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Solve the programming task below in a Python markdown code block. A few years ago Sajjad left his school and register to another one due to security reasons. Now he wishes to find Amir, one of his schoolmates and good friends. There are n schools numerated from 1 to n. One can travel between each pair of them, to do so, he needs to buy a ticket. The ticker between schools i and j costs $(i + j) \operatorname{mod}(n + 1)$ and can be used multiple times. Help Sajjad to find the minimum cost he needs to pay for tickets to visit all schools. He can start and finish in any school. -----Input----- The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of schools. -----Output----- Print single integer: the minimum cost of tickets needed to visit all schools. -----Examples----- Input 2 Output 0 Input 10 Output 4 -----Note----- In the first example we can buy a ticket between the schools that costs $(1 + 2) \operatorname{mod}(2 + 1) = 0$. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. With one die of 6 sides we will have six different possible results:``` 1, 2, 3, 4, 5, 6``` . With 2 dice of six sides, we will have 36 different possible results: ``` (1,1),(1,2),(2,1),(1,3),(3,1),(1,4),(4,1),(1,5), (5,1), (1,6),(6,1),(2,2),(2,3),(3,2),(2,4),(4,2), (2,5),(5,2)(2,6),(6,2),(3,3),(3,4),(4,3),(3,5),(5,3), (3,6),(6,3),(4,4),(4,5),(5,4),(4,6),(6,4),(5,5), (5,6),(6,5),(6,6) ``` So, with 2 dice of 6 sides we get 36 different events. ``` ([6,6] ---> 36) ``` But with 2 different dice we can get for this case, the same number of events. One die of ```4 sides``` and another of ```9 sides``` will produce the exact amount of events. ``` ([4,9] ---> 36) ``` We say that the dice set ```[4,9]``` is equivalent to ```[6,6]``` because both produce the same number of events. Also we may have an amount of three dice producing the same amount of events. It will be for: ``` [4,3,3] ---> 36 ``` (One die of 4 sides and two dice of 3 sides each) Perhaps you may think that the following set is equivalent: ```[6,3,2]``` but unfortunately dice have a minimum of three sides (well, really a tetrahedron with one empty side) The task for this kata is to get the amount of equivalent dice sets, having 2 dice at least,for a given set. For example, for the previous case: [6,6] we will have 3 equivalent sets that are: ``` [4, 3, 3], [12, 3], [9, 4]``` . You may assume that dice are available from 3 and above for any value up to an icosahedral die (20 sides). ``` [5,6,4] ---> 5 (they are [10, 4, 3], [8, 5, 3], [20, 6], [15, 8], [12, 10]) ``` For the cases we cannot get any equivalent set the result will be `0`. For example for the set `[3,3]` we will not have equivalent dice. Range of inputs for Random Tests: ``` 3 <= sides <= 15 2 <= dices <= 7 ``` See examples in the corresponding box. Enjoy it!! Write your solution by modifying this code: ```python def eq_dice(set_): ``` Your solution should implemented in the function "eq_dice". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given an array of $n$ positive integers $a_1, a_2, \ldots, a_n$. Your task is to calculate the number of arrays of $n$ positive integers $b_1, b_2, \ldots, b_n$ such that: $1 \le b_i \le a_i$ for every $i$ ($1 \le i \le n$), and $b_i \neq b_{i+1}$ for every $i$ ($1 \le i \le n - 1$). The number of such arrays can be very large, so print it modulo $998\,244\,353$. -----Input----- The first line contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the array $a$. The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$). -----Output----- Print the answer modulo $998\,244\,353$ in a single line. -----Examples----- Input 3 2 2 2 Output 2 Input 2 2 3 Output 4 Input 3 1 1 1 Output 0 -----Note----- In the first test case possible arrays are $[1, 2, 1]$ and $[2, 1, 2]$. In the second test case possible arrays are $[1, 2]$, $[1, 3]$, $[2, 1]$ and $[2, 3]$. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The Little Elephant loves playing with arrays. He has array a, consisting of n positive integers, indexed from 1 to n. Let's denote the number with index i as ai. Additionally the Little Elephant has m queries to the array, each query is characterised by a pair of integers lj and rj (1 ≤ lj ≤ rj ≤ n). For each query lj, rj the Little Elephant has to count, how many numbers x exist, such that number x occurs exactly x times among numbers alj, alj + 1, ..., arj. Help the Little Elephant to count the answers to all queries. Input The first line contains two space-separated integers n and m (1 ≤ n, m ≤ 105) — the size of array a and the number of queries to it. The next line contains n space-separated positive integers a1, a2, ..., an (1 ≤ ai ≤ 109). Next m lines contain descriptions of queries, one per line. The j-th of these lines contains the description of the j-th query as two space-separated integers lj and rj (1 ≤ lj ≤ rj ≤ n). Output In m lines print m integers — the answers to the queries. The j-th line should contain the answer to the j-th query. Examples Input 7 2 3 1 2 2 3 3 7 1 7 3 4 Output 3 1 Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You have a playlist consisting of $n$ songs. The $i$-th song is characterized by two numbers $t_i$ and $b_i$ — its length and beauty respectively. The pleasure of listening to set of songs is equal to the total length of the songs in the set multiplied by the minimum beauty among them. For example, the pleasure of listening to a set of $3$ songs having lengths $[5, 7, 4]$ and beauty values $[11, 14, 6]$ is equal to $(5 + 7 + 4) \cdot 6 = 96$. You need to choose at most $k$ songs from your playlist, so the pleasure of listening to the set of these songs them is maximum possible. -----Input----- The first line contains two integers $n$ and $k$ ($1 \le k \le n \le 3 \cdot 10^5$) – the number of songs in the playlist and the maximum number of songs you can choose, respectively. Each of the next $n$ lines contains two integers $t_i$ and $b_i$ ($1 \le t_i, b_i \le 10^6$) — the length and beauty of $i$-th song. -----Output----- Print one integer — the maximum pleasure you can get. -----Examples----- Input 4 3 4 7 15 1 3 6 6 8 Output 78 Input 5 3 12 31 112 4 100 100 13 55 55 50 Output 10000 -----Note----- In the first test case we can choose songs ${1, 3, 4}$, so the total pleasure is $(4 + 3 + 6) \cdot 6 = 78$. In the second test case we can choose song $3$. The total pleasure will be equal to $100 \cdot 100 = 10000$. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Filled with optimism, Hyunuk will host a conference about how great this new year will be! The conference will have $n$ lectures. Hyunuk has two candidate venues $a$ and $b$. For each of the $n$ lectures, the speaker specified two time intervals $[sa_i, ea_i]$ ($sa_i \le ea_i$) and $[sb_i, eb_i]$ ($sb_i \le eb_i$). If the conference is situated in venue $a$, the lecture will be held from $sa_i$ to $ea_i$, and if the conference is situated in venue $b$, the lecture will be held from $sb_i$ to $eb_i$. Hyunuk will choose one of these venues and all lectures will be held at that venue. Two lectures are said to overlap if they share any point in time in common. Formally, a lecture held in interval $[x, y]$ overlaps with a lecture held in interval $[u, v]$ if and only if $\max(x, u) \le \min(y, v)$. We say that a participant can attend a subset $s$ of the lectures if the lectures in $s$ do not pairwise overlap (i.e. no two lectures overlap). Note that the possibility of attending may depend on whether Hyunuk selected venue $a$ or venue $b$ to hold the conference. A subset of lectures $s$ is said to be venue-sensitive if, for one of the venues, the participant can attend $s$, but for the other venue, the participant cannot attend $s$. A venue-sensitive set is problematic for a participant who is interested in attending the lectures in $s$ because the participant cannot be sure whether the lecture times will overlap. Hyunuk will be happy if and only if there are no venue-sensitive sets. Determine whether Hyunuk will be happy. -----Input----- The first line contains an integer $n$ ($1 \le n \le 100000$), the number of lectures held in the conference. Each of the next $n$ lines contains four integers $sa_i$, $ea_i$, $sb_i$, $eb_i$ ($1 \le sa_i, ea_i, sb_i, eb_i \le 10^9$, $sa_i \le ea_i, sb_i \le eb_i$). -----Output----- Print "YES" if Hyunuk will be happy. Print "NO" otherwise. You can print each letter in any case (upper or lower). -----Examples----- Input 2 1 2 3 6 3 4 7 8 Output YES Input 3 1 3 2 4 4 5 6 7 3 4 5 5 Output NO Input 6 1 5 2 9 2 4 5 8 3 6 7 11 7 10 12 16 8 11 13 17 9 12 14 18 Output YES -----Note----- In second example, lecture set $\{1, 3\}$ is venue-sensitive. Because participant can't attend this lectures in venue $a$, but can attend in venue $b$. In first and third example, venue-sensitive set does not exist. