL\nL\nL\n"
] | none | [
{
"input": "1 0 2 0 1\n3\nXL\nXXL\nM",
"output": "XXL\nL\nL"
},
{
"input": "0 0 0 0 1\n1\nS",
"output": "XXL"
},
{
"input": "1 0 1 0 1\n1\nS",
"output": "S"
},
{
"input": "1 0 0 0 1\n2\nS\nL",
"output": "S\nXXL"
},
{
"input": "1 1 1 1 1\n2\nXL\nM",
"output": "... | 2,000 | 307,200 | 0 | 2,701 |
117 | Elevator | [
"implementation",
"math"
] | null | null | And now the numerous qualifying tournaments for one of the most prestigious Russian contests Russian Codec Cup are over. All *n* participants who have made it to the finals found themselves in a huge *m*-floored 108-star hotel. Of course the first thought to come in a place like this is "How about checking out the elevator?".
The hotel's elevator moves between floors according to one never changing scheme. Initially (at the moment of time 0) the elevator is located on the 1-st floor, then it moves to the 2-nd floor, then — to the 3-rd floor and so on until it reaches the *m*-th floor. After that the elevator moves to floor *m*<=-<=1, then to floor *m*<=-<=2, and so on until it reaches the first floor. This process is repeated infinitely. We know that the elevator has infinite capacity; we also know that on every floor people get on the elevator immediately. Moving between the floors takes a unit of time.
For each of the *n* participant you are given *s**i*, which represents the floor where the *i*-th participant starts, *f**i*, which represents the floor the *i*-th participant wants to reach, and *t**i*, which represents the time when the *i*-th participant starts on the floor *s**i*.
For each participant print the minimum time of his/her arrival to the floor *f**i*.
If the elevator stops on the floor *s**i* at the time *t**i*, then the *i*-th participant can enter the elevator immediately. If the participant starts on the floor *s**i* and that's the floor he wanted to reach initially (*s**i*<==<=*f**i*), then the time of arrival to the floor *f**i* for this participant is considered equal to *t**i*. | The first line contains two space-separated integers *n* and *m* (1<=≤<=*n*<=≤<=105,<=2<=≤<=*m*<=≤<=108).
Next *n* lines contain information about the participants in the form of three space-separated integers *s**i* *f**i* *t**i* (1<=≤<=*s**i*,<=*f**i*<=≤<=*m*,<=0<=≤<=*t**i*<=≤<=108), described in the problem statement. | Print *n* lines each containing one integer — the time of the arrival for each participant to the required floor. | [
"7 4\n2 4 3\n1 2 0\n2 2 0\n1 2 1\n4 3 5\n1 2 2\n4 2 0\n",
"5 5\n1 5 4\n1 3 1\n1 3 4\n3 1 5\n4 2 5\n"
] | [
"9\n1\n0\n7\n10\n7\n5\n",
"12\n10\n10\n8\n7\n"
] | Let's consider the first sample. The first participant starts at floor *s* = 2 by the time equal to *t* = 3. To get to the floor *f* = 4, he has to wait until the time equals 7, that's the time when the elevator will go upwards for the second time. Then the first participant should get on the elevator and go two floors up. In this case the first participant gets to the floor *f* at time equal to 9. The second participant starts at the time *t* = 0 on the floor *s* = 1, enters the elevator immediately, and arrives to the floor *f* = 2. The third participant doesn't wait for the elevator, because he needs to arrive to the same floor where he starts. | [
{
"input": "7 4\n2 4 3\n1 2 0\n2 2 0\n1 2 1\n4 3 5\n1 2 2\n4 2 0",
"output": "9\n1\n0\n7\n10\n7\n5"
},
{
"input": "5 5\n1 5 4\n1 3 1\n1 3 4\n3 1 5\n4 2 5",
"output": "12\n10\n10\n8\n7"
},
{
"input": "5 5\n1 3 4\n4 4 2\n3 2 1\n2 4 0\n1 5 3",
"output": "10\n2\n7\n3\n12"
},
{
"i... | 124 | 0 | 0 | 2,706 | |
628 | Magic Numbers | [
"dp"
] | null | null | Consider the decimal presentation of an integer. Let's call a number d-magic if digit *d* appears in decimal presentation of the number on even positions and nowhere else.
For example, the numbers 1727374, 17, 1 are 7-magic but 77, 7, 123, 34, 71 are not 7-magic. On the other hand the number 7 is 0-magic, 123 is 2-magic, 34 is 4-magic and 71 is 1-magic.
Find the number of d-magic numbers in the segment [*a*,<=*b*] that are multiple of *m*. Because the answer can be very huge you should only find its value modulo 109<=+<=7 (so you should find the remainder after dividing by 109<=+<=7). | The first line contains two integers *m*,<=*d* (1<=≤<=*m*<=≤<=2000, 0<=≤<=*d*<=≤<=9) — the parameters from the problem statement.
The second line contains positive integer *a* in decimal presentation (without leading zeroes).
The third line contains positive integer *b* in decimal presentation (without leading zeroes).
It is guaranteed that *a*<=≤<=*b*, the number of digits in *a* and *b* are the same and don't exceed 2000. | Print the only integer *a* — the remainder after dividing by 109<=+<=7 of the number of d-magic numbers in segment [*a*,<=*b*] that are multiple of *m*. | [
"2 6\n10\n99\n",
"2 0\n1\n9\n",
"19 7\n1000\n9999\n"
] | [
"8\n",
"4\n",
"6\n"
] | The numbers from the answer of the first example are 16, 26, 36, 46, 56, 76, 86 and 96.
The numbers from the answer of the second example are 2, 4, 6 and 8.
The numbers from the answer of the third example are 1767, 2717, 5757, 6707, 8797 and 9747. | [
{
"input": "2 6\n10\n99",
"output": "8"
},
{
"input": "2 0\n1\n9",
"output": "4"
},
{
"input": "19 7\n1000\n9999",
"output": "6"
},
{
"input": "9 4\n33\n52",
"output": "0"
},
{
"input": "10 8\n18\n59",
"output": "0"
},
{
"input": "43 3\n587\n850",
... | 2,000 | 307,200 | 0 | 2,713 | |
14 | Letter | [
"implementation"
] | A. Letter | 1 | 64 | A boy Bob likes to draw. Not long ago he bought a rectangular graph (checked) sheet with *n* rows and *m* columns. Bob shaded some of the squares on the sheet. Having seen his masterpiece, he decided to share it with his elder brother, who lives in Flatland. Now Bob has to send his picture by post, but because of the world economic crisis and high oil prices, he wants to send his creation, but to spend as little money as possible. For each sent square of paper (no matter whether it is shaded or not) Bob has to pay 3.14 burles. Please, help Bob cut out of his masterpiece a rectangle of the minimum cost, that will contain all the shaded squares. The rectangle's sides should be parallel to the sheet's sides. | The first line of the input data contains numbers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=50), *n* — amount of lines, and *m* — amount of columns on Bob's sheet. The following *n* lines contain *m* characters each. Character «.» stands for a non-shaded square on the sheet, and «*» — for a shaded square. It is guaranteed that Bob has shaded at least one square. | Output the required rectangle of the minimum cost. Study the output data in the sample tests to understand the output format better. | [
"6 7\n.......\n..***..\n..*....\n..***..\n..*....\n..***..\n",
"3 3\n***\n*.*\n***\n"
] | [
"***\n*..\n***\n*..\n***\n",
"***\n*.*\n***\n"
] | none | [
{
"input": "6 7\n.......\n..***..\n..*....\n..***..\n..*....\n..***..",
"output": "***\n*..\n***\n*..\n***"
},
{
"input": "3 3\n***\n*.*\n***",
"output": "***\n*.*\n***"
},
{
"input": "1 1\n*",
"output": "*"
},
{
"input": "2 1\n*\n*",
"output": "*\n*"
},
{
"input"... | 154 | 1,331,200 | 3.913082 | 2,720 |
268 | Beautiful Sets of Points | [
"constructive algorithms",
"implementation"
] | null | null | Manao has invented a new mathematical term — a beautiful set of points. He calls a set of points on a plane beautiful if it meets the following conditions:
1. The coordinates of each point in the set are integers. 1. For any two points from the set, the distance between them is a non-integer.
Consider all points (*x*,<=*y*) which satisfy the inequations: 0<=≤<=*x*<=≤<=*n*; 0<=≤<=*y*<=≤<=*m*; *x*<=+<=*y*<=><=0. Choose their subset of maximum size such that it is also a beautiful set of points. | The single line contains two space-separated integers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=100). | In the first line print a single integer — the size *k* of the found beautiful set. In each of the next *k* lines print a pair of space-separated integers — the *x*- and *y*- coordinates, respectively, of a point from the set.
If there are several optimal solutions, you may print any of them. | [
"2 2\n",
"4 3\n"
] | [
"3\n0 1\n1 2\n2 0\n",
"4\n0 3\n2 1\n3 0\n4 2\n"
] | Consider the first sample. The distance between points (0, 1) and (1, 2) equals <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/bfe16f27ebc966df6f10ba356a1547b6e7242dd7.png" style="max-width: 100.0%;max-height: 100.0%;"/>, between (0, 1) and (2, 0) — <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/23d63d8a57cddda72562a512c05111054cd85870.png" style="max-width: 100.0%;max-height: 100.0%;"/>, between (1, 2) and (2, 0) — <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/23d63d8a57cddda72562a512c05111054cd85870.png" style="max-width: 100.0%;max-height: 100.0%;"/>. Thus, these points form a beautiful set. You cannot form a beautiful set with more than three points out of the given points. Note that this is not the only solution. | [
{
"input": "2 2",
"output": "3\n0 1\n1 2\n2 0"
},
{
"input": "4 3",
"output": "4\n0 3\n2 1\n3 0\n4 2"
},
{
"input": "21 21",
"output": "22\n21 0\n20 1\n19 2\n18 3\n17 4\n16 5\n15 6\n14 7\n13 8\n12 9\n11 10\n10 11\n9 12\n8 13\n7 14\n6 15\n5 16\n4 17\n3 18\n2 19\n1 20\n0 21"
},
{
... | 92 | 0 | 0 | 2,741 | |
438 | The Child and Sequence | [
"data structures",
"math"
] | null | null | At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite sequence of Picks.
Fortunately, Picks remembers how to repair the sequence. Initially he should create an integer array *a*[1],<=*a*[2],<=...,<=*a*[*n*]. Then he should perform a sequence of *m* operations. An operation can be one of the following:
1. Print operation *l*,<=*r*. Picks should write down the value of . 1. Modulo operation *l*,<=*r*,<=*x*. Picks should perform assignment *a*[*i*]<==<=*a*[*i*] *mod* *x* for each *i* (*l*<=≤<=*i*<=≤<=*r*). 1. Set operation *k*,<=*x*. Picks should set the value of *a*[*k*] to *x* (in other words perform an assignment *a*[*k*]<==<=*x*).
Can you help Picks to perform the whole sequence of operations? | The first line of input contains two integer: *n*,<=*m* (1<=≤<=*n*,<=*m*<=≤<=105). The second line contains *n* integers, separated by space: *a*[1],<=*a*[2],<=...,<=*a*[*n*] (1<=≤<=*a*[*i*]<=≤<=109) — initial value of array elements.
Each of the next *m* lines begins with a number *type* .
- If *type*<==<=1, there will be two integers more in the line: *l*,<=*r* (1<=≤<=*l*<=≤<=*r*<=≤<=*n*), which correspond the operation 1. - If *type*<==<=2, there will be three integers more in the line: *l*,<=*r*,<=*x* (1<=≤<=*l*<=≤<=*r*<=≤<=*n*; 1<=≤<=*x*<=≤<=109), which correspond the operation 2. - If *type*<==<=3, there will be two integers more in the line: *k*,<=*x* (1<=≤<=*k*<=≤<=*n*; 1<=≤<=*x*<=≤<=109), which correspond the operation 3. | For each operation 1, please print a line containing the answer. Notice that the answer may exceed the 32-bit integer. | [
"5 5\n1 2 3 4 5\n2 3 5 4\n3 3 5\n1 2 5\n2 1 3 3\n1 1 3\n",
"10 10\n6 9 6 7 6 1 10 10 9 5\n1 3 9\n2 7 10 9\n2 5 10 8\n1 4 7\n3 3 7\n2 7 9 9\n1 2 4\n1 6 6\n1 5 9\n3 1 10\n"
] | [
"8\n5\n",
"49\n15\n23\n1\n9\n"
] | Consider the first testcase:
- At first, *a* = {1, 2, 3, 4, 5}. - After operation 1, *a* = {1, 2, 3, 0, 1}. - After operation 2, *a* = {1, 2, 5, 0, 1}. - At operation 3, 2 + 5 + 0 + 1 = 8. - After operation 4, *a* = {1, 2, 2, 0, 1}. <li> At operation 5, 1 + 2 + 2 = 5. <ul> | [
{
"input": "5 5\n1 2 3 4 5\n2 3 5 4\n3 3 5\n1 2 5\n2 1 3 3\n1 1 3",
"output": "8\n5"
},
{
"input": "10 10\n6 9 6 7 6 1 10 10 9 5\n1 3 9\n2 7 10 9\n2 5 10 8\n1 4 7\n3 3 7\n2 7 9 9\n1 2 4\n1 6 6\n1 5 9\n3 1 10",
"output": "49\n15\n23\n1\n9"
},
{
"input": "1 1\n1\n1 1 1",
"output": "1"
... | 46 | 0 | 0 | 2,743 | |
962 | Make a Square | [
"brute force",
"implementation",
"math"
] | null | null | You are given a positive integer $n$, written without leading zeroes (for example, the number 04 is incorrect).
In one operation you can delete any digit of the given integer so that the result remains a positive integer without leading zeros.
Determine the minimum number of operations that you need to consistently apply to the given integer $n$ to make from it the square of some positive integer or report that it is impossible.
An integer $x$ is the square of some positive integer if and only if $x=y^2$ for some positive integer $y$. | The first line contains a single integer $n$ ($1 \le n \le 2 \cdot 10^{9}$). The number is given without leading zeroes. | If it is impossible to make the square of some positive integer from $n$, print -1. In the other case, print the minimal number of operations required to do it. | [
"8314\n",
"625\n",
"333\n"
] | [
"2\n",
"0\n",
"-1\n"
] | In the first example we should delete from $8314$ the digits $3$ and $4$. After that $8314$ become equals to $81$, which is the square of the integer $9$.
In the second example the given $625$ is the square of the integer $25$, so you should not delete anything.
In the third example it is impossible to make the square from $333$, so the answer is -1. | [
{
"input": "8314",
"output": "2"
},
{
"input": "625",
"output": "0"
},
{
"input": "333",
"output": "-1"
},
{
"input": "1881388645",
"output": "6"
},
{
"input": "1059472069",
"output": "3"
},
{
"input": "1354124829",
"output": "4"
},
{
"inpu... | 249 | 7,065,600 | 0 | 2,746 | |
609 | USB Flash Drives | [
"greedy",
"implementation",
"sortings"
] | null | null | Sean is trying to save a large file to a USB flash drive. He has *n* USB flash drives with capacities equal to *a*1,<=*a*2,<=...,<=*a**n* megabytes. The file size is equal to *m* megabytes.
Find the minimum number of USB flash drives needed to write Sean's file, if he can split the file between drives. | The first line contains positive integer *n* (1<=≤<=*n*<=≤<=100) — the number of USB flash drives.
The second line contains positive integer *m* (1<=≤<=*m*<=≤<=105) — the size of Sean's file.
Each of the next *n* lines contains positive integer *a**i* (1<=≤<=*a**i*<=≤<=1000) — the sizes of USB flash drives in megabytes.
It is guaranteed that the answer exists, i. e. the sum of all *a**i* is not less than *m*. | Print the minimum number of USB flash drives to write Sean's file, if he can split the file between drives. | [
"3\n5\n2\n1\n3\n",
"3\n6\n2\n3\n2\n",
"2\n5\n5\n10\n"
] | [
"2\n",
"3\n",
"1\n"
] | In the first example Sean needs only two USB flash drives — the first and the third.
In the second example Sean needs all three USB flash drives.
In the third example Sean needs only one USB flash drive and he can use any available USB flash drive — the first or the second. | [
{
"input": "3\n5\n2\n1\n3",
"output": "2"
},
{
"input": "3\n6\n2\n3\n2",
"output": "3"
},
{
"input": "2\n5\n5\n10",
"output": "1"
},
{
"input": "5\n16\n8\n1\n3\n4\n9",
"output": "2"
},
{
"input": "10\n121\n10\n37\n74\n56\n42\n39\n6\n68\n8\n100",
"output": "2"
... | 109 | 0 | 3 | 2,764 | |
625 | Guest From the Past | [
"implementation",
"math"
] | null | null | Kolya Gerasimov loves kefir very much. He lives in year 1984 and knows all the details of buying this delicious drink. One day, as you probably know, he found himself in year 2084, and buying kefir there is much more complicated.
Kolya is hungry, so he went to the nearest milk shop. In 2084 you may buy kefir in a plastic liter bottle, that costs *a* rubles, or in glass liter bottle, that costs *b* rubles. Also, you may return empty glass bottle and get *c* (*c*<=<<=*b*) rubles back, but you cannot return plastic bottles.
Kolya has *n* rubles and he is really hungry, so he wants to drink as much kefir as possible. There were no plastic bottles in his 1984, so Kolya doesn't know how to act optimally and asks for your help. | First line of the input contains a single integer *n* (1<=≤<=*n*<=≤<=1018) — the number of rubles Kolya has at the beginning.
Then follow three lines containing integers *a*, *b* and *c* (1<=≤<=*a*<=≤<=1018, 1<=≤<=*c*<=<<=*b*<=≤<=1018) — the cost of one plastic liter bottle, the cost of one glass liter bottle and the money one can get back by returning an empty glass bottle, respectively. | Print the only integer — maximum number of liters of kefir, that Kolya can drink. | [
"10\n11\n9\n8\n",
"10\n5\n6\n1\n"
] | [
"2\n",
"2\n"
] | In the first sample, Kolya can buy one glass bottle, then return it and buy one more glass bottle. Thus he will drink 2 liters of kefir.
In the second sample, Kolya can buy two plastic bottle and get two liters of kefir, or he can buy one liter glass bottle, then return it and buy one plastic bottle. In both cases he will drink two liters of kefir. | [
{
"input": "10\n11\n9\n8",
"output": "2"
},
{
"input": "10\n5\n6\n1",
"output": "2"
},
{
"input": "2\n2\n2\n1",
"output": "1"
},
{
"input": "10\n3\n3\n1",
"output": "4"
},
{
"input": "10\n1\n2\n1",
"output": "10"
},
{
"input": "10\n2\n3\n1",
"outpu... | 62 | 0 | 0 | 2,766 | |
707 | Brain's Photos | [
"implementation"
] | null | null | Small, but very brave, mouse Brain was not accepted to summer school of young villains. He was upset and decided to postpone his plans of taking over the world, but to become a photographer instead.
As you may know, the coolest photos are on the film (because you can specify the hashtag #film for such).
Brain took a lot of colourful pictures on colored and black-and-white film. Then he developed and translated it into a digital form. But now, color and black-and-white photos are in one folder, and to sort them, one needs to spend more than one hour!
As soon as Brain is a photographer not programmer now, he asks you to help him determine for a single photo whether it is colored or black-and-white.
Photo can be represented as a matrix sized *n*<=×<=*m*, and each element of the matrix stores a symbol indicating corresponding pixel color. There are only 6 colors:
- 'C' (cyan)- 'M' (magenta)- 'Y' (yellow)- 'W' (white)- 'G' (grey)- 'B' (black)
The photo is considered black-and-white if it has only white, black and grey pixels in it. If there are any of cyan, magenta or yellow pixels in the photo then it is considered colored. | The first line of the input contains two integers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=100) — the number of photo pixel matrix rows and columns respectively.
Then *n* lines describing matrix rows follow. Each of them contains *m* space-separated characters describing colors of pixels in a row. Each character in the line is one of the 'C', 'M', 'Y', 'W', 'G' or 'B'. | Print the "#Black&White" (without quotes), if the photo is black-and-white and "#Color" (without quotes), if it is colored, in the only line. | [
"2 2\nC M\nY Y\n",
"3 2\nW W\nW W\nB B\n",
"1 1\nW\n"
] | [
"#Color",
"#Black&White",
"#Black&White"
] | none | [
{
"input": "2 2\nC M\nY Y",
"output": "#Color"
},
{
"input": "3 2\nW W\nW W\nB B",
"output": "#Black&White"
},
{
"input": "1 1\nW",
"output": "#Black&White"
},
{
"input": "2 3\nW W W\nB G Y",
"output": "#Color"
},
{
"input": "1 1\nW",
"output": "#Black&White"
... | 46 | 0 | 0 | 2,769 | |
285 | Building Permutation | [
"greedy",
"implementation",
"sortings"
] | null | null | Permutation *p* is an ordered set of integers *p*1,<=<=*p*2,<=<=...,<=<=*p**n*, consisting of *n* distinct positive integers, each of them doesn't exceed *n*. We'll denote the *i*-th element of permutation *p* as *p**i*. We'll call number *n* the size or the length of permutation *p*1,<=<=*p*2,<=<=...,<=<=*p**n*.
You have a sequence of integers *a*1,<=*a*2,<=...,<=*a**n*. In one move, you are allowed to decrease or increase any number by one. Count the minimum number of moves, needed to build a permutation from this sequence. | The first line contains integer *n* (1<=≤<=*n*<=≤<=3·105) — the size of the sought permutation. The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (<=-<=109<=≤<=*a**i*<=≤<=109). | Print a single number — the minimum number of moves.