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. On February 14 Denis decided to give Valentine to Nastya and did not come up with anything better than to draw a huge red heart on the door of the length $k$ ($k \ge 3$). Nastya was very confused by this present, so she decided to break the door, throwing it on the mountains. Mountains are described by a sequence of heights $a_1, a_2, \dots, a_n$ in order from left to right ($k \le n$). It is guaranteed that neighboring heights are not equal to each other (that is, $a_i \ne a_{i+1}$ for all $i$ from $1$ to $n-1$). Peaks of mountains on the segment $[l,r]$ (from $l$ to $r$) are called indexes $i$ such that $l < i < r$, $a_{i - 1} < a_i$ and $a_i > a_{i + 1}$. It is worth noting that the boundary indexes $l$ and $r$ for the segment are not peaks. For example, if $n=8$ and $a=[3,1,4,1,5,9,2,6]$, then the segment $[1,8]$ has only two peaks (with indexes $3$ and $6$), and there are no peaks on the segment $[3, 6]$. To break the door, Nastya throws it to a segment $[l,l+k-1]$ of consecutive mountains of length $k$ ($1 \le l \le n-k+1$). When the door touches the peaks of the mountains, it breaks into two parts, after that these parts will continue to fall in different halves and also break into pieces when touching the peaks of the mountains, and so on. Formally, the number of parts that the door will break into will be equal to $p+1$, where $p$ is the number of peaks on the segment $[l,l+k-1]$. Nastya wants to break it into as many pieces as possible. Help her choose such a segment of mountains $[l, l+k-1]$ that the number of peaks on it is maximum. If there are several optimal segments, Nastya wants to find one for which the value $l$ is minimal. Formally, you need to choose a segment of mountains $[l, l+k-1]$ that has the maximum number of peaks. Among all such segments, you need to find the segment that has the minimum possible value $l$. -----Input----- The first line contains an integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases. Then the descriptions of the test cases follow. The first line of each test case contains two integers $n$ and $k$ ($3 \leq k \leq n \leq 2 \cdot 10^5$) — the number of mountains and the length of the door. The second line of the input data set contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \leq a_i \leq 10 ^ 9$, $a_i \neq a_{i + 1}$) — the heights of mountains. It is guaranteed that the sum of $n$ over all the test cases will not exceed $2 \cdot 10^5$. -----Output----- For each test case, output two integers $t$ and $l$ — the maximum number of parts that the door can split into, and the left border of the segment of length $k$ that the door should be reset to. -----Example----- Input 5 8 6 1 2 4 1 2 4 1 2 5 3 3 2 3 2 1 10 4 4 3 4 3 2 3 2 1 0 1 15 7 3 7 4 8 2 3 4 5 21 2 3 4 2 1 3 7 5 1 2 3 4 5 6 1 Output 3 2 2 2 2 1 3 1 2 3 -----Note----- In the first example, you need to select a segment of mountains from $2$ to $7$. In this segment, the indexes $3$ and $6$ are peaks, so the answer is $3$ (only $2$ peaks, so the door will break into $3$ parts). It is not difficult to notice that the mountain segments $[1, 6]$ and $[3, 8]$ are not suitable since they only have a $1$ peak (for the first segment, the $6$ index is not a peak, and for the second segment, the $3$ index is not a peak). In the second example, you need to select a segment of mountains from $2$ to $4$. In this segment, the index $3$ is a peak, so the answer is $2$ (only $1$ peak, so the door will break into $2$ parts). In the third example, you need to select a segment of mountains from $1$ to $4$. In this segment, the index $3$ is a peak, so the answer is $2$ (only $1$ peak, so the door will break into $2$ parts). You can see that on the segments $[2, 5]$, $[4, 7]$ and $[5, 8]$ the number of peaks is also $1$, but these segments have a left border greater than the segment $[1, 4]$, so they are not the correct answer. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Kode Festival is an anual contest where the hardest stone in the world is determined. (Kode is a Japanese word for "hardness".) This year, 2^N stones participated. The hardness of the i-th stone is A_i. In the contest, stones are thrown at each other in a knockout tournament. When two stones with hardness X and Y are thrown at each other, the following will happen: * When X > Y: The stone with hardness Y will be destroyed and eliminated. The hardness of the stone with hardness X will become X-Y. * When X = Y: One of the stones will be destroyed and eliminated. The hardness of the other stone will remain the same. * When X < Y: The stone with hardness X will be destroyed and eliminated. The hardness of the stone with hardness Y will become Y-X. The 2^N stones will fight in a knockout tournament as follows: 1. The following pairs will fight: (the 1-st stone versus the 2-nd stone), (the 3-rd stone versus the 4-th stone), ... 2. The following pairs will fight: (the winner of (1-st versus 2-nd) versus the winner of (3-rd versus 4-th)), (the winner of (5-th versus 6-th) versus the winner of (7-th versus 8-th)), ... 3. And so forth, until there is only one stone remaining. Determine the eventual hardness of the last stone remaining. Constraints * 1 \leq N \leq 18 * 1 \leq A_i \leq 10^9 * A_i is an integer. Input The input is given from Standard Input in the following format: N A_1 A_2 : A_{2^N} Output Print the eventual hardness of the last stone remaining. Examples Input 2 1 3 10 19 Output 7 Input 3 1 3 2 4 6 8 100 104 Output 2 Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Jzzhu have n non-negative integers a1, a2, ..., an. We will call a sequence of indexes i1, i2, ..., ik (1 ≤ i1 < i2 < ... < ik ≤ n) a group of size k. Jzzhu wonders, how many groups exists such that ai1 & ai2 & ... & aik = 0 (1 ≤ k ≤ n)? Help him and print this number modulo 1000000007 (109 + 7). Operation x & y denotes bitwise AND operation of two numbers. Input The first line contains a single integer n (1 ≤ n ≤ 106). The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 106). Output Output a single integer representing the number of required groups modulo 1000000007 (109 + 7). Examples Input 3 2 3 3 Output 0 Input 4 0 1 2 3 Output 10 Input 6 5 2 0 5 2 1 Output 53 Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Little girl Tanya is learning how to decrease a number by one, but she does it wrong with a number consisting of two or more digits. Tanya subtracts one from a number by the following algorithm: if the last digit of the number is non-zero, she decreases the number by one; if the last digit of the number is zero, she divides the number by 10 (i.e. removes the last digit). You are given an integer number $n$. Tanya will subtract one from it $k$ times. Your task is to print the result after all $k$ subtractions. It is guaranteed that the result will be positive integer number. -----Input----- The first line of the input contains two integer numbers $n$ and $k$ ($2 \le n \le 10^9$, $1 \le k \le 50$) — the number from which Tanya will subtract and the number of subtractions correspondingly. -----Output----- Print one integer number — the result of the decreasing $n$ by one $k$ times. It is guaranteed that the result will be positive integer number. -----Examples----- Input 512 4 Output 50 Input 1000000000 9 Output 1 -----Note----- The first example corresponds to the following sequence: $512 \rightarrow 511 \rightarrow 510 \rightarrow 51 \rightarrow 50$. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You have an axis-aligned rectangle room with width $W$ and height $H$, so the lower left corner is in point $(0, 0)$ and the upper right corner is in $(W, H)$. There is a rectangular table standing in this room. The sides of the table are parallel to the walls, the lower left corner is in $(x_1, y_1)$, and the upper right corner in $(x_2, y_2)$. You want to place another rectangular table in this room with width $w$ and height $h$ with the width of the table parallel to the width of the room. The problem is that sometimes there is not enough space to place the second table without intersecting with the first one (there are no problems with tables touching, though). You can't rotate any of the tables, but you can move the first table inside the room. Example of how you may move the first table. What is the minimum distance you should move the first table to free enough space for the second one? -----Input----- The first line contains the single integer $t$ ($1 \le t \le 5000$) — the number of the test cases. The first line of each test case contains two integers $W$ and $H$ ($1 \le W, H \le 10^8$) — the width and the height of the room. The second line contains four integers $x_1$, $y_1$, $x_2$ and $y_2$ ($0 \le x_1 < x_2 \le W$; $0 \le y_1 < y_2 \le H$) — the coordinates of the corners of the first table. The third line contains two integers $w$ and $h$ ($1 \le w \le W$; $1 \le h \le H$) — the width and the height of the second table. -----Output----- For each test case, print the minimum distance you should move the first table, or $-1$ if there is no way to free enough space for the second table. Your answer will be considered correct if its absolute or relative error doesn't exceed $10^{-6}$. -----Examples----- Input 5 8 5 2 1 7 4 4 2 5 4 2 2 5 4 3 3 1 8 0 3 1 6 1 5 8 1 3 0 6 1 5 1 8 10 4 5 7 8 8 5 Output 1.000000000 -1 2.000000000 2.000000000 0.000000000 -----Note----- The configuration of the first test case is shown in the picture. But the movement of the first table is not optimal. One of the optimal movement, for example, is to move the table by $(0, -1)$, so the lower left corner will move from $(2, 1)$ to $(2, 0)$. Then you can place the second table at $(0, 3)-(4, 5)$. In the second test case, there is no way to fit both tables in the room without intersecting. In the third test case, you can move the first table by $(0, 2)$, so the lower left corner will move from $(0, 3)$ to $(0, 5)$. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Parsa has a humongous tree on $n$ vertices. On each vertex $v$ he has written two integers $l_v$ and $r_v$. To make Parsa's tree look even more majestic, Nima wants to assign a number $a_v$ ($l_v \le a_v \le r_v$) to each vertex $v$ such that the beauty of Parsa's tree is maximized. Nima's sense of the beauty is rather bizarre. He defines the beauty of the tree as the sum of $\|a_u - a_v\|$ over all edges $(u, v)$ of the tree. Since Parsa's tree is too large, Nima can't maximize its beauty on his own. Your task is to find the maximum possible beauty for Parsa's tree. -----Input----- The first line contains an integer $t$ $(1\le t\le 250)$ — the number of test cases. The description of the test cases follows. The first line of each test case contains a single integer $n$ $(2\le n\le 10^5)$ — the number of vertices in Parsa's tree. The $i$-th of the following $n$ lines contains two integers $l_i$ and $r_i$ $(1 \le l_i \le r_i \le 10^9)$. Each of the next $n-1$ lines contains two integers $u$ and $v$ $(1 \le u , v \le n, u\neq v)$ meaning that there is an edge between the vertices $u$ and $v$ in Parsa's tree. It is guaranteed that the given graph is a tree. It is guaranteed that the sum of $n$ over all test cases doesn't exceed $2 \cdot 10^5$. -----Output----- For each test case print the maximum possible beauty for Parsa's tree. -----Examples----- Input 3 2 1 6 3 8 1 2 3 1 3 4 6 7 9 1 2 2 3 6 3 14 12 20 12 19 2 12 10 17 3 17 3 2 6 5 1 5 2 6 4 6 Output 7 8 62 -----Note----- The trees in the example: In the first test case, one possible assignment is $a = \{1, 8\}$ which results in $\|1 - 8\| = 7$. In the second test case, one of the possible assignments is $a = \{1, 5, 9\}$ which results in a beauty of $\|1 - 5\| + \|5 - 9\| = 8$ Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. This problem is a complicated version of D1, but it has significant differences, so read the whole statement. Polycarp has an array of $n$ ($n$ is even) integers $a_1, a_2, \dots, a_n$. Polycarp conceived of a positive integer $k$. After that, Polycarp began performing the following operations on the array: take an index $i$ ($1 \le i \le n$) and reduce the number $a_i$ by $k$. After Polycarp performed some (possibly zero) number of such operations, it turned out that at least half of the numbers in the array became the same. Find the maximum $k$ at which such a situation is possible, or print $-1$ if such a number can be arbitrarily large. -----Input----- The first line contains one integer $t$ ($1 \le t \le 10$) — the number of test cases. Then $t$ test cases follow. Each test case consists of two lines. The first line contains an even integer $n$ ($4 \le n \le 40$) ($n$ is even). The second line contains $n$ integers $a_1, a_2, \dots a_n$ ($-10^6 \le a_i \le 10^6$). It is guaranteed that the sum of all $n$ specified in the given test cases does not exceed $100$. -----Output----- For each test case output on a separate line an integer $k$ ($k \ge 1$) — the maximum possible number that Polycarp used in operations on the array, or $-1$, if such a number can be arbitrarily large. -----Examples----- Input 4 6 48 13 22 -15 16 35 8 -1 0 1 -1 0 1 -1 0 4 100 -1000 -1000 -1000 4 1 1 1 1 Output 13 2 -1 -1 -----Note----- None Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Ho ho! So you think you know integers, do you? Well then, young wizard, tell us what the Nth digit of the [Champernowne constant](https://en.wikipedia.org/wiki/Champernowne_constant) is! The constant proceeds like this: `0.12345678910111213141516...` I hope you see the pattern! Conjure a function that will accept an integer, `n`, and return the (one-indexed) `n`th digit of Champernowne's constant. Can you get it to run in _constant_ time? For example: `n = 1` should return `0` (the very first digit) `n = 2` should return `1` (we ignore the period character since it's not a digit!) `n = 20` should return `4` (that's the `4` in the number `14`, 20th in sequence) For any invalid values, such as `0` and below, or non-integers, return... `NaN`! I hope (for your sake) that you've been practicing your mathemagical spells, because a naïve solution will _not_ be fast enough to compete in this championship! Invoke with _precision_, and be wary of rounding errors in the realms of enormity! May the best integer win! Write your solution by modifying this code: ```python def champernowneDigit(n): ``` Your solution should implemented in the function "champernowneDigit". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. # A wolf in sheep's clothing Wolves have been reintroduced to Great Britain. You are a sheep farmer, and are now plagued by wolves which pretend to be sheep. Fortunately, you are good at spotting them. Warn the sheep in front of the wolf that it is about to be eaten. Remember that you are standing at the front of the queue which is at the end of the array: ``` [sheep, sheep, sheep, sheep, sheep, wolf, sheep, sheep] (YOU ARE HERE AT THE FRONT OF THE QUEUE) 7 6 5 4 3 2 1 ``` If the wolf is the closest animal to you, return `"Pls go away and stop eating my sheep"`. Otherwise, return `"Oi! Sheep number N! You are about to be eaten by a wolf!"` where `N` is the sheep's position in the queue. Note: there will always be exactly one wolf in the array. ## Examples ```python warn_the_sheep(["sheep", "sheep", "sheep", "wolf", "sheep"]) == 'Oi! Sheep number 1! You are about to be eaten by a wolf!' warn_the_sheep(['sheep', 'sheep', 'wolf']) == 'Pls go away and stop eating my sheep' ``` Write your solution by modifying this code: ```python def warn_the_sheep(queue): ``` Your solution should implemented in the function "warn_the_sheep". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The phantom thief "Lupin IV" is told by the beautiful "Fujiko Mine", a descendant of the Aizu clan, that the military funds left by the Aizu clan are sleeping in Aizuwakamatsu city. According to a report by Lupine's longtime companion, "Ishikawa Koshiemon," military funds are stored in several warehouses in a Senryobako box. There is no lookout in the warehouse, but it is tightly locked. However, Koshiemon says that if he uses the secret "steel slashing" technique taught by his father, he can instantly break the warehouse. <image> The remaining problem is the transportation of Senryobako. Lupine and Yuemon, who have no physical strength, cannot carry a Senryobako. So, I asked the reliable man "Infinity" to carry it. In order to carry out all the Senryobako, Lupine made the following plan. First, drive Lupine to the first warehouse and drop off Koshiemon and Daisuke. * Koshiemon breaks the warehouse * Daisuke carries out all Senryobako * While holding the Senryobako, head to the next warehouse decided by Lupine Repeat this and carry out the Senryobako to the last warehouse. Meanwhile, Lupine prepares a helicopter and carries a thousand boxes with them in the last warehouse and escapes. Daisuke can carry anything heavy, but the speed of movement slows down depending on the weight of the luggage. Lupine must take this into consideration when deciding the order in which to break the warehouse. Instead of Lupine, create a program that outputs the order of breaking the warehouse so that the travel time from breaking the first warehouse to reaching the last warehouse is minimized. However, * All the warehouses face the street that runs straight north from Tsuruga Castle. The number of warehouses is at most 15, and the distance from the castle is at most 10,000 meters or less. * Each Senryobako weighs 20 kilograms. The number of Senryobako in each warehouse is less than 10,000. * To move from warehouse to warehouse, use the underground passage that is installed underground along the street. * Daisuke travels at 2,000 / (70 + w) meters per minute to carry w kilograms of luggage. The input data is given the number of the warehouse (integer of 100 or less), the distance from the castle (meters), and the number of Senryobako stored in the warehouse for each warehouse. Input The input is given in the following format: n s1 d1 v1 s2 d2 v2 :: sn dn vn The number of warehouses n (n ≤ 15) is given in the first line, and the information of the i-th warehouse is given in the following n lines. As information on the warehouse, the number si (1 ≤ si ≤ 100), the distance from the castle di (1 ≤ di ≤ 10000), and the number of Senryobako vi (1 ≤ vi ≤ 10000) are given in one line. Output Please output the order of breaking the warehouse on one line. Please separate the warehouse numbers with a blank. Examples Input 2 1 100 1 2 200 2 Output 1 2 Input 3 11 100 1 13 200 20 12 300 3 Output 11 12 13 Input 5 13 199 1 51 1000 1 37 350 10 27 300 2 99 200 1000 Output 51 37 27 13 99 Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Vasya is an active Internet user. One day he came across an Internet resource he liked, so he wrote its address in the notebook. We know that the address of the written resource has format: <protocol>://<domain>.ru[/<context>] where: <protocol> can equal either "http" (without the quotes) or "ftp" (without the quotes), <domain> is a non-empty string, consisting of lowercase English letters, the /<context> part may not be present. If it is present, then <context> is a non-empty string, consisting of lowercase English letters. If string <context> isn't present in the address, then the additional character "/" isn't written. Thus, the address has either two characters "/" (the ones that go before the domain), or three (an extra one in front of the context). When the boy came home, he found out that the address he wrote in his notebook had no punctuation marks. Vasya must have been in a lot of hurry and didn't write characters ":", "/", ".". Help Vasya to restore the possible address of the recorded Internet resource. -----Input----- The first line contains a non-empty string that Vasya wrote out in his notebook. This line consists of lowercase English letters only. It is guaranteed that the given string contains at most 50 letters. It is guaranteed that the given string can be obtained from some correct Internet resource address, described above. -----Output----- Print a single line — the address of the Internet resource that Vasya liked. If there are several addresses that meet the problem limitations, you are allowed to print any of them. -----Examples----- Input httpsunrux Output http://sun.ru/x Input ftphttprururu Output ftp://http.ru/ruru -----Note----- In the second sample there are two more possible answers: "ftp://httpruru.ru" and "ftp://httpru.ru/ru". Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Consider the infinite sequence of integers: 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5.... The sequence is built in the following way: at first the number 1 is written out, then the numbers from 1 to 2, then the numbers from 1 to 3, then the numbers from 1 to 4 and so on. Note that the sequence contains numbers, not digits. For example number 10 first appears in the sequence in position 55 (the elements are numerated from one). Find the number on the n-th position of the sequence. -----Input----- The only line contains integer n (1 ≤ n ≤ 10^14) — the position of the number to find. Note that the given number is too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type. -----Output----- Print the element in the n-th position of the sequence (the elements are numerated from one). -----Examples----- Input 3 Output 2 Input 5 Output 2 Input 10 Output 4 Input 55 Output 10 Input 56 Output 1 Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Monocarp has decided to buy a new TV set and hang it on the wall in his flat. The wall has enough free space so Monocarp can buy a TV set with screen width not greater than $a$ and screen height not greater than $b$. Monocarp is also used to TV sets with a certain aspect ratio: formally, if the width of the screen is $w$, and the height of the screen is $h$, then the following condition should be met: $\frac{w}{h} = \frac{x}{y}$. There are many different TV sets in the shop. Monocarp is sure that for any pair of positive integers $w$ and $h$ there is a TV set with screen width $w$ and height $h$ in the shop. Monocarp isn't ready to choose the exact TV set he is going to buy. Firstly he wants to determine the optimal screen resolution. He has decided to try all possible variants of screen size. But he must count the number of pairs of positive integers $w$ and $h$, beforehand, such that $(w \le a)$, $(h \le b)$ and $(\frac{w}{h} = \frac{x}{y})$. In other words, Monocarp wants to determine the number of TV sets having aspect ratio $\frac{x}{y}$, screen width not exceeding $a$, and screen height not exceeding $b$. Two TV sets are considered different if they have different screen width or different screen height. -----Input----- The first line contains four integers $a$, $b$, $x$, $y$ ($1 \le a, b, x, y \le 10^{18}$) — the constraints on the screen width and height, and on the aspect ratio. -----Output----- Print one integer — the number of different variants to choose TV screen width and screen height so that they meet the aforementioned constraints. -----Examples----- Input 17 15 5 3 Output 3 Input 14 16 7 22 Output 0 Input 4 2 6 4 Output 1 Input 1000000000000000000 1000000000000000000 999999866000004473 999999822000007597 Output 1000000063 -----Note----- In the first example, there are $3$ possible variants: $(5, 3)$, $(10, 6)$, $(15, 9)$. In the second example, there is no TV set meeting the constraints. In the third example, there is only one variant: $(3, 2)$. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Guy-Manuel and Thomas are going to build a polygon spaceship. You're given a strictly convex (i. e. no three points are collinear) polygon P which is defined by coordinates of its vertices. Define P(x,y) as a polygon obtained by translating P by vector \overrightarrow {(x,y)}. The picture below depicts an example of the translation: <image> Define T as a set of points which is the union of all P(x,y) such that the origin (0,0) lies in P(x,y) (both strictly inside and on the boundary). There is also an equivalent definition: a point (x,y) lies in T only if there are two points A,B in P such that \overrightarrow {AB} = \overrightarrow {(x,y)}. One can prove T is a polygon too. For example, if P is a regular triangle then T is a regular hexagon. At the picture below P is drawn in black and some P(x,y) which contain the origin are drawn in colored: <image> The spaceship has the best aerodynamic performance if P and T are similar. Your task is to check whether the polygons P and T are [similar](https://tinyurl.com/vp5m7vl). Input The first line of input will contain a single integer n (3 ≤ n ≤ 10^5) — the number of points. The i-th of the next n lines contains two integers x_i, y_i (\|x_i\|, \|y_i\| ≤ 10^9), denoting the coordinates of the i-th vertex. It is guaranteed that these points are listed in counterclockwise order and these points form a strictly convex polygon. Output Output "YES" in a separate line, if P and T are similar. Otherwise, output "NO" in a separate line. You can print each letter in any case (upper or lower). Examples Input 4 1 0 4 1 3 4 0 3 Output YES Input 3 100 86 50 0 150 0 Output nO Input 8 0 0 1 0 2 1 3 3 4 6 3 6 2 5 1 3 Output YES Note The following image shows the first sample: both P and T are squares. The second sample was shown in the statements. <image> Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Lunar New Year is approaching, and you bought a matrix with lots of "crosses". This matrix $M$ of size $n \times n$ contains only 'X' and '.' (without quotes). The element in the $i$-th row and the $j$-th column $(i, j)$ is defined as $M(i, j)$, where $1 \leq i, j \leq n$. We define a cross appearing in the $i$-th row and the $j$-th column ($1 < i, j < n$) if and only if $M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = $ 'X'. The following figure illustrates a cross appearing at position $(2, 2)$ in a $3 \times 3$ matrix. X.X .X. X.X Your task is to find out the number of crosses in the given matrix $M$. Two crosses are different if and only if they appear in different rows or columns. -----Input----- The first line contains only one positive integer $n$ ($1 \leq n \leq 500$), denoting the size of the matrix $M$. The following $n$ lines illustrate the matrix $M$. Each line contains exactly $n$ characters, each of them is 'X' or '.'. The $j$-th element in the $i$-th line represents $M(i, j)$, where $1 \leq i, j \leq n$. -----Output----- Output a single line containing only one integer number $k$ — the number of crosses in the given matrix $M$. -----Examples----- Input 5 ..... .XXX. .XXX. .XXX. ..... Output 1 Input 2 XX XX Output 0 Input 6 ...... X.X.X. .X.X.X X.X.X. .X.X.X ...... Output 4 -----Note----- In the first sample, a cross appears at $(3, 3)$, so the answer is $1$. In the second sample, no crosses appear since $n < 3$, so the answer is $0$. In the third sample, crosses appear at $(3, 2)$, $(3, 4)$, $(4, 3)$, $(4, 5)$, so the answer is $4$. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Input The first line of the input contains a single integer N (1 ≤ N ≤ 24). The next N lines contain 5 space-separated integers each. The first three integers will be between 0 and 2, inclusive. The last two integers will be between 0 and 3, inclusive. The sum of the first three integers will be equal to the sum of the last two integers. Output Output the result – a string of lowercase English letters. Examples Input 1 1 0 0 1 0 Output a Input 10 2 0 0 1 1 1 1 1 2 1 2 1 0 1 2 1 1 0 1 1 2 1 0 2 1 1 1 1 2 1 1 2 1 3 1 2 0 0 1 1 1 1 0 1 1 1 1 2 2 2 Output codeforcez Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Petya has an array of integers a_1, a_2, …, a_n. He only likes sorted arrays. Unfortunately, the given array could be arbitrary, so Petya wants to sort it. Petya likes to challenge himself, so he wants to sort array using only 3-cycles. More formally, in one operation he can pick 3 pairwise distinct indices i, j, and k (1 ≤ i, j, k ≤ n) and apply i → j → k → i cycle to the array a. It simultaneously places a_i on position j, a_j on position k, and a_k on position i, without changing any other element. For example, if a is [10, 50, 20, 30, 40, 60] and he chooses i = 2, j = 1, k = 5, then the array becomes [\underline{50}, \underline{40}, 20, 30, \underline{10}, 60]. Petya can apply arbitrary number of 3-cycles (possibly, zero). You are to determine if Petya can sort his array a, i. e. make it non-decreasing. Input Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 5 ⋅ 10^5). Description of the test cases follows. The first line of each test case contains a single integer n (1 ≤ n ≤ 5 ⋅ 10^5) — the length of the array a. The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ n). It is guaranteed that the sum of n over all test cases does not exceed 5 ⋅ 10^5. Output For each test case, print "YES" (without quotes) if Petya can sort the array a using 3-cycles, and "NO" (without quotes) otherwise. You can print each letter in any case (upper or lower). Example Input 7 1 1 2 2 2 2 2 1 3 1 2 3 3 2 1 3 3 3 1 2 4 2 1 4 3 Output YES YES NO YES NO YES YES Note In the 6-th test case Petya can use the 3-cycle 1 → 3 → 2 → 1 to sort the array. In the 7-th test case Petya can apply 1 → 3 → 2 → 1 and make a = [1, 4, 2, 3]. Then he can apply 2 → 4 → 3 → 2 and finally sort the array. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given a picture consisting of $n$ rows and $m$ columns. Rows are numbered from $1$ to $n$ from the top to the bottom, columns are numbered from $1$ to $m$ from the left to the right. Each cell is painted either black or white. You think that this picture is not interesting enough. You consider a picture to be interesting if there is at least one cross in it. A cross is represented by a pair of numbers $x$ and $y$, where $1 \le x \le n$ and $1 \le y \le m$, such that all cells in row $x$ and all cells in column $y$ are painted black. For examples, each of these pictures contain crosses: [Image] The fourth picture contains 4 crosses: at $(1, 3)$, $(1, 5)$, $(3, 3)$ and $(3, 5)$. Following images don't contain crosses: [Image] You have a brush and a can of black paint, so you can make this picture interesting. Each minute you may choose a white cell and paint it black. What is the minimum number of minutes you have to spend so the resulting picture contains at least one cross? You are also asked to answer multiple independent queries. -----Input----- The first line contains an integer $q$ ($1 \le q \le 5 \cdot 10^4$) — the number of queries. The first line of each query contains two integers $n$ and $m$ ($1 \le n, m \le 5 \cdot 10^4$, $n \cdot m \le 4 \cdot 10^5$) — the number of rows and the number of columns in the picture. Each of the next $n$ lines contains $m$ characters — '.' if the cell is painted white and '' if the cell is painted black. It is guaranteed that $\sum n \le 5 \cdot 10^4$ and $\sum n \cdot m \le 4 \cdot 10^5$. -----Output----- Print $q$ lines, the $i$-th line should contain a single integer — the answer to the $i$-th query, which is the minimum number of minutes you have to spend so the resulting picture contains at least one cross. -----Example----- Input 9 5 5 .... .... **** .... .... 3 4 **** ... ... 4 3 *** .. .. .. 5 5 **** ..* ***** ... ..* 1 4 ** 5 5 ..... .... .*. .... ..... 5 3 ... .. .. *** .. 3 3 .. . .. 4 4 .** .... .* .