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier. | [
"2\n3 0\n",
"3\n-1 -1 2\n"
] | [
"2\n",
"6\n"
] | In the first sample you should decrease the first number by one and then increase the second number by one. The resulting permutation is (2, 1).
In the second sample you need 6 moves to build permutation (1, 3, 2). | [
{
"input": "2\n3 0",
"output": "2"
},
{
"input": "3\n-1 -1 2",
"output": "6"
},
{
"input": "5\n-3 5 -3 3 3",
"output": "10"
},
{
"input": "10\n9 6 -2 4 1 1 1 9 6 2",
"output": "18"
},
{
"input": "9\n2 0 0 6 5 4 1 9 3",
"output": "15"
},
{
"input": "100... | 436 | 24,473,600 | 3 | 2,771 | |
9 | How many trees? | [
"combinatorics",
"divide and conquer",
"dp"
] | D. How many trees? | 1 | 64 | In one very old text file there was written Great Wisdom. This Wisdom was so Great that nobody could decipher it, even Phong — the oldest among the inhabitants of Mainframe. But still he managed to get some information from there. For example, he managed to learn that User launches games for pleasure — and then terrible Game Cubes fall down on the city, bringing death to those modules, who cannot win the game...
For sure, as guard Bob appeared in Mainframe many modules stopped fearing Game Cubes. Because Bob (as he is alive yet) has never been defeated by User, and he always meddles with Game Cubes, because he is programmed to this.
However, unpleasant situations can happen, when a Game Cube falls down on Lost Angles. Because there lives a nasty virus — Hexadecimal, who is... mmm... very strange. And she likes to play very much. So, willy-nilly, Bob has to play with her first, and then with User.
This time Hexadecimal invented the following entertainment: Bob has to leap over binary search trees with *n* nodes. We should remind you that a binary search tree is a binary tree, each node has a distinct key, for each node the following is true: the left sub-tree of a node contains only nodes with keys less than the node's key, the right sub-tree of a node contains only nodes with keys greater than the node's key. All the keys are different positive integer numbers from 1 to *n*. Each node of such a tree can have up to two children, or have no children at all (in the case when a node is a leaf).
In Hexadecimal's game all the trees are different, but the height of each is not lower than *h*. In this problem «height» stands for the maximum amount of nodes on the way from the root to the remotest leaf, the root node and the leaf itself included. When Bob leaps over a tree, it disappears. Bob gets the access to a Cube, when there are no trees left. He knows how many trees he will have to leap over in the worst case. And you? | The input data contains two space-separated positive integer numbers *n* and *h* (*n*<=≤<=35, *h*<=≤<=*n*). | Output one number — the answer to the problem. It is guaranteed that it does not exceed 9·1018. | [
"3 2\n",
"3 3\n"
] | [
"5",
"4"
] | none | [
{
"input": "3 2",
"output": "5"
},
{
"input": "3 3",
"output": "4"
},
{
"input": "1 1",
"output": "1"
},
{
"input": "2 1",
"output": "2"
},
{
"input": "2 2",
"output": "2"
},
{
"input": "27 11",
"output": "61162698256896"
},
{
"input": "32 ... | 154 | 4,608,000 | 3.888668 | 2,772 |
56 | Bar | [
"implementation"
] | A. Bar | 2 | 256 | According to Berland laws it is only allowed to sell alcohol to people not younger than 18 years. Vasya's job is to monitor the law's enforcement. Tonight he entered a bar and saw *n* people sitting there. For every one of them Vasya happened to determine either the age or the drink the person is having. Vasya can check any person, i.e. learn his age and the drink he is having at the same time. What minimal number of people should Vasya check additionally to make sure that there are no clients under 18 having alcohol drinks?
The list of all alcohol drinks in Berland is: ABSINTH, BEER, BRANDY, CHAMPAGNE, GIN, RUM, SAKE, TEQUILA, VODKA, WHISKEY, WINE | The first line contains an integer *n* (1<=≤<=*n*<=≤<=100) which is the number of the bar's clients. Then follow *n* lines, each describing one visitor. A line either contains his age (an integer from 0 to 1000) or his drink (a string of capital Latin letters from 1 to 100 in length). It is guaranteed that the input data does not contain spaces and other unnecessary separators.
Only the drinks from the list given above should be considered alcohol. | Print a single number which is the number of people Vasya should check to guarantee the law enforcement. | [
"5\n18\nVODKA\nCOKE\n19\n17\n"
] | [
"2\n"
] | In the sample test the second and fifth clients should be checked. | [
{
"input": "5\n18\nVODKA\nCOKE\n19\n17",
"output": "2"
},
{
"input": "2\n2\nGIN",
"output": "2"
},
{
"input": "3\nWHISKEY\n3\nGIN",
"output": "3"
},
{
"input": "4\n813\nIORBQITQXMPTFAEMEQDQIKFGKGOTNKTOSZCBRPXJLUKVLVHJYNRUJXK\nRUM\nRHVRWGODYWWTYZFLFYKCVUFFRTQDINKNWPKFHZBFWBHWI... | 154 | 6,041,600 | -1 | 2,773 |
671 | Recycling Bottles | [
"dp",
"geometry",
"greedy",
"implementation"
] | null | null | It was recycling day in Kekoland. To celebrate it Adil and Bera went to Central Perk where they can take bottles from the ground and put them into a recycling bin.
We can think Central Perk as coordinate plane. There are *n* bottles on the ground, the *i*-th bottle is located at position (*x**i*,<=*y**i*). Both Adil and Bera can carry only one bottle at once each.
For both Adil and Bera the process looks as follows:
1. Choose to stop or to continue to collect bottles. 1. If the choice was to continue then choose some bottle and walk towards it. 1. Pick this bottle and walk to the recycling bin. 1. Go to step 1.
Adil and Bera may move independently. They are allowed to pick bottles simultaneously, all bottles may be picked by any of the two, it's allowed that one of them stays still while the other one continues to pick bottles.
They want to organize the process such that the total distance they walk (the sum of distance walked by Adil and distance walked by Bera) is minimum possible. Of course, at the end all bottles should lie in the recycling bin. | First line of the input contains six integers *a**x*, *a**y*, *b**x*, *b**y*, *t**x* and *t**y* (0<=≤<=*a**x*,<=*a**y*,<=*b**x*,<=*b**y*,<=*t**x*,<=*t**y*<=≤<=109) — initial positions of Adil, Bera and recycling bin respectively.
The second line contains a single integer *n* (1<=≤<=*n*<=≤<=100<=000) — the number of bottles on the ground.
Then follow *n* lines, each of them contains two integers *x**i* and *y**i* (0<=≤<=*x**i*,<=*y**i*<=≤<=109) — position of the *i*-th bottle.
It's guaranteed that positions of Adil, Bera, recycling bin and all bottles are distinct. | Print one real number — the minimum possible total distance Adil and Bera need to walk in order to put all bottles into recycling bin. 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 1 1 2 0 0\n3\n1 1\n2 1\n2 3\n",
"5 0 4 2 2 0\n5\n5 2\n3 0\n5 5\n3 5\n3 3\n"
] | [
"11.084259940083\n",
"33.121375178000\n"
] | Consider the first sample.
Adil will use the following path: <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/37eea809c04afe04f2670475cc5b21df4a90afd1.png" style="max-width: 100.0%;max-height: 100.0%;"/>.
Bera will use the following path: <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/08e917ff238fec015f897516a95529b6d9aed5c7.png" style="max-width: 100.0%;max-height: 100.0%;"/>.
Adil's path will be <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/f58aa00f71a0b723b5de3c8e56ce41dc8afec7f8.png" style="max-width: 100.0%;max-height: 100.0%;"/> units long, while Bera's path will be <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/3615db76a2cdd77d711b73d2894f03bdd52af736.png" style="max-width: 100.0%;max-height: 100.0%;"/> units long. | [
{
"input": "3 1 1 2 0 0\n3\n1 1\n2 1\n2 3",
"output": "11.084259940083"
},
{
"input": "5 0 4 2 2 0\n5\n5 2\n3 0\n5 5\n3 5\n3 3",
"output": "33.121375178000"
},
{
"input": "107 50 116 37 104 118\n12\n16 78\n95 113\n112 84\n5 88\n54 85\n112 80\n19 98\n25 14\n48 76\n95 70\n77 94\n38 32",
... | 93 | 23,142,400 | 0 | 2,788 | |
386 | Second-Price Auction | [
"implementation"
] | null | null | In this problem we consider a special type of an auction, which is called the second-price auction. As in regular auction *n* bidders place a bid which is price a bidder ready to pay. The auction is closed, that is, each bidder secretly informs the organizer of the auction price he is willing to pay. After that, the auction winner is the participant who offered the highest price. However, he pay not the price he offers, but the highest price among the offers of other participants (hence the name: the second-price auction).
Write a program that reads prices offered by bidders and finds the winner and the price he will pay. Consider that all of the offered prices are different. | The first line of the input contains *n* (2<=≤<=*n*<=≤<=1000) — number of bidders. The second line contains *n* distinct integer numbers *p*1,<=*p*2,<=... *p**n*, separated by single spaces (1<=≤<=*p**i*<=≤<=10000), where *p**i* stands for the price offered by the *i*-th bidder. | The single output line should contain two integers: index of the winner and the price he will pay. Indices are 1-based. | [
"2\n5 7\n",
"3\n10 2 8\n",
"6\n3 8 2 9 4 14\n"
] | [
"2 5\n",
"1 8\n",
"6 9\n"
] | none | [
{
"input": "2\n5 7",
"output": "2 5"
},
{
"input": "3\n10 2 8",
"output": "1 8"
},
{
"input": "6\n3 8 2 9 4 14",
"output": "6 9"
},
{
"input": "4\n4707 7586 4221 5842",
"output": "2 5842"
},
{
"input": "5\n3304 4227 4869 6937 6002",
"output": "4 6002"
},
{... | 140 | 20,172,800 | 3 | 2,789 | |
955 | Feed the cat | [
"greedy",
"math"
] | null | null | After waking up at *hh*:*mm*, Andrew realised that he had forgotten to feed his only cat for yet another time (guess why there's only one cat). The cat's current hunger level is *H* points, moreover each minute without food increases his hunger by *D* points.
At any time Andrew can visit the store where tasty buns are sold (you can assume that is doesn't take time to get to the store and back). One such bun costs *C* roubles and decreases hunger by *N* points. Since the demand for bakery drops heavily in the evening, there is a special 20% discount for buns starting from 20:00 (note that the cost might become rational). Of course, buns cannot be sold by parts.
Determine the minimum amount of money Andrew has to spend in order to feed his cat. The cat is considered fed if its hunger level is less than or equal to zero. | The first line contains two integers *hh* and *mm* (00<=≤<=*hh*<=≤<=23,<=00<=≤<=*mm*<=≤<=59) — the time of Andrew's awakening.