* Output 0 0 0 0 0 4 1 1 2 -----Note----- The example contains all the pictures from above in the same order. The first 5 pictures already contain a cross, thus you don't have to paint anything. You can paint $(1, 3)$, $(3, 1)$, $(5, 3)$ and $(3, 5)$ on the $6$-th picture to get a cross in $(3, 3)$. That'll take you $4$ minutes. You can paint $(1, 2)$ on the $7$-th picture to get a cross in $(4, 2)$. You can paint $(2, 2)$ on the $8$-th picture to get a cross in $(2, 2)$. You can, for example, paint $(1, 3)$, $(3, 1)$ and $(3, 3)$ to get a cross in $(3, 3)$ but that will take you $3$ minutes instead of $1$. There are 9 possible crosses you can get in minimum time on the $9$-th picture. One of them is in $(1, 1)$: paint $(1, 2)$ and $(2, 1)$. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Problem There are coins with front and back sides and dice with rolls from $ 1 $ to $ N $. Gacho decided to play the following games using these. The game starts with a score of $ 0 $ and proceeds as follows. 1. Roll the dice $ 1 $ and add the number of rolls to the score. 2. If the current score is $ K $ or more, the game is cleared and the game ends. 3. If the current score is less than $ K $, toss a coin and return to 1. if the front appears, and if the back appears, the game is over and the game ends. When a coin is thrown, it has a probability of $ A \% $ and a probability of $ (100-A) \% $. Also, when the dice are rolled, each eye appears with equal probability. At this time, find the probability that Gacho can clear the game in one game. When the probability to be calculated is expressed as $ \ frac {P} {Q} $ using relatively prime integers $ P and Q $, it becomes $ R \ times Q \ equiv P \ bmod 998244353 $ $ 0 $ or more and $ 998244352 $ or less. Output the integer $ R $ of. Under the constraints of this problem, such $ R $ always exists uniquely. Constraints The input satisfies the following conditions. * $ 1 \ leq N \ leq 10 ^ 5 $ * $ 1 \ leq K \ leq 10 ^ 5 $ * $ 1 \ leq A \ leq 99 $ * All inputs are integers Input The input is given in the following format. $ N $ $ K $ $ A $ $ N, K, A $ are given on one line separated by blanks. Output When the probability of clearing the game is expressed as $ \ frac {P} {Q} $ using relatively prime integers $ P and Q $, it becomes $ R \ times Q \ equiv P \ bmod 998244353 $. Output an integer $ R $ that is greater than or equal to $ 0 $ and less than or equal to $ 998244352 $. Examples Input 1 1 50 Output 1 Input 2 2 10 Output 648858830 Input 6 10 99 Output 650893870 Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Mad scientist Mike entertains himself by arranging rows of dominoes. He doesn't need dominoes, though: he uses rectangular magnets instead. Each magnet has two poles, positive (a "plus") and negative (a "minus"). If two magnets are put together at a close distance, then the like poles will repel each other and the opposite poles will attract each other. Mike starts by laying one magnet horizontally on the table. During each following step Mike adds one more magnet horizontally to the right end of the row. Depending on how Mike puts the magnet on the table, it is either attracted to the previous one (forming a group of multiple magnets linked together) or repelled by it (then Mike lays this magnet at some distance to the right from the previous one). We assume that a sole magnet not linked to others forms a group of its own. [Image] Mike arranged multiple magnets in a row. Determine the number of groups that the magnets formed. -----Input----- The first line of the input contains an integer n (1 ≤ n ≤ 100000) — the number of magnets. Then n lines follow. The i-th line (1 ≤ i ≤ n) contains either characters "01", if Mike put the i-th magnet in the "plus-minus" position, or characters "10", if Mike put the magnet in the "minus-plus" position. -----Output----- On the single line of the output print the number of groups of magnets. -----Examples----- Input 6 10 10 10 01 10 10 Output 3 Input 4 01 01 10 10 Output 2 -----Note----- The first testcase corresponds to the figure. The testcase has three groups consisting of three, one and two magnets. The second testcase has two groups, each consisting of two magnets. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Let's introduce some definitions that will be needed later. Let $prime(x)$ be the set of prime divisors of $x$. For example, $prime(140) = \{ 2, 5, 7 \}$, $prime(169) = \{ 13 \}$. Let $g(x, p)$ be the maximum possible integer $p^k$ where $k$ is an integer such that $x$ is divisible by $p^k$. For example: $g(45, 3) = 9$ ($45$ is divisible by $3^2=9$ but not divisible by $3^3=27$), $g(63, 7) = 7$ ($63$ is divisible by $7^1=7$ but not divisible by $7^2=49$). Let $f(x, y)$ be the product of $g(y, p)$ for all $p$ in $prime(x)$. For example: $f(30, 70) = g(70, 2) \cdot g(70, 3) \cdot g(70, 5) = 2^1 \cdot 3^0 \cdot 5^1 = 10$, $f(525, 63) = g(63, 3) \cdot g(63, 5) \cdot g(63, 7) = 3^2 \cdot 5^0 \cdot 7^1 = 63$. You have integers $x$ and $n$. Calculate $f(x, 1) \cdot f(x, 2) \cdot \ldots \cdot f(x, n) \bmod{(10^{9} + 7)}$. -----Input----- The only line contains integers $x$ and $n$ ($2 \le x \le 10^{9}$, $1 \le n \le 10^{18}$) — the numbers used in formula. -----Output----- Print the answer. -----Examples----- Input 10 2 Output 2 Input 20190929 1605 Output 363165664 Input 947 987654321987654321 Output 593574252 -----Note----- In the first example, $f(10, 1) = g(1, 2) \cdot g(1, 5) = 1$, $f(10, 2) = g(2, 2) \cdot g(2, 5) = 2$. In the second example, actual value of formula is approximately $1.597 \cdot 10^{171}$. Make sure you print the answer modulo $(10^{9} + 7)$. In the third example, be careful about overflow issue. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Alice has just learned addition. However, she hasn't learned the concept of "carrying" fully — instead of carrying to the next column, she carries to the column two columns to the left. For example, the regular way to evaluate the sum $2039 + 2976$ would be as shown: However, Alice evaluates it as shown: In particular, this is what she does: add $9$ and $6$ to make $15$, and carry the $1$ to the column two columns to the left, i. e. to the column "$0$ $9$"; add $3$ and $7$ to make $10$ and carry the $1$ to the column two columns to the left, i. e. to the column "$2$ $2$"; add $1$, $0$, and $9$ to make $10$ and carry the $1$ to the column two columns to the left, i. e. to the column above the plus sign; add $1$, $2$ and $2$ to make $5$; add $1$ to make $1$. Thus, she ends up with the incorrect result of $15005$. Alice comes up to Bob and says that she has added two numbers to get a result of $n$. However, Bob knows that Alice adds in her own way. Help Bob find the number of ordered pairs of positive integers such that when Alice adds them, she will get a result of $n$. Note that pairs $(a, b)$ and $(b, a)$ are considered different if $a \ne b$. -----Input----- The input consists of multiple test cases. The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of test cases. The description of the test cases follows. The only line of each test case contains an integer $n$ ($2 \leq n \leq 10^9$) — the number Alice shows Bob. -----Output----- For each test case, output one integer — the number of ordered pairs of positive integers such that when Alice adds them, she will get a result of $n$. -----Examples----- Input 5 100 12 8 2021 10000 Output 9 4 7 44 99 -----Note----- In the first test case, when Alice evaluates any of the sums $1 + 9$, $2 + 8$, $3 + 7$, $4 + 6$, $5 + 5$, $6 + 4$, $7 + 3$, $8 + 2$, or $9 + 1$, she will get a result of $100$. The picture below shows how Alice evaluates $6 + 4$: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. A progress bar is an element of graphical interface that displays the progress of a process for this very moment before it is completed. Let's take a look at the following form of such a bar. A bar is represented as n squares, located in line. To add clarity, let's number them with positive integers from 1 to n from the left to the right. Each square has saturation (ai for the i-th square), which is measured by an integer from 0 to k. When the bar for some i (1 ≤ i ≤ n) is displayed, squares 1, 2, ... , i - 1 has the saturation k, squares i + 1, i + 2, ... , n has the saturation 0, and the saturation of the square i can have any value from 0 to k. So some first squares of the progress bar always have the saturation k. Some last squares always have the saturation 0. And there is no more than one square that has the saturation different from 0 and k. The degree of the process's completion is measured in percents. Let the process be t% completed. Then the following inequation is fulfilled: <image> An example of such a bar can be seen on the picture. <image> For the given n, k, t determine the measures of saturation for all the squares ai of the progress bar. Input We are given 3 space-separated integers n, k, t (1 ≤ n, k ≤ 100, 0 ≤ t ≤ 100). Output Print n numbers. The i-th of them should be equal to ai. Examples Input 10 10 54 Output 10 10 10 10 10 4 0 0 0 0 Input 11 13 37 Output 13 13 13 13 0 0 0 0 0 0 0 Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. On the way to Rio de Janeiro Ostap kills time playing with a grasshopper he took with him in a special box. Ostap builds a line of length n such that some cells of this line are empty and some contain obstacles. Then, he places his grasshopper to one of the empty cells and a small insect in another empty cell. The grasshopper wants to eat the insect. Ostap knows that grasshopper is able to jump to any empty cell that is exactly k cells away from the current (to the left or to the right). Note that it doesn't matter whether intermediate cells are empty or not as the grasshopper makes a jump over them. For example, if k = 1 the grasshopper can jump to a neighboring cell only, and if k = 2 the grasshopper can jump over a single cell. Your goal is to determine whether there is a sequence of jumps such that grasshopper will get from his initial position to the cell with an insect. -----Input----- The first line of the input contains two integers n and k (2 ≤ n ≤ 100, 1 ≤ k ≤ n - 1) — the number of cells in the line and the length of one grasshopper's jump. The second line contains a string of length n consisting of characters '.', '#', 'G' and 'T'. Character '.' means that the corresponding cell is empty, character '#' means that the corresponding cell contains an obstacle and grasshopper can't jump there. Character 'G' means that the grasshopper starts at this position and, finally, 'T' means that the target insect is located at this cell. It's guaranteed that characters 'G' and 'T' appear in this line exactly once. -----Output----- If there exists a sequence of jumps (each jump of length k), such that the grasshopper can get from his initial position to the cell with the insect, print "YES" (without quotes) in the only line of the input. Otherwise, print "NO" (without quotes). -----Examples----- Input 5 2 #G#T# Output YES Input 6 1 T....G Output YES Input 7 3 T..#..G Output NO Input 6 2 ..GT.. Output NO -----Note----- In the first sample, the grasshopper can make one jump to the right in order to get from cell 2 to cell 4. In the second sample, the grasshopper is only able to jump to neighboring cells but the way to the insect is free — he can get there by jumping left 5 times. In the third sample, the grasshopper can't make a single jump. In the fourth sample, the grasshopper can only jump to the cells with odd indices, thus he won't be able to reach the insect. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Given time in 24-hour format, convert it to words. ``` For example: 13:00 = one o'clock 13:09 = nine minutes past one 13:15 = quarter past one 13:29 = twenty nine minutes past one 13:30 = half past one 13:31 = twenty nine minutes to two 13:45 = quarter to two 00:48 = twelve minutes to one 00:08 = eight minutes past midnight 12:00 = twelve o'clock 00:00 = midnight Note: If minutes == 0, use 'o'clock'. If minutes <= 30, use 'past', and for minutes > 30, use 'to'. ``` More examples in test cases. Good luck! Write your solution by modifying this code: ```python def solve(time): ``` Your solution should implemented in the function "solve". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are an experienced Codeforces user. Today you found out that during your activity on Codeforces you have made y submissions, out of which x have been successful. Thus, your current success rate on Codeforces is equal to x / y. Your favorite rational number in the [0;1] range is p / q. Now you wonder: what is the smallest number of submissions you have to make if you want your success rate to be p / q? -----Input----- The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases. Each of the next t lines contains four integers x, y, p and q (0 ≤ x ≤ y ≤ 10^9; 0 ≤ p ≤ q ≤ 10^9; y > 0; q > 0). It is guaranteed that p / q is an irreducible fraction. Hacks. For hacks, an additional constraint of t ≤ 5 must be met. -----Output----- For each test case, output a single integer equal to the smallest number of submissions you have to make if you want your success rate to be equal to your favorite rational number, or -1 if this is impossible to achieve. -----Example----- Input 4 3 10 1 2 7 14 3 8 20 70 2 7 5 6 1 1 Output 4 10 0 -1 -----Note----- In the first example, you have to make 4 successful submissions. Your success rate will be equal to 7 / 14, or 1 / 2. In the second example, you have to make 2 successful and 8 unsuccessful submissions. Your success rate will be equal to 9 / 24, or 3 / 8. In the third example, there is no need to make any new submissions. Your success rate is already equal to 20 / 70, or 2 / 7. In the fourth example, the only unsuccessful submission breaks your hopes of having the success rate equal to 1. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Student A and student B are giving each other test answers during a test. They don't want to be caught so they are sending each other coded messages. Student A is sending student B the message: `Answer to Number 5 Part b`. He starts of with a square grid (in this example the grid = 5x5). He writes the message down (with spaces): ``` Answe r to Numbe r 5 P art b ``` He then starts writing the message down one column at a time (from the top to the bottom). The new message is now: `ArNran u rstm5twob e ePb` You are the teacher of this class. Your job is to decipher this message and bust the students. # Task Write a function `decipher_message`. This function will take one parameter (`message`). This function will return the original message. * Note: The length of the string is always going to be a prefect square * Hint: You should probably decipher the example message first before you start coding Have fun !!! Write your solution by modifying this code: ```python def decipher_message(message): ``` Your solution should implemented in the function "decipher_message". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Vasya is sitting on an extremely boring math class. To have fun, he took a piece of paper and wrote out n numbers on a single line. After that, Vasya began to write out different ways to put pluses ("+") in the line between certain digits in the line so that the result was a correct arithmetic expression; formally, no two pluses in such a partition can stand together (between any two adjacent pluses there must be at least one digit), and no plus can stand at the beginning or the end of a line. For example, in the string 100500, ways 100500 (add no pluses), 1+00+500 or 10050+0 are correct, and ways 100++500, +1+0+0+5+0+0 or 100500+ are incorrect. The lesson was long, and Vasya has written all the correct ways to place exactly k pluses in a string of digits. At this point, he got caught having fun by a teacher and he was given the task to calculate the sum of all the resulting arithmetic expressions by the end of the lesson (when calculating the value of an expression the leading zeros should be ignored). As the answer can be large, Vasya is allowed to get only its remainder modulo 10^9 + 7. Help him! -----Input----- The first line contains two integers, n and k (0 ≤ k < n ≤ 10^5). The second line contains a string consisting of n digits. -----Output----- Print the answer to the problem modulo 10^9 + 7. -----Examples----- Input 3 1 108 Output 27 Input 3 2 108 Output 9 -----Note----- In the first sample the result equals (1 + 08) + (10 + 8) = 27. In the second sample the result equals 1 + 0 + 8 = 9. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. An eviternity number is a number which: * contains only digits 8, 5 and 3, and * the count of the digit `8` >= count of digit `5` >= count of digit `3`. The first few eviternity numbers are as follows. ```Haskell [8, 58, 85, 88, 358, 385, 538, 583, 588, 835, 853, 858, 885, 888] ``` You will be given two integers, `a` and `b`, and your task is to return the number of eviternity numbers in the range `>= a and < b`. ```Haskell For example: solve(0,1000) = 14, because they are [8, 58, 85, 88, 358, 385, 538, 583, 588, 835, 853, 858, 885, 888] ``` The upper bound will not exceed `500,000`. More examples in test cases. Good luck! Write your solution by modifying this code: ```python def solve(a, b): ``` Your solution should implemented in the function "solve". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Connect the countless points with lines, till we reach the faraway yonder. There are n points on a coordinate plane, the i-th of which being (i, y_{i}). Determine whether it's possible to draw two parallel and non-overlapping lines, such that every point in the set lies on exactly one of them, and each of them passes through at least one point in the set. -----Input----- The first line of input contains a positive integer n (3 ≤ n ≤ 1 000) — the number of points. The second line contains n space-separated integers y_1, y_2, ..., y_{n} ( - 10^9 ≤ y_{i} ≤ 10^9) — the vertical coordinates of each point. -----Output----- Output "Yes" (without quotes) if it's possible to fulfill the requirements, and "No" otherwise. You can print each letter in any case (upper or lower). -----Examples----- Input 5 7 5 8 6 9 Output Yes Input 5 -1 -2 0 0 -5 Output No Input 5 5 4 3 2 1 Output No Input 5 1000000000 0 0 0 0 Output Yes -----Note----- In the first example, there are five points: (1, 7), (2, 5), (3, 8), (4, 6) and (5, 9). It's possible to draw a line that passes through points 1, 3, 5, and another one that passes through points 2, 4 and is parallel to the first one. In the second example, while it's possible to draw two lines that cover all points, they cannot be made parallel. In the third example, it's impossible to satisfy both requirements at the same time. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Основой любой социальной сети является отношение дружбы между двумя пользователями в том или ином смысле. В одной известной социальной сети дружба симметрична, то есть если a является другом b, то b также является другом a. В этой же сети есть функция, которая демонстрирует множество людей, имеющих высокую вероятность быть знакомыми для пользователя. Эта функция работает следующим образом. Зафиксируем пользователя x. Пусть некоторый другой человек y, не являющийся другом x на текущий момент, является другом не менее, чем для k% друзей x. Тогда он является предполагаемым другом для x. У каждого человека в социальной сети есть свой уникальный идентификатор — это целое число от 1 до 10^9. Вам дан список пар пользователей, являющихся друзьями. Определите для каждого упомянутого пользователя множество его предполагаемых друзей. -----Входные данные----- В первой строке следуют два целых числа m и k (1 ≤ m ≤ 100, 0 ≤ k ≤ 100) — количество пар друзей и необходимый процент общих друзей для того, чтобы считаться предполагаемым другом. В последующих m строках записано по два числа a_{i}, b_{i} (1 ≤ a_{i}, b_{i} ≤ 10^9, a_{i} ≠ b_{i}), обозначающих идентификаторы пользователей, являющихся друзьями. Гарантируется, что каждая пара людей фигурирует в списке не более одного раза. -----Выходные данные----- Для всех упомянутых людей в порядке возрастания id выведите информацию о предполагаемых друзьях. Информация должна иметь вид "id: k id_1 id_2 ... id_{k}", где id — это id самого человека, k — количество его предполагаемых друзей, а id_1, id_2, ..., id_{k} — идентификаторы его предполагаемых друзей в возрастающем порядке. -----Примеры----- Входные данные 5 51 10 23 23 42 39 42 10 39 39 58 Выходные данные 10: 1 42 23: 1 39 39: 1 23 42: 1 10 58: 2 10 42 Входные данные 5 100 1 2 1 3 1 4 2 3 2 4 Выходные данные 1: 0 2: 0 3: 1 4 4: 1 3 Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Challenge: Given two null-terminated strings in the arguments "string" and "prefix", determine if "string" starts with the "prefix" string. Return 1 (or any other "truthy" value) if true, 0 if false. Example: ``` startsWith("hello world!", "hello"); // should return 1. startsWith("hello world!", "HELLO"); // should return 0. startsWith("nowai", "nowaisir"); // should return 0. ``` Addendum: For this problem, an empty "prefix" string should always return 1 (true) for any value of "string". If the length of the "prefix" string is greater than the length of the "string", return 0. The check should be case-sensitive, i.e. startsWith("hello", "HE") should return 0, whereas startsWith("hello", "he") should return 1. The length of the "string" as well as the "prefix" can be defined by the formula: 0 <= length < +Infinity No characters should be ignored and/or omitted during the test, e.g. whitespace characters should not be ignored. Write your solution by modifying this code: ```python def starts_with(st, prefix): ``` Your solution should implemented in the function "starts_with". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Absent-minded Masha got set of n cubes for her birthday. At each of 6 faces of each cube, there is exactly one digit from 0 to 9. Masha became interested what is the largest natural x such she can make using her new cubes all integers from 1 to x. To make a number Masha can rotate her cubes and put them in a row. After that, she looks at upper faces of cubes from left to right and reads the number. The number can't contain leading zeros. It's not required to use all cubes to build a number. Pay attention: Masha can't make digit 6 from digit 9 and vice-versa using cube rotations. -----Input----- In first line integer n is given (1 ≤ n ≤ 3) — the number of cubes, Masha got for her birthday. Each of next n lines contains 6 integers a_{i}_{j} (0 ≤ a_{i}_{j} ≤ 9) — number on j-th face of i-th cube. -----Output----- Print single integer — maximum number x such Masha can make any integers from 1 to x using her cubes or 0 if Masha can't make even 1. -----Examples----- Input 3 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 Output 87 Input 3 0 1 3 5 6 8 1 2 4 5 7 8 2 3 4 6 7 9 Output 98 -----Note----- In the first test case, Masha can build all numbers from 1 to 87, but she can't make 88 because there are no two cubes with digit 8. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Meikyokan University is very famous for its research and education in the area of computer science. This university has a computer center that has advanced and secure computing facilities including supercomputers and many personal computers connected to the Internet. One of the policies of the computer center is to let the students select their own login names. Unfortunately, students are apt to select similar login names, and troubles caused by mistakes in entering or specifying login names are relatively common. These troubles are a burden on the staff of the computer center. To avoid such troubles, Dr. Choei Takano, the chief manager of the computer center, decided to stamp out similar and confusing login names. To this end, Takano has to develop a program that detects confusing login names. Based on the following four operations on strings, the distance between two login names is determined as the minimum number of operations that transforms one login name to the other. 1. Deleting a character at an arbitrary position. 2. Inserting a character into an arbitrary position. 3. Replacing a character at an arbitrary position with another character. 4. Swapping two adjacent characters at an arbitrary position. For example, the distance between “omura” and “murai” is two, because the following sequence of operations transforms “omura” to “murai”. delete ‘o’ insert ‘i’ omura --> mura --> murai Another example is that the distance between “akasan” and “kaason” is also two. swap ‘a’ and ‘k’ replace ‘a’ with ‘o’ akasan --> kaasan --> kaason Takano decided that two login names with a small distance are confusing and thus must be avoided. Your job is to write a program that enumerates all the confusing pairs of login names. Beware that the rules may combine in subtle ways. For instance, the distance between “ant” and “neat” is two. swap ‘a’ and ‘n’ insert ‘e’ ant --> nat --> neat Input The input consists of multiple datasets. Each dataset is given in the following format. n d name1 name2 ... namen The first integer n is the number of login names. Then comes a positive integer d. Two login names whose distance is less than or equal to d are deemed to be confusing. You may assume that 0 < n ≤ 200 and 0 < d ≤ 2. The i-th student’s login name is given by namei, which is composed of only lowercase letters. Its length is less than 16. You can assume that there are no duplicates in namei (1 ≤ i ≤ n). The end of the input is indicated by a line that solely contains a zero. Output For each dataset, your program should output all pairs of confusing login names, one pair per line, followed by the total number of confusing pairs in the dataset. In each pair, the two login names are to be separated only by a comma character (,), and the login name that is alphabetically preceding the other should appear first. The entire output of confusing pairs for each dataset must be sorted as follows. For two pairs “w1,w2” and “w3,w4”, if w1 alphabetically precedes w3, or they are the same and w2 precedes w4, then “w1,w2” must appear before “w3,w4”. Example Input 8 2 omura toshio raku tanaka imura yoshoi hayashi miura 3 1 tasaka nakata tanaka 1 1 foo 5 2 psqt abcdef abzdefa pqrst abdxcef 0 Output imura,miura imura,omura miura,omura toshio,yoshoi 4 tanaka,tasaka 1 0 abcdef,abdxcef abcdef,abzdefa pqrst,psqt 3 Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. There are $n$ cities and $m$ roads in Berland. Each road connects a pair of cities. The roads in Berland are one-way. What is the minimum number of new roads that need to be built to make all the cities reachable from the capital? New roads will also be one-way. -----Input----- The first line of input consists of three integers $n$, $m$ and $s$ ($1 \le n \le 5000, 0 \le m \le 5000, 1 \le s \le n$) — the number of cities, the number of roads and the index of the capital. Cities are indexed from $1$ to $n$. The following $m$ lines contain roads: road $i$ is given as a pair of cities $u_i$, $v_i$ ($1 \le u_i, v_i \le n$, $u_i \ne v_i$). For each pair of cities $(u, v)$, there can be at most one road from $u$ to $v$. Roads in opposite directions between a pair of cities are allowed (i.e. from $u$ to $v$ and from $v$ to $u$). -----Output----- Print one integer — the minimum number of extra roads needed to make all the cities reachable from city $s$. If all the cities are already reachable from $s$, print 0. -----Examples----- Input 9 9 1 1 2 1 3 2 3 1 5 5 6 6 1 1 8 9 8 7 1 Output 3 Input 5 4 5 1 2 2 3 3 4 4 1 Output 1 -----Note----- The first example is illustrated by the following: [Image] For example, you can add roads ($6, 4$), ($7, 9$), ($1, 7$) to make all the cities reachable from $s = 1$. The second example is illustrated by the following: [Image] In this example, you can add any one of the roads ($5, 1$), ($5, 2$), ($5, 3$), ($5, 4$) to make all the cities reachable from $s = 5$. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. In 1862, the lord of Aizu was ordered to serve as a guardian of Kyoto. The Kyoto Shugoshoku is an important role to protect Kyoto at the end of the Edo period when security has deteriorated. You have to patrol the city by sharing it with the shogunate and other clan. However, when it came time to decide the sharing route, the following order was received from a stubborn old man who is famous among his vassals. <image> It was a big deal. Even the lord cannot ignore the statement of this vassal. Depending on the selection of the sharing route, it will be "the samurai's face is not noticeable". So, please make a program to judge whether the above three conditions are met by inputting the information of the start point, the goal point, and the intersection, and give it to the lord. The start point is represented by 1, the goal point is represented by 2, and other intersections are represented by integers of 3 or more. A road is represented by a set of intersection numbers that the roads connect to. The number of intersections shall be 100 or less, and there shall be one or more routes from all intersections to the start point and goal point. input Given multiple datasets. Each dataset is given in the following format: a1 b1 a2 b2 : : 0 0 The two integers in each row indicate that there is a road connecting intersection ai and intersection bi. When both ai and bi are 0, it indicates the end of inputting intersection information. The number of datasets does not exceed 50. output For each data set, if the samurai's face stands out (if the three conditions are met), OK, otherwise (if the three conditions are not met), output NG on one line. Example Input 1 3 3 4 3 5 3 6 4 6 4 7 4 7 5 6 6 7 5 8 5 8 6 8 6 9 7 9 8 9 9 2 0 0 1 3 3 4 3 4 4 2 0 0 Output OK NG Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Ilya is very fond of graphs, especially trees. During his last trip to the forest Ilya found a very interesting tree rooted at vertex 1. There is an integer number written on each vertex of the tree; the number written on vertex i is equal to a_{i}. Ilya believes that the beauty of the vertex x is the greatest common divisor