The second line contains four integers *H*, *D*, *C* and *N* (1<=≤<=*H*<=≤<=105,<=1<=≤<=*D*,<=*C*,<=*N*<=≤<=102). | Output the minimum amount of money to within three decimal digits. You answer is considered correct, if its absolute or relative error does not exceed 10<=-<=4.
Formally, let your answer be *a*, and the jury's answer be *b*. Your answer is considered correct if . | [
"19 00\n255 1 100 1\n",
"17 41\n1000 6 15 11\n"
] | [
"25200.0000\n",
"1365.0000\n"
] | In the first sample Andrew can visit the store at exactly 20:00. The cat's hunger will be equal to 315, hence it will be necessary to purchase 315 buns. The discount makes the final answer 25200 roubles.
In the second sample it's optimal to visit the store right after he wakes up. Then he'll have to buy 91 bins per 15 roubles each and spend a total of 1365 roubles. | [
{
"input": "19 00\n255 1 100 1",
"output": "25200.0000"
},
{
"input": "17 41\n1000 6 15 11",
"output": "1365.0000"
},
{
"input": "16 34\n61066 14 50 59",
"output": "43360.0000"
},
{
"input": "18 18\n23331 86 87 41",
"output": "49590.0000"
},
{
"input": "10 48\n684... | 78 | 7,372,800 | 3 | 2,795 | |
867 | Between the Offices | [
"implementation"
] | null | null | As you may know, MemSQL has American offices in both San Francisco and Seattle. Being a manager in the company, you travel a lot between the two cities, always by plane.
You prefer flying from Seattle to San Francisco than in the other direction, because it's warmer in San Francisco. You are so busy that you don't remember the number of flights you have made in either direction. However, for each of the last *n* days you know whether you were in San Francisco office or in Seattle office. You always fly at nights, so you never were at both offices on the same day. Given this information, determine if you flew more times from Seattle to San Francisco during the last *n* days, or not. | The first line of input contains single integer *n* (2<=≤<=*n*<=≤<=100) — the number of days.
The second line contains a string of length *n* consisting of only capital 'S' and 'F' letters. If the *i*-th letter is 'S', then you were in Seattle office on that day. Otherwise you were in San Francisco. The days are given in chronological order, i.e. today is the last day in this sequence. | Print "YES" if you flew more times from Seattle to San Francisco, and "NO" otherwise.
You can print each letter in any case (upper or lower). | [
"4\nFSSF\n",
"2\nSF\n",
"10\nFFFFFFFFFF\n",
"10\nSSFFSFFSFF\n"
] | [
"NO\n",
"YES\n",
"NO\n",
"YES\n"
] | In the first example you were initially at San Francisco, then flew to Seattle, were there for two days and returned to San Francisco. You made one flight in each direction, so the answer is "NO".
In the second example you just flew from Seattle to San Francisco, so the answer is "YES".
In the third example you stayed the whole period in San Francisco, so the answer is "NO".
In the fourth example if you replace 'S' with ones, and 'F' with zeros, you'll get the first few digits of π in binary representation. Not very useful information though. | [
{
"input": "4\nFSSF",
"output": "NO"
},
{
"input": "2\nSF",
"output": "YES"
},
{
"input": "10\nFFFFFFFFFF",
"output": "NO"
},
{
"input": "10\nSSFFSFFSFF",
"output": "YES"
},
{
"input": "20\nSFSFFFFSSFFFFSSSSFSS",
"output": "NO"
},
{
"input": "20\nSSFFF... | 108 | 0 | 3 | 2,796 | |
257 | Sockets | [
"greedy",
"implementation",
"sortings"
] | null | null | Vasya has got many devices that work on electricity. He's got *n* supply-line filters to plug the devices, the *i*-th supply-line filter has *a**i* sockets.
Overall Vasya has got *m* devices and *k* electrical sockets in his flat, he can plug the devices or supply-line filters directly. Of course, he can plug the supply-line filter to any other supply-line filter. The device (or the supply-line filter) is considered plugged to electricity if it is either plugged to one of *k* electrical sockets, or if it is plugged to some supply-line filter that is in turn plugged to electricity.
What minimum number of supply-line filters from the given set will Vasya need to plug all the devices he has to electricity? Note that all devices and supply-line filters take one socket for plugging and that he can use one socket to plug either one device or one supply-line filter. | The first line contains three integers *n*, *m*, *k* (1<=≤<=*n*,<=*m*,<=*k*<=≤<=50) — the number of supply-line filters, the number of devices and the number of sockets that he can plug to directly, correspondingly. The second line contains *n* space-separated integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=50) — number *a**i* stands for the number of sockets on the *i*-th supply-line filter. | Print a single number — the minimum number of supply-line filters that is needed to plug all the devices to electricity. If it is impossible to plug all the devices even using all the supply-line filters, print -1. | [
"3 5 3\n3 1 2\n",
"4 7 2\n3 3 2 4\n",
"5 5 1\n1 3 1 2 1\n"
] | [
"1\n",
"2\n",
"-1\n"
] | In the first test case he can plug the first supply-line filter directly to electricity. After he plug it, he get 5 (3 on the supply-line filter and 2 remaining sockets for direct plugging) available sockets to plug. Thus, one filter is enough to plug 5 devices.
One of the optimal ways in the second test sample is to plug the second supply-line filter directly and plug the fourth supply-line filter to one of the sockets in the second supply-line filter. Thus, he gets exactly 7 sockets, available to plug: one to plug to the electricity directly, 2 on the second supply-line filter, 4 on the fourth supply-line filter. There's no way he can plug 7 devices if he use one supply-line filter. | [
{
"input": "3 5 3\n3 1 2",
"output": "1"
},
{
"input": "4 7 2\n3 3 2 4",
"output": "2"
},
{
"input": "5 5 1\n1 3 1 2 1",
"output": "-1"
},
{
"input": "4 5 8\n3 2 4 3",
"output": "0"
},
{
"input": "5 10 1\n4 3 4 2 4",
"output": "3"
},
{
"input": "7 13 2... | 92 | 0 | 0 | 2,802 | |
275 | Convex Shape | [
"constructive algorithms",
"implementation"
] | null | null | Consider an *n*<=×<=*m* grid. Initially all the cells of the grid are colored white. Lenny has painted some of the cells (at least one) black. We call a painted grid convex if one can walk from any black cell to any another black cell using a path of side-adjacent black cells changing his direction at most once during the path. In the figure below, the left grid is convex while the right one is not convex, because there exist two cells which need more than one time to change direction in their path.
You're given a painted grid in the input. Tell Lenny if the grid is convex or not. | The first line of the input contains two integers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=50) — the size of the grid. Each of the next *n* lines contains *m* characters "B" or "W". Character "B" denotes a black cell of the grid and "W" denotes a white cell of the grid.
It's guaranteed that the grid has at least one black cell. | On the only line of the output print "YES" if the grid is convex, otherwise print "NO". Do not print quotes. | [
"3 4\nWWBW\nBWWW\nWWWB\n",
"3 1\nB\nB\nW\n"
] | [
"NO\n",
"YES\n"
] | none | [
{
"input": "3 4\nWWBW\nBWWW\nWWWB",
"output": "NO"
},
{
"input": "3 1\nB\nB\nW",
"output": "YES"
},
{
"input": "1 1\nB",
"output": "YES"
},
{
"input": "1 2\nBB",
"output": "YES"
},
{
"input": "2 1\nB\nB",
"output": "YES"
},
{
"input": "1 2\nBW",
"o... | 280 | 7,680,000 | -1 | 2,805 | |
690 | The Wall (easy) | [] | null | null | "The zombies are lurking outside. Waiting. Moaning. And when they come..."
"When they come?"
"I hope the Wall is high enough."
Zombie attacks have hit the Wall, our line of defense in the North. Its protection is failing, and cracks are showing. In places, gaps have appeared, splitting the wall into multiple segments. We call on you for help. Go forth and explore the wall! Report how many disconnected segments there are.
The wall is a two-dimensional structure made of bricks. Each brick is one unit wide and one unit high. Bricks are stacked on top of each other to form columns that are up to *R* bricks high. Each brick is placed either on the ground or directly on top of another brick. Consecutive non-empty columns form a wall segment. The entire wall, all the segments and empty columns in-between, is *C* columns wide. | The first line of the input consists of two space-separated integers *R* and *C*, 1<=≤<=*R*,<=*C*<=≤<=100. The next *R* lines provide a description of the columns as follows:
- each of the *R* lines contains a string of length *C*, - the *c*-th character of line *r* is B if there is a brick in column *c* and row *R*<=-<=*r*<=+<=1, and . otherwise. | The number of wall segments in the input configuration. | [
"3 7\n.......\n.......\n.BB.B..\n",
"4 5\n..B..\n..B..\nB.B.B\nBBB.B\n",
"4 6\n..B...\nB.B.BB\nBBB.BB\nBBBBBB\n",
"1 1\nB\n",
"10 7\n.......\n.......\n.......\n.......\n.......\n.......\n.......\n.......\n...B...\nB.BB.B.\n",
"8 8\n........\n........\n........\n........\n.B......\n.B.....B\n.B.....B\n.BB.... | [
"2\n",
"2\n",
"1\n",
"1\n",
"3\n",
"2\n"
] | In the first sample case, the 2nd and 3rd columns define the first wall segment, and the 5th column defines the second. | [
{
"input": "3 7\n.......\n.......\n.BB.B..",
"output": "2"
},
{
"input": "4 5\n..B..\n..B..\nB.B.B\nBBB.B",
"output": "2"
},
{
"input": "4 6\n..B...\nB.B.BB\nBBB.BB\nBBBBBB",
"output": "1"
},
{
"input": "1 1\nB",
"output": "1"
},
{
"input": "10 7\n.......\n.......... | 62 | 0 | 3 | 2,810 | |
485 | Factory | [
"implementation",
"math",
"matrices"
] | null | null | One industrial factory is reforming working plan. The director suggested to set a mythical detail production norm. If at the beginning of the day there were *x* details in the factory storage, then by the end of the day the factory has to produce (remainder after dividing *x* by *m*) more details. Unfortunately, no customer has ever bought any mythical detail, so all the details produced stay on the factory.
The board of directors are worried that the production by the given plan may eventually stop (that means that there will be а moment when the current number of details on the factory is divisible by *m*).
Given the number of details *a* on the first day and number *m* check if the production stops at some moment. | The first line contains two integers *a* and *m* (1<=≤<=*a*,<=*m*<=≤<=105). | Print "Yes" (without quotes) if the production will eventually stop, otherwise print "No". | [
"1 5\n",
"3 6\n"
] | [
"No\n",
"Yes\n"
] | none | [
{
"input": "1 5",
"output": "No"
},
{
"input": "3 6",
"output": "Yes"
},
{
"input": "1 8",
"output": "Yes"
},
{
"input": "2 3",
"output": "No"
},
{
"input": "3 24",
"output": "Yes"
},
{
"input": "1 1",
"output": "Yes"
},
{
"input": "100000 ... | 46 | 0 | 0 | 2,811 | |
334 | Eight Point Sets | [
"sortings"
] | null | null | Gerald is very particular to eight point sets. He thinks that any decent eight point set must consist of all pairwise intersections of three distinct integer vertical straight lines and three distinct integer horizontal straight lines, except for the average of these nine points. In other words, there must be three integers *x*1,<=*x*2,<=*x*3 and three more integers *y*1,<=*y*2,<=*y*3, such that *x*1<=<<=*x*2<=<<=*x*3, *y*1<=<<=*y*2<=<<=*y*3 and the eight point set consists of all points (*x**i*,<=*y**j*) (1<=≤<=*i*,<=*j*<=≤<=3), except for point (*x*2,<=*y*2).
You have a set of eight points. Find out if Gerald can use this set? | The input consists of eight lines, the *i*-th line contains two space-separated integers *x**i* and *y**i* (0<=≤<=*x**i*,<=*y**i*<=≤<=106). You do not have any other conditions for these points. | In a single line print word "respectable", if the given set of points corresponds to Gerald's decency rules, and "ugly" otherwise. | [
"0 0\n0 1\n0 2\n1 0\n1 2\n2 0\n2 1\n2 2\n",
"0 0\n1 0\n2 0\n3 0\n4 0\n5 0\n6 0\n7 0\n",
"1 1\n1 2\n1 3\n2 1\n2 2\n2 3\n3 1\n3 2\n"
] | [
"respectable\n",
"ugly\n",
"ugly\n"
] | none | [
{
"input": "0 0\n0 1\n0 2\n1 0\n1 2\n2 0\n2 1\n2 2",
"output": "respectable"
},
{
"input": "0 0\n1 0\n2 0\n3 0\n4 0\n5 0\n6 0\n7 0",
"output": "ugly"
},
{
"input": "1 1\n1 2\n1 3\n2 1\n2 2\n2 3\n3 1\n3 2",
"output": "ugly"
},
{
"input": "0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0... | 216 | 307,200 | 3 | 2,812 | |
788 | Functions again | [
"dp",
"two pointers"
] | null | null | Something happened in Uzhlyandia again... There are riots on the streets... Famous Uzhlyandian superheroes Shean the Sheep and Stas the Giraffe were called in order to save the situation. Upon the arriving, they found that citizens are worried about maximum values of the Main Uzhlyandian Function *f*, which is defined as follows:
In the above formula, 1<=≤<=*l*<=<<=*r*<=≤<=*n* must hold, where *n* is the size of the Main Uzhlyandian Array *a*, and |*x*| means absolute value of *x*. But the heroes skipped their math lessons in school, so they asked you for help. Help them calculate the maximum value of *f* among all possible values of *l* and *r* for the given array *a*. | The first line contains single integer *n* (2<=≤<=*n*<=≤<=105) — the size of the array *a*.
The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (-109<=≤<=*a**i*<=≤<=109) — the array elements. | Print the only integer — the maximum value of *f*. | [
"5\n1 4 2 3 1\n",
"4\n1 5 4 7\n"
] | [
"3",
"6"
] | In the first sample case, the optimal value of *f* is reached on intervals [1, 2] and [2, 5].
In the second case maximal value of *f* is reachable only on the whole array. | [
{
"input": "5\n1 4 2 3 1",
"output": "3"
},
{
"input": "4\n1 5 4 7",
"output": "6"
},
{
"input": "8\n16 14 12 10 8 100 50 0",
"output": "92"
},
{
"input": "2\n1 1",
"output": "0"
},
{
"input": "50\n-5 -9 0 44 -10 37 34 -49 11 -22 -26 44 8 -13 23 -46 34 12 -24 2 -4... | 31 | 4,608,000 | -1 | 2,813 | |
883 | Lost in Transliteration | [
"implementation"
] | null | null | There are some ambiguities when one writes Berland names with the letters of the Latin alphabet.
For example, the Berland sound u can be written in the Latin alphabet as "u", and can be written as "oo". For this reason, two words "ulyana" and "oolyana" denote the same name.
The second ambiguity is about the Berland sound h: one can use both "h" and "kh" to write it. For example, the words "mihail" and "mikhail" denote the same name.
There are *n* users registered on the Polycarp's website. Each of them indicated a name represented by the Latin letters. How many distinct names are there among them, if two ambiguities described above are taken into account?
Formally, we assume that two words denote the same name, if using the replacements "u" "oo" and "h" "kh", you can make the words equal. One can make replacements in both directions, in any of the two words an arbitrary number of times. A letter that resulted from the previous replacement can participate in the next replacements.
For example, the following pairs of words denote the same name:
- "koouper" and "kuooper". Making the replacements described above, you can make both words to be equal: "koouper" "kuuper" and "kuooper" "kuuper". - "khun" and "kkkhoon". With the replacements described above you can make both words to be equal: "khun" "khoon" and "kkkhoon" "kkhoon" "khoon".
For a given list of words, find the minimal number of groups where the words in each group denote the same name. | The first line contains integer number *n* (2<=≤<=*n*<=≤<=400) — number of the words in the list.
The following *n* lines contain words, one word per line. Each word consists of only lowercase Latin letters. The length of each word is between 1 and 20 letters inclusive. | Print the minimal number of groups where the words in each group denote the same name. | [
"10\nmihail\noolyana\nkooooper\nhoon\nulyana\nkoouper\nmikhail\nkhun\nkuooper\nkkkhoon\n",
"9\nhariton\nhkariton\nbuoi\nkkkhariton\nboooi\nbui\nkhariton\nboui\nboi\n",
"2\nalex\nalex\n"
] | [
"4\n",
"5\n",
"1\n"
] | There are four groups of words in the first example. Words in each group denote same name:
1. "mihail", "mikhail" 1. "oolyana", "ulyana" 1. "kooooper", "koouper" 1. "hoon", "khun", "kkkhoon"
There are five groups of words in the second example. Words in each group denote same name:
1. "hariton", "kkkhariton", "khariton" 1. "hkariton" 1. "buoi", "boooi", "boui" 1. "bui" 1. "boi"
In the third example the words are equal, so they denote the same name. | [
{
"input": "10\nmihail\noolyana\nkooooper\nhoon\nulyana\nkoouper\nmikhail\nkhun\nkuooper\nkkkhoon",
"output": "4"
},
{
"input": "9\nhariton\nhkariton\nbuoi\nkkkhariton\nboooi\nbui\nkhariton\nboui\nboi",
"output": "5"
},
{
"input": "2\nalex\nalex",
"output": "1"
},
{
"input": ... | 77 | 23,040,000 | 0 | 2,814 | |
390 | Inna and Alarm Clock | [
"implementation"
] | null | null | Inna loves sleeping very much, so she needs *n* alarm clocks in total to wake up. Let's suppose that Inna's room is a 100<=×<=100 square with the lower left corner at point (0,<=0) and with the upper right corner at point (100,<=100). Then the alarm clocks are points with integer coordinates in this square.
The morning has come. All *n* alarm clocks in Inna's room are ringing, so Inna wants to turn them off. For that Inna has come up with an amusing game:
- First Inna chooses a type of segments that she will use throughout the game. The segments can be either vertical or horizontal. - Then Inna makes multiple moves. In a single move, Inna can paint a segment of any length on the plane, she chooses its type at the beginning of the game (either vertical or horizontal), then all alarm clocks that are on this segment switch off. The game ends when all the alarm clocks are switched off.
Inna is very sleepy, so she wants to get through the alarm clocks as soon as possible. Help her, find the minimum number of moves in the game that she needs to turn off all the alarm clocks! | The first line of the input contains integer *n* (1<=≤<=*n*<=≤<=105) — the number of the alarm clocks. The next *n* lines describe the clocks: the *i*-th line contains two integers *x**i*, *y**i* — the coordinates of the *i*-th alarm clock (0<=≤<=*x**i*,<=*y**i*<=≤<=100).
Note that a single point in the room can contain any number of alarm clocks and the alarm clocks can lie on the sides of the square that represents the room. | In a single line print a single integer — the minimum number of segments Inna will have to draw if she acts optimally. | [
"4\n0 0\n0 1\n0 2\n1 0\n",
"4\n0 0\n0 1\n1 0\n1 1\n",
"4\n1 1\n1 2\n2 3\n3 3\n"
] | [
"2\n",
"2\n",
"3\n"
] | In the first sample, Inna first chooses type "vertical segments", and then she makes segments with ends at : (0, 0), (0, 2); and, for example, (1, 0), (1, 1). If she paints horizontal segments, she will need at least 3 segments.
In the third sample it is important to note that Inna doesn't have the right to change the type of the segments during the game. That's why she will need 3 horizontal or 3 vertical segments to end the game. | [
{
"input": "4\n0 0\n0 1\n0 2\n1 0",
"output": "2"
},
{
"input": "4\n0 0\n0 1\n1 0\n1 1",
"output": "2"
},
{
"input": "4\n1 1\n1 2\n2 3\n3 3",
"output": "3"
},
{
"input": "1\n0 0",
"output": "1"
},
{
"input": "42\n28 87\n26 16\n59 90\n47 61\n28 83\n36 30\n67 10\n6 ... | 764 | 9,216,000 | 3 | 2,836 | |
651 | Beautiful Paintings | [
"greedy",
"sortings"
] | null | null | There are *n* pictures delivered for the new exhibition. The *i*-th painting has beauty *a**i*. We know that a visitor becomes happy every time he passes from a painting to a more beautiful one.
We are allowed to arranged pictures in any order. What is the maximum possible number of times the visitor may become happy while passing all pictures from first to last? In other words, we are allowed to rearrange elements of *a* in any order. What is the maximum possible number of indices *i* (1<=≤<=*i*<=≤<=*n*<=-<=1), such that *a**i*<=+<=1<=><=*a**i*. | The first line of the input contains integer *n* (1<=≤<=*n*<=≤<=1000) — the number of painting.
The second line contains the sequence *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=1000), where *a**i* means the beauty of the *i*-th painting. | Print one integer — the maximum possible number of neighbouring pairs, such that *a**i*<=+<=1<=><=*a**i*, after the optimal rearrangement. | [
"5\n20 30 10 50 40\n",
"4\n200 100 100 200\n"
] | [
"4\n",
"2\n"
] | In the first sample, the optimal order is: 10, 20, 30, 40, 50.
In the second sample, the optimal order is: 100, 200, 100, 200. | [
{
"input": "5\n20 30 10 50 40",
"output": "4"
},
{
"input": "4\n200 100 100 200",
"output": "2"
},
{
"input": "10\n2 2 2 2 2 2 2 2 2 2",
"output": "0"
},
{
"input": "1\n1000",
"output": "0"
},
{
"input": "2\n444 333",
"output": "1"
},
{
"input": "100\n... | 140 | 20,172,800 | 0 | 2,859 | |
457 | Golden System | [
"math",
"meet-in-the-middle"
] | null | null | Piegirl got bored with binary, decimal and other integer based counting systems. Recently she discovered some interesting properties about number , in particular that *q*2<==<=*q*<=+<=1, and she thinks it would make a good base for her new unique system. She called it "golden system". In golden system the number is a non-empty string containing 0's and 1's as digits. The decimal value of expression *a*0*a*1...*a**n* equals to .
Soon Piegirl found out that this system doesn't have same properties that integer base systems do and some operations can not be performed on it. She wasn't able to come up with a fast way of comparing two numbers. She is asking for your help.
Given two numbers written in golden system notation, determine which of them has larger decimal value. | Input consists of two lines — one for each number. Each line contains non-empty string consisting of '0' and '1' characters. The length of each string does not exceed 100000. | Print ">" if the first number is larger, "<" if it is smaller and "=" if they are equal. | [
"1000\n111\n",
"00100\n11\n",
"110\n101\n"
] | [
"<\n",
"=\n",
">\n"
] | In the first example first number equals to <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/9c955eec678d6e7dcdc7c94fb203e922d2ad19ad.png" style="max-width: 100.0%;max-height: 100.0%;"/>, while second number is approximately 1.618033988<sup class="upper-index">2</sup> + 1.618033988 + 1 ≈ 5.236, which is clearly a bigger number.
In the second example numbers are equal. Each of them is ≈ 2.618. | [
{
"input": "1000\n111",
"output": "<"
},
{
"input": "00100\n11",
"output": "="
},
{
"input": "110\n101",
"output": ">"
},
{
"input": "0\n0",
"output": "="
},
{
"input": "1\n10",
"output": "<"
},
{
"input": "11\n10",
"output": ">"
},
{
"inpu... | 46 | 0 | -1 | 2,869 | |
831 | Keyboard Layouts | [
"implementation",
"strings"
] | null | null | There are two popular keyboard layouts in Berland, they differ only in letters positions. All the other keys are the same. In Berland they use alphabet with 26 letters which coincides with English alphabet.
You are given two strings consisting of 26 distinct letters each: all keys of the first and the second layouts in the same order.
You are also given some text consisting of small and capital English letters and digits. It is known that it was typed in the first layout, but the writer intended to type it in the second layout. Print the text if the same keys were pressed in the second layout.
Since all keys but letters are the same in both layouts, the capitalization of the letters should remain the same, as well as all other characters. | The first line contains a string of length 26 consisting of distinct lowercase English letters. This is the first layout.
The second line contains a string of length 26 consisting of distinct lowercase English letters. This is the second layout.
The third line contains a non-empty string *s* consisting of lowercase and uppercase English letters and digits. This is the text typed in the first layout. The length of *s* does not exceed 1000. | Print the text if the same keys were pressed in the second layout. | [
"qwertyuiopasdfghjklzxcvbnm\nveamhjsgqocnrbfxdtwkylupzi\nTwccpQZAvb2017\n",
"mnbvcxzlkjhgfdsapoiuytrewq\nasdfghjklqwertyuiopzxcvbnm\n7abaCABAABAcaba7\n"
] | [
"HelloVKCup2017\n",
"7uduGUDUUDUgudu7\n"
] | none | [
{
"input": "qwertyuiopasdfghjklzxcvbnm\nveamhjsgqocnrbfxdtwkylupzi\nTwccpQZAvb2017",
"output": "HelloVKCup2017"
},
{
"input": "mnbvcxzlkjhgfdsapoiuytrewq\nasdfghjklqwertyuiopzxcvbnm\n7abaCABAABAcaba7",
"output": "7uduGUDUUDUgudu7"
},
{
"input": "ayvguplhjsoiencbkxdrfwmqtz\nkhzvtbspcndier... | 124 | 1,433,600 | 3 | 2,870 | |
610 | Vika and Squares | [
"constructive algorithms",
"implementation"
] | null | null | Vika has *n* jars with paints of distinct colors. All the jars are numbered from 1 to *n* and the *i*-th jar contains *a**i* liters of paint of color *i*.
Vika also has an infinitely long rectangular piece of paper of width 1, consisting of squares of size 1<=×<=1. Squares are numbered 1, 2, 3 and so on. Vika decided that she will start painting squares one by one from left to right, starting from the square number 1 and some arbitrary color. If the square was painted in color *x*, then the next square will be painted in color *x*<=+<=1. In case of *x*<==<=*n*, next square is painted in color 1. If there is no more paint of the color Vika wants to use now, then she stops.
Square is always painted in only one color, and it takes exactly 1 liter of paint. Your task is to calculate the maximum number of squares that might be painted, if Vika chooses right color to paint the first square. | The first line of the input contains a single integer *n* (1<=≤<=*n*<=≤<=200<=000) — the number of jars with colors Vika has.
The second line of the input contains a sequence of integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=109), where *a**i* is equal to the number of liters of paint in the *i*-th jar, i.e. the number of liters of color *i* that Vika has. | The only line of the output should contain a single integer — the maximum number of squares that Vika can paint if she follows the rules described above. | [
"5\n2 4 2 3 3\n",
"3\n5 5 5\n",
"6\n10 10 10 1 10 10\n"
] | [
"12\n",
"15\n",
"11\n"
] | In the first sample the best strategy is to start painting using color 4. Then the squares will be painted in the following colors (from left to right): 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5.
In the second sample Vika can start to paint using any color.
In the third sample Vika should start painting using color number 5. | [
{
"input": "5\n2 4 2 3 3",
"output": "12"
},
{
"input": "3\n5 5 5",
"output": "15"
},
{
"input": "6\n10 10 10 1 10 10",
"output": "11"
},
{
"input": "1\n167959139",
"output": "167959139"
},
{
"input": "10\n896619242 805194919 844752453 848347723 816995848 85681361... | 171 | 16,588,800 | 0 | 2,873 | |
602 | Two Bases | [
"brute force",
"implementation"
] | null | null | After seeing the "ALL YOUR BASE ARE BELONG TO US" meme for the first time, numbers *X* and *Y* realised that they have different bases, which complicated their relations.
You're given a number *X* represented in base *b**x* and a number *Y* represented in base *b**y*. Compare those two numbers. | The first line of the input contains two space-separated integers *n* and *b**x* (1<=≤<=*n*<=≤<=10, 2<=≤<=*b**x*<=≤<=40), where *n* is the number of digits in the *b**x*-based representation of *X*.
The second line contains *n* space-separated integers *x*1,<=*x*2,<=...,<=*x**n* (0<=≤<=*x**i*<=<<=*b**x*) — the digits of *X*. They are given in the order from the most significant digit to the least significant one.
The following two lines describe *Y* in the same way: the third line contains two space-separated integers *m* and *b**y* (1<=≤<=*m*<=≤<=10, 2<=≤<=*b**y*<=≤<=40, *b**x*<=≠<=*b**y*), where *m* is the number of digits in the *b**y*-based representation of *Y*, and the fourth line contains *m* space-separated integers *y*1,<=*y*2,<=...,<=*y**m* (0<=≤<=*y**i*<=<<=*b**y*) — the digits of *Y*.
There will be no leading zeroes. Both *X* and *Y* will be positive. All digits of both numbers are given in the standard decimal numeral system. | Output a single character (quotes for clarity):
- '<' if *X*<=<<=*Y* - '>' if *X*<=><=*Y* - '=' if *X*<==<=*Y* | [
"6 2\n1 0 1 1 1 1\n2 10\n4 7\n",
"3 3\n1 0 2\n2 5\n2 4\n",
"7 16\n15 15 4 0 0 7 10\n7 9\n4 8 0 3 1 5 0\n"
] | [
"=\n",
"<\n",
">\n"
] | In the first sample, *X* = 101111<sub class="lower-index">2</sub> = 47<sub class="lower-index">10</sub> = *Y*.
In the second sample, *X* = 102<sub class="lower-index">3</sub> = 21<sub class="lower-index">5</sub> and *Y* = 24<sub class="lower-index">5</sub> = 112<sub class="lower-index">3</sub>, thus *X* < *Y*.
In the third sample, <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/603a342b0ae3e56fed542d1c50c0a5ff6ce2cbaa.png" style="max-width: 100.0%;max-height: 100.0%;"/> and *Y* = 4803150<sub class="lower-index">9</sub>. We may notice that *X* starts with much larger digits and *b*<sub class="lower-index">*x*</sub> is much larger than *b*<sub class="lower-index">*y*</sub>, so *X* is clearly larger than *Y*. | [
{
"input": "6 2\n1 0 1 1 1 1\n2 10\n4 7",
"output": "="
},
{
"input": "3 3\n1 0 2\n2 5\n2 4",
"output": "<"
},
{
"input": "7 16\n15 15 4 0 0 7 10\n7 9\n4 8 0 3 1 5 0",
"output": ">"
},
{
"input": "2 2\n1 0\n2 3\n1 0",
"output": "<"
},
{
"input": "2 2\n1 0\n1 3\n1"... | 62 | 0 | 3 | 2,878 | |
847 | Packmen | [
"binary search",
"dp"
] | null | null | A game field is a strip of 1<=×<=*n* square cells. In some cells there are Packmen, in some cells — asterisks, other cells are empty.
Packman can move to neighboring cell in 1 time unit. If there is an asterisk in the target cell then Packman eats it. Packman doesn't spend any time to eat an asterisk.
In the initial moment of time all Packmen begin to move. Each Packman can change direction of its move unlimited number of times, but it is not allowed to go beyond the boundaries of the game field. Packmen do not interfere with the movement of other packmen; in one cell there can be any number of packmen moving in any directions.
Your task is to determine minimum possible time after which Packmen can eat all the asterisks. | The first line contains a single integer *n* (2<=≤<=*n*<=≤<=105) — the length of the game field.
The second line contains the description of the game field consisting of *n* symbols. If there is symbol '.' in position *i* — the cell *i* is empty. If there is symbol '*' in position *i* — in the cell *i* contains an asterisk. If there is symbol 'P' in position *i* — Packman is in the cell *i*.
It is guaranteed that on the game field there is at least one Packman and at least one asterisk. | Print minimum possible time after which Packmen can eat all asterisks. | [
"7\n*..P*P*\n",
"10\n.**PP.*P.*\n"
] | [
"3\n",
"2\n"
] | In the first example Packman in position 4 will move to the left and will eat asterisk in position 1. He will spend 3 time units on it. During the same 3 time units Packman in position 6 will eat both of neighboring with it asterisks. For example, it can move to the left and eat asterisk in position 5 (in 1 time unit) and then move from the position 5 to the right and eat asterisk in the position 7 (in 2 time units). So in 3 time units Packmen will eat all asterisks on the game field.
In the second example Packman in the position 4 will move to the left and after 2 time units will eat asterisks in positions 3 and 2. Packmen in positions 5 and 8 will move to the right and in 2 time units will eat asterisks in positions 7 and 10, respectively. So 2 time units is enough for Packmen to eat all asterisks on the game field. | [
{
"input": "7\n*..P*P*",
"output": "3"
},
{
"input": "10\n.**PP.*P.*",
"output": "2"
},
{
"input": "19\n**P.*..*..P..*.*P**",
"output": "7"
},
{
"input": "12\nP**.*P*P*P**",
"output": "3"
},
{
"input": "58\n..P.P*.P*.P...PPP...P*....*..*.**......*P.*P.....**P...*P... | 15 | 0 | -1 | 2,880 | |
0 | none | [
"none"
] | null | null | Andrew and Eugene are playing a game. Initially, Andrew has string *s*, consisting of digits. Eugene sends Andrew multiple queries of type "*d**i*<=→<=*t**i*", that means "replace all digits *d**i* in string *s* with substrings equal to *t**i*". For example, if *s*<==<=123123, then query "2<=→<=00" transforms *s* to 10031003, and query "3<=→<=" ("replace 3 by an empty string") transforms it to *s*<==<=1212. After all the queries Eugene asks Andrew to find the remainder after division of number with decimal representation equal to *s* by 1000000007 (109<=+<=7). When you represent *s* as a decimal number, please ignore the leading zeroes; also if *s* is an empty string, then it's assumed that the number equals to zero.
Andrew got tired of processing Eugene's requests manually and he asked you to write a program for that. Help him! | The first line contains string *s* (1<=≤<=|*s*|<=≤<=105), consisting of digits — the string before processing all the requests.
The second line contains a single integer *n* (0<=≤<=*n*<=≤<=105) — the number of queries.
The next *n* lines contain the descriptions of the queries. The *i*-th query is described by string "*d**i*->*t**i*", where *d**i* is exactly one digit (from 0 to 9), *t**i* is a string consisting of digits (*t**i* can be an empty string). The sum of lengths of *t**i* for all queries doesn't exceed 105. The queries are written in the order in which they need to be performed. | Print a single integer — remainder of division of the resulting number by 1000000007 (109<=+<=7). | [
"123123\n1\n2->00\n",
"123123\n1\n3->\n",
"222\n2\n2->0\n0->7\n",
"1000000008\n0\n"
] | [
"10031003\n",
"1212\n",
"777\n",
"1\n"
] | Note that the leading zeroes are not removed from string *s* after the replacement (you can see it in the third sample). | [
{
"input": "123123\n1\n2->00",
"output": "10031003"
},
{
"input": "123123\n1\n3->",
"output": "1212"
},
{
"input": "222\n2\n2->0\n0->7",
"output": "777"
},
{
"input": "1000000008\n0",
"output": "1"
},
{
"input": "100\n5\n1->301\n0->013\n1->013\n0->103\n0->103",
... | 311 | 120,320,000 | -1 | 2,883 | |
954 | String Typing | [
"implementation",
"strings"
] | null | null | You are given a string *s* consisting of *n* lowercase Latin letters. You have to type this string using your keyboard.
Initially, you have an empty string. Until you type the whole string, you may perform the following operation:
- add a character to the end of the string.
Besides, at most once you may perform one additional operation: copy the string and append it to itself.
For example, if you have to type string abcabca, you can type it in 7 operations if you type all the characters one by one. However, you can type it in 5 operations if you type the string abc first and then copy it and type the last character.
If you have to type string aaaaaaaaa, the best option is to type 4 characters one by one, then copy the string, and then type the remaining character.
Print the minimum number of operations you need to type the given string. | The first line of the input containing only one integer number *n* (1<=≤<=*n*<=≤<=100) — the length of the string you have to type. The second line containing the string *s* consisting of *n* lowercase Latin letters. | Print one integer number — the minimum number of operations you need to type the given string. | [
"7\nabcabca\n",
"8\nabcdefgh\n"
] | [
"5\n",
"8\n"
] | The first test described in the problem statement.
In the second test you can only type all the characters one by one. | [
{
"input": "7\nabcabca",
"output": "5"
},
{
"input": "8\nabcdefgh",
"output": "8"
},
{
"input": "100\nmhnzadklojbuumkrxjayikjhwuxihgkinllackcavhjpxlydxcmhnzadklojbuumkrxjayikjhwuxihgkinllackcavhjpxlydxc",
"output": "51"
},
{
"input": "99\ntrolnjmzxxrfxuexcqpjvefndwuxwsukxwmjh... | 77 | 0 | 3 | 2,895 | |
41 | Email address | [
"expression parsing",
"implementation"
] | C. Email address | 2 | 256 | Sometimes one has to spell email addresses over the phone. Then one usually pronounces a dot as dot, an at sign as at. As a result, we get something like vasyaatgmaildotcom. Your task is to transform it into a proper email address ([[email protected]](/cdn-cgi/l/email-protection)).
It is known that a proper email address contains only such symbols as . @ and lower-case Latin letters, doesn't start with and doesn't end with a dot. Also, a proper email address doesn't start with and doesn't end with an at sign. Moreover, an email address contains exactly one such symbol as @, yet may contain any number (possible, zero) of dots.
You have to carry out a series of replacements so that the length of the result was as short as possible and it was a proper email address. If the lengths are equal, you should print the lexicographically minimal result.
Overall, two variants of replacement are possible: dot can be replaced by a dot, at can be replaced by an at. | The first line contains the email address description. It is guaranteed that that is a proper email address with all the dots replaced by dot an the at signs replaced by at. The line is not empty and its length does not exceed 100 symbols. | Print the shortest email address, from which the given line could be made by the described above replacements. If there are several solutions to that problem, print the lexicographically minimal one (the lexicographical comparison of the lines are implemented with an operator < in modern programming languages).
In the ASCII table the symbols go in this order: . @ ab...z | [
"vasyaatgmaildotcom\n",
"dotdotdotatdotdotat\n",
"aatt\n"
] | [
"[email protected]\n",
"[email protected]\n",
"a@t\n"
] | none | [
{
"input": "vasyaatgmaildotcom",
"output": "vasya@gmail.com"
},
{
"input": "dotdotdotatdotdotat",
"output": "dot..@..at"
},
{
"input": "aatt",
"output": "a@t"
},
{
"input": "zdotdotatdotz",
"output": "z..@.z"
},
{
"input": "dotdotdotdotatdotatatatdotdotdot",
"... | 92 | 0 | 0 | 2,899 |
583 | Asphalting Roads | [
"implementation"
] | null | null | City X consists of *n* vertical and *n* horizontal infinite roads, forming *n*<=×<=*n* intersections. Roads (both vertical and horizontal) are numbered from 1 to *n*, and the intersections are indicated by the numbers of the roads that form them.
Sand roads have long been recognized out of date, so the decision was made to asphalt them. To do this, a team of workers was hired and a schedule of work was made, according to which the intersections should be asphalted.
Road repairs are planned for *n*2 days. On the *i*-th day of the team arrives at the *i*-th intersection in the list and if none of the two roads that form the intersection were already asphalted they asphalt both roads. Otherwise, the team leaves the intersection, without doing anything with the roads.
According to the schedule of road works tell in which days at least one road will be asphalted. | The first line contains integer *n* (1<=≤<=*n*<=≤<=50) — the number of vertical and horizontal roads in the city.
Next *n*2 lines contain the order of intersections in the schedule. The *i*-th of them contains two numbers *h**i*,<=*v**i* (1<=≤<=*h**i*,<=*v**i*<=≤<=*n*), separated by a space, and meaning that the intersection that goes *i*-th in the timetable is at the intersection of the *h**i*-th horizontal and *v**i*-th vertical roads. It is guaranteed that all the intersections in the timetable are distinct. | In the single line print the numbers of the days when road works will be in progress in ascending order. The days are numbered starting from 1. | [
"2\n1 1\n1 2\n2 1\n2 2\n",
"1\n1 1\n"
] | [
"1 4 \n",
"1 \n"
] | In the sample the brigade acts like that:
1. On the first day the brigade comes to the intersection of the 1-st horizontal and the 1-st vertical road. As none of them has been asphalted, the workers asphalt the 1-st vertical and the 1-st horizontal road; 1. On the second day the brigade of the workers comes to the intersection of the 1-st horizontal and the 2-nd vertical road. The 2-nd vertical road hasn't been asphalted, but as the 1-st horizontal road has been asphalted on the first day, the workers leave and do not asphalt anything; 1. On the third day the brigade of the workers come to the intersection of the 2-nd horizontal and the 1-st vertical road. The 2-nd horizontal road hasn't been asphalted but as the 1-st vertical road has been asphalted on the first day, the workers leave and do not asphalt anything; 1. On the fourth day the brigade come to the intersection formed by the intersection of the 2-nd horizontal and 2-nd vertical road. As none of them has been asphalted, the workers asphalt the 2-nd vertical and the 2-nd horizontal road. | [
{
"input": "2\n1 1\n1 2\n2 1\n2 2",
"output": "1 4 "
},
{
"input": "1\n1 1",
"output": "1 "
},
{
"input": "2\n1 1\n2 2\n1 2\n2 1",
"output": "1 2 "
},
{
"input": "2\n1 2\n2 2\n2 1\n1 1",
"output": "1 3 "
},
{
"input": "3\n2 2\n1 2\n3 2\n3 3\n1 1\n2 3\n1 3\n3 1\n2 ... | 202 | 23,142,400 | 3 | 2,900 | |
958 | Guard Duty (easy) | [
"brute force",
"geometry",
"greedy",
"math"
] | null | null | The Rebel fleet is afraid that the Empire might want to strike back again. Princess Heidi needs to know if it is possible to assign *R* Rebel spaceships to guard *B* bases so that every base has exactly one guardian and each spaceship has exactly one assigned base (in other words, the assignment is a perfect matching). Since she knows how reckless her pilots are, she wants to be sure that any two (straight) paths – from a base to its assigned spaceship – do not intersect in the galaxy plane (that is, in 2D), and so there is no risk of collision. | The first line contains two space-separated integers *R*,<=*B*(1<=≤<=*R*,<=*B*<=≤<=10). For 1<=≤<=*i*<=≤<=*R*, the *i*<=+<=1-th line contains two space-separated integers *x**i* and *y**i* (|*x**i*|,<=|*y**i*|<=≤<=10000) denoting the coordinates of the *i*-th Rebel spaceship. The following *B* lines have the same format, denoting the position of bases. It is guaranteed that no two points coincide and that no three points are on the same line. | If it is possible to connect Rebel spaceships and bases so as satisfy the constraint, output Yes, otherwise output No (without quote). | [
"3 3\n0 0\n2 0\n3 1\n-2 1\n0 3\n2 2\n",
"2 1\n1 0\n2 2\n3 1\n"
] | [
"Yes\n",
"No\n"
] | For the first example, one possible way is to connect the Rebels and bases in order.
For the second example, there is no perfect matching between Rebels and bases. | [
{
"input": "3 3\n0 0\n2 0\n3 1\n-2 1\n0 3\n2 2",
"output": "Yes"
},
{
"input": "2 1\n1 0\n2 2\n3 1",
"output": "No"
},
{
"input": "1 1\n3686 4362\n-7485 5112",
"output": "Yes"
},
{
"input": "1 2\n1152 -7324\n-5137 -35\n-6045 -5271",
"output": "No"
},
{
"input": "1... | 233 | 26,009,600 | 3 | 2,901 | |
614 | Link/Cut Tree | [
"brute force",
"implementation"
] | null | null | Programmer Rostislav got seriously interested in the Link/Cut Tree data structure, which is based on Splay trees. Specifically, he is now studying the *expose* procedure.
Unfortunately, Rostislav is unable to understand the definition of this procedure, so he decided to ask programmer Serezha to help him. Serezha agreed to help if Rostislav solves a simple task (and if he doesn't, then why would he need Splay trees anyway?)
Given integers *l*, *r* and *k*, you need to print all powers of number *k* within range from *l* to *r* inclusive. However, Rostislav doesn't want to spent time doing this, as he got interested in playing a network game called Agar with Gleb. Help him! | The first line of the input contains three space-separated integers *l*, *r* and *k* (1<=≤<=*l*<=≤<=*r*<=≤<=1018, 2<=≤<=*k*<=≤<=109). | Print all powers of number *k*, that lie within range from *l* to *r* in the increasing order. If there are no such numbers, print "-1" (without the quotes). | [
"1 10 2\n",
"2 4 5\n"
] | [
"1 2 4 8 ",
"-1"
] | Note to the first sample: numbers 2<sup class="upper-index">0</sup> = 1, 2<sup class="upper-index">1</sup> = 2, 2<sup class="upper-index">2</sup> = 4, 2<sup class="upper-index">3</sup> = 8 lie within the specified range. The number 2<sup class="upper-index">4</sup> = 16 is greater then 10, thus it shouldn't be printed. | [
{
"input": "1 10 2",
"output": "1 2 4 8 "
},
{
"input": "2 4 5",
"output": "-1"
},
{
"input": "18102 43332383920 28554",
"output": "28554 815330916 "
},
{
"input": "19562 31702689720 17701",
"output": "313325401 "
},
{
"input": "11729 55221128400 313",
"output... | 140 | 0 | 3 | 2,911 | |
779 | Dishonest Sellers | [
"constructive algorithms",
"greedy",
"sortings"
] | null | null | Igor found out discounts in a shop and decided to buy *n* items. Discounts at the store will last for a week and Igor knows about each item that its price now is *a**i*, and after a week of discounts its price will be *b**i*.
Not all of sellers are honest, so now some products could be more expensive than after a week of discounts.
Igor decided that buy at least *k* of items now, but wait with the rest of the week in order to save money as much as possible. Your task is to determine the minimum money that Igor can spend to buy all *n* items. | In the first line there are two positive integer numbers *n* and *k* (1<=≤<=*n*<=≤<=2·105, 0<=≤<=*k*<=≤<=*n*) — total number of items to buy and minimal number of items Igor wants to by right now.
The second line contains sequence of integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=104) — prices of items during discounts (i.e. right now).
The third line contains sequence of integers *b*1,<=*b*2,<=...,<=*b**n* (1<=≤<=*b**i*<=≤<=104) — prices of items after discounts (i.e. after a week). | Print the minimal amount of money Igor will spend to buy all *n* items. Remember, he should buy at least *k* items right now. | [
"3 1\n5 4 6\n3 1 5\n",
"5 3\n3 4 7 10 3\n4 5 5 12 5\n"
] | [
"10\n",
"25\n"
] | In the first example Igor should buy item 3 paying 6. But items 1 and 2 he should buy after a week. He will pay 3 and 1 for them. So in total he will pay 6 + 3 + 1 = 10.
In the second example Igor should buy right now items 1, 2, 4 and 5, paying for them 3, 4, 10 and 3, respectively. Item 3 he should buy after a week of discounts, he will pay 5 for it. In total he will spend 3 + 4 + 10 + 3 + 5 = 25. | [
{
"input": "3 1\n5 4 6\n3 1 5",
"output": "10"
},
{
"input": "5 3\n3 4 7 10 3\n4 5 5 12 5",
"output": "25"
},
{
"input": "1 0\n9\n8",
"output": "8"
},
{
"input": "2 0\n4 10\n1 2",
"output": "3"
},
{
"input": "4 2\n19 5 17 13\n3 18 8 10",
"output": "29"
},
... | 405 | 21,401,600 | 0 | 2,919 | |
0 | none | [
"none"
] | null | null | A new innovative ticketing systems for public transport is introduced in Bytesburg. Now there is a single travel card for all transport. To make a trip a passenger scan his card and then he is charged according to the fare.
The fare is constructed in the following manner. There are three types of tickets:
1. a ticket for one trip costs 20 byteland rubles, 1. a ticket for 90 minutes costs 50 byteland rubles, 1. a ticket for one day (1440 minutes) costs 120 byteland rubles.
Note that a ticket for *x* minutes activated at time *t* can be used for trips started in time range from *t* to *t*<=+<=*x*<=-<=1, inclusive. Assume that all trips take exactly one minute.
To simplify the choice for the passenger, the system automatically chooses the optimal tickets. After each trip starts, the system analyses all the previous trips and the current trip and chooses a set of tickets for these trips with a minimum total cost. Let the minimum total cost of tickets to cover all trips from the first to the current is *a*, and the total sum charged before is *b*. Then the system charges the passenger the sum *a*<=-<=*b*.
You have to write a program that, for given trips made by a passenger, calculates the sum the passenger is charged after each trip. | The first line of input contains integer number *n* (1<=≤<=*n*<=≤<=105) — the number of trips made by passenger.
Each of the following *n* lines contains the time of trip *t**i* (0<=≤<=*t**i*<=≤<=109), measured in minutes from the time of starting the system. All *t**i* are different, given in ascending order, i. e. *t**i*<=+<=1<=><=*t**i* holds for all 1<=≤<=*i*<=<<=*n*. | Output *n* integers. For each trip, print the sum the passenger is charged after it. | [
"3\n10\n20\n30\n",
"10\n13\n45\n46\n60\n103\n115\n126\n150\n256\n516\n"
] | [
"20\n20\n10\n",
"20\n20\n10\n0\n20\n0\n0\n20\n20\n10\n"
] | In the first example, the system works as follows: for the first and second trips it is cheaper to pay for two one-trip tickets, so each time 20 rubles is charged, after the third trip the system understands that it would be cheaper to buy a ticket for 90 minutes. This ticket costs 50 rubles, and the passenger had already paid 40 rubles, so it is necessary to charge 10 rubles only. | [
{
"input": "3\n10\n20\n30",
"output": "20\n20\n10"
},
{
"input": "10\n13\n45\n46\n60\n103\n115\n126\n150\n256\n516",
"output": "20\n20\n10\n0\n20\n0\n0\n20\n20\n10"
},
{
"input": "7\n100\n138\n279\n308\n396\n412\n821",
"output": "20\n20\n20\n20\n20\n20\n0"
},
{
"input": "8\n0... | 358 | 14,950,400 | 3 | 2,921 | |
209 | Multicolored Marbles | [
"dp",
"math"
] | null | null | Polycarpus plays with red and blue marbles. He put *n* marbles from the left to the right in a row. As it turned out, the marbles form a zebroid.
A non-empty sequence of red and blue marbles is a zebroid, if the colors of the marbles in this sequence alternate. For example, sequences (red; blue; red) and (blue) are zebroids and sequence (red; red) is not a zebroid.
Now Polycarpus wonders, how many ways there are to pick a zebroid subsequence from this sequence. Help him solve the problem, find the number of ways modulo 1000000007 (109<=+<=7). | The first line contains a single integer *n* (1<=≤<=*n*<=≤<=106) — the number of marbles in Polycarpus's sequence. | Print a single number — the answer to the problem modulo 1000000007 (109<=+<=7). | [
"3\n",
"4\n"
] | [
"6\n",
"11\n"
] | Let's consider the first test sample. Let's assume that Polycarpus initially had sequence (red; blue; red), so there are six ways to pick a zebroid:
- pick the first marble; - pick the second marble; - pick the third marble; - pick the first and second marbles; - pick the second and third marbles; - pick the first, second and third marbles.
It can be proven that if Polycarpus picks (blue; red; blue) as the initial sequence, the number of ways won't change. | [
{
"input": "3",
"output": "6"
},
{
"input": "4",
"output": "11"
},
{
"input": "1",
"output": "1"
},
{
"input": "2",
"output": "3"
},
{
"input": "5",
"output": "19"
},
{
"input": "6",
"output": "32"
},
{
"input": "7",
"output": "53"
},... | 904 | 100,044,800 | 3 | 2,925 | |
772 | Volatile Kite | [
"geometry"
] | null | null | You are given a convex polygon *P* with *n* distinct vertices *p*1,<=*p*2,<=...,<=*p**n*. Vertex *p**i* has coordinates (*x**i*,<=*y**i*) in the 2D plane. These vertices are listed in clockwise order.
You can choose a real number *D* and move each vertex of the polygon a distance of at most *D* from their original positions.
Find the maximum value of *D* such that no matter how you move the vertices, the polygon does not intersect itself and stays convex. | The first line has one integer *n* (4<=≤<=*n*<=≤<=1<=000) — the number of vertices.
The next *n* lines contain the coordinates of the vertices. Line *i* contains two integers *x**i* and *y**i* (<=-<=109<=≤<=*x**i*,<=*y**i*<=≤<=109) — the coordinates of the *i*-th vertex. These points are guaranteed to be given in clockwise order, and will form a strictly convex polygon (in particular, no three consecutive points lie on the same straight line). | Print one real number *D*, which is the maximum real number such that no matter how you move the vertices, the polygon stays convex.
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 . | [
"4\n0 0\n0 1\n1 1\n1 0\n",
"6\n5 0\n10 0\n12 -4\n10 -8\n5 -8\n3 -4\n"
] | [
"0.3535533906\n",
"1.0000000000\n"
] | Here is a picture of the first sample
<img class="tex-graphics" src="https://espresso.codeforces.com/f83aa076d2f437f9bb785cae769c3ae310eff351.png" style="max-width: 100.0%;max-height: 100.0%;"/>
Here is an example of making the polygon non-convex.
<img class="tex-graphics" src="https://espresso.codeforces.com/fbadb81630251ca642bd4ddf9088876ade761630.png" style="max-width: 100.0%;max-height: 100.0%;"/>
This is not an optimal solution, since the maximum distance we moved one point is ≈ 0.4242640687, whereas we can make it non-convex by only moving each point a distance of at most ≈ 0.3535533906. | [
{
"input": "4\n0 0\n0 1\n1 1\n1 0",
"output": "0.3535533906"
},
{
"input": "6\n5 0\n10 0\n12 -4\n10 -8\n5 -8\n3 -4",
"output": "1.0000000000"
},
{
"input": "19\n449447997 711296339\n530233434 692216537\n535464528 613140435\n535533467 100893188\n530498867 -265063956\n519107979 -271820709\... | 62 | 5,632,000 | 3 | 2,927 |
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