of all numbers written on the vertices on the path from the root to x, including this vertex itself. In addition, Ilya can change the number in one arbitrary vertex to 0 or leave all vertices unchanged. Now for each vertex Ilya wants to know the maximum possible beauty it can have. For each vertex the answer must be considered independently. The beauty of the root equals to number written on it. -----Input----- First line contains one integer number n — the number of vertices in tree (1 ≤ n ≤ 2·10^5). Next line contains n integer numbers a_{i} (1 ≤ i ≤ n, 1 ≤ a_{i} ≤ 2·10^5). Each of next n - 1 lines contains two integer numbers x and y (1 ≤ x, y ≤ n, x ≠ y), which means that there is an edge (x, y) in the tree. -----Output----- Output n numbers separated by spaces, where i-th number equals to maximum possible beauty of vertex i. -----Examples----- Input 2 6 2 1 2 Output 6 6 Input 3 6 2 3 1 2 1 3 Output 6 6 6 Input 1 10 Output 10 Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. In Math, an improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number) For example: ```5/3``` (five third). A mixed numeral is a whole number and a fraction combined into one "mixed" number. For example: ```1 1/2``` (one and a half) is a mixed numeral. ## Task Write a function `convertToMixedNumeral` to convert the improper fraction into a mixed numeral. The input will be given as a ```string``` (e.g. ```'4/3'```). The output should be a ```string```, with a space in between the whole number and the fraction (e.g. ```'1 1/3'```). You do not need to reduce the result to its simplest form. For the purpose of this exercise, there will be no ```0```, ```empty string``` or ```null``` input value. However, the input can be: - a negative fraction - a fraction that does not require conversion - a fraction that can be converted into a whole number ## Example Write your solution by modifying this code: ```python def convert_to_mixed_numeral(parm): ``` Your solution should implemented in the function "convert_to_mixed_numeral". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. # Task A cake is sliced with `n` straight lines. Your task is to calculate the maximum number of pieces the cake can have. # Example For `n = 0`, the output should be `1`. For `n = 1`, the output should be `2`. For `n = 2`, the output should be `4`. For `n = 3`, the output should be `7`. See the following image to understand it: ![](https://cdn2.scratch.mit.edu/get_image/project/92275349_500x400.png?v=1450672809.79) # Input/Output - `[input]` integer `n` `0 ≤ n ≤ 10000` - `[output]` an integer The maximum number of pieces the sliced cake can have. Write your solution by modifying this code: ```python def cake_slice(n): ``` Your solution should implemented in the function "cake_slice". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Dolphin loves programming contests. Today, he will take part in a contest in AtCoder. In this country, 24-hour clock is used. For example, 9:00 p.m. is referred to as "21 o'clock". The current time is A o'clock, and a contest will begin in exactly B hours. When will the contest begin? Answer in 24-hour time. -----Constraints----- - 0 \leq A,B \leq 23 - A and B are integers. -----Input----- The input is given from Standard Input in the following format: A B -----Output----- Print the hour of the starting time of the contest in 24-hour time. -----Sample Input----- 9 12 -----Sample Output----- 21 In this input, the current time is 9 o'clock, and 12 hours later it will be 21 o'clock in 24-hour time. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Input The input contains two integers N, M (1 ≤ N ≤ 1024, 2 ≤ M ≤ 16), separated by a single space. Output Output "YES" or "NO". Examples Input 2 3 Output YES Input 3 2 Output NO Input 33 16 Output YES Input 26 5 Output NO Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Did you ever hear about 'crossing the bridge noodle' ? Let me tell you that it's not some kind of bridge made of noodles. It's a dish, a kind of rice noodle soup. Mr.Ping makes the best noodle soup and his son Po is eagerly waiting for the user reviews in his father's blog. Users can vote with a (+) or a (-) and accordingly +1 or -1 is added to the total score respectively. Note that if a user votes multiple times, only his/her latest vote is counted towards the total score. Po opens the blog to see initial score of 0. To see the updated score without refreshing the page, he has to keep voting himself. After each of Po's clicks on (+) or (-), he can see the current total score, of course that considers Po's vote too. He is wondering how many users other than him could have possibly voted. Given the sequence of clicks made by Po and the total score displayed just after each of his clicks, can you tell him the minimum number of users that could have possibly voted at least once, other than Po. ------ Input ------ There are multiple test cases ( at most 21 ). Each case starts with an integer N ( 1 ≤ N ≤ 1000 ), the number of Po's clicks. Sequence of N clicks follows, one on each line of the form "vote score" (without quotes, separated by a space), where vote is either a 'P' or a 'M', representing Plus(+) and Minus(-) respectively, the one clicked by Po and score is the score displayed after Po's click ( -1,000,000,000 ≤ score ≤ 1,000,000,000 ). The last case has N = 0 and should not be processed. Each case is followed by an empty line. ------ Output ------ For each test case, output the minimum number of users that could have possibly voted at least once. ----- Sample Input 1 ------ 2 P 1 P 2 2 P 2 M -2 0 ----- Sample Output 1 ------ 1 1 ----- explanation 1 ------ Case 1 : P 1 , Po voted (+) and score = 1 is possibly Po's vote itself. P 2 , Po again voted (+), but as only latest vote of a user is counted, Po contributed only +1 to the score, so possibly one more user voted with a (+). Remember that we have to find the number of users other than Po, so answer is 1 Case 2 : P 2 , Po voted (+) and score = 2, possibly another user A also voted (+) M -2 , Po voted (-) and score = -2. Possibly the same user A also voted (-) So there can possibly be just one other user A Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. In computing, there are two primary byte order formats: big-endian and little-endian. Big-endian is used primarily for networking (e.g., IP addresses are transmitted in big-endian) whereas little-endian is used mainly by computers with microprocessors. Here is an example (using 32-bit integers in hex format): Little-Endian: 00 6D F4 C9 = 7,206,089 Big-Endian: C9 F4 6D 00 = 3,388,239,104 Your job is to write a function that switches the byte order of a given integer. The function should take an integer n for the first argument, and the bit-size of the integer for the second argument. The bit size must be a power of 2 greater than or equal to 8. Your function should return a None value if the integer is negative, if the specified bit size is not a power of 2 that is 8 or larger, or if the integer is larger than the specified bit size can handle. In this kata, assume that all integers are unsigned (non-negative) and that all input arguments are integers (no floats, strings, None/nil values, etc.). Remember that you will need to account for padding of null (00) bytes. Hint: bitwise operators are very helpful! :) Write your solution by modifying this code: ```python def switch_endian(n, bits): ``` Your solution should implemented in the function "switch_endian". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Takahashi has two integers X and Y. He computed X + Y and X - Y, and the results were A and B, respectively. Now he cannot remember what X and Y were. Find X and Y for him. -----Constraints----- - -100 \leq A, B \leq 100 - For the given integers A and B, there uniquely exist integers X and Y such that X + Y = A and X - Y = B. - All values in input are integers. -----Input----- Input is given from Standard Input in the following format: A B -----Output----- Print X and Y. -----Sample Input----- 2 -2 -----Sample Output----- 0 2 If X = 0 and Y = 2, they match the situation: 0 + 2 = 2 and 0 - 2 = -2. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. # The die is cast! Your task in this kata is to write a "dice roller" that interprets a subset of [dice notation](http://en.wikipedia.org/wiki/Dice_notation). # Description In most role-playing games, die rolls required by the system are given in the form `AdX`. `A` and `X` are variables, separated by the letter d, which stands for die or dice. - `A` is the number of dice to be rolled (usually omitted if 1). - `X` is the number of faces of each die. Here are some examples of input: # Modifiers As an addition to the above rules the input may also contain modifiers in the form `+N` or `-N` where `N` is an integer. Here are some examples of input containing modifiers: Modifiers must be applied after* all dice has been summed up.* # Output Your function must support two types of output depending on the second argument; verbose and summed. ## Summed output If the verbose flag isn't set your function should sum up all the dice and modifiers and return the result as an integer. ## Verbose output With the verbose flag your function should return an object/hash containing an array (`dice`) with all the dice rolls, and a integer (`modifier`) containing the sum of the modifiers which defaults to zero. Example of verbose output: # Invalid input Here are some examples of invalid inputs: # Additional information - Your solution should ignore all whitespace. - `roll` should return `false` for invalid input. Write your solution by modifying this code: ```python def roll(desc, verbose=False): ``` Your solution should implemented in the function "roll". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Arkady invited Anna for a dinner to a sushi restaurant. The restaurant is a bit unusual: it offers $n$ pieces of sushi aligned in a row, and a customer has to choose a continuous subsegment of these sushi to buy. The pieces of sushi are of two types: either with tuna or with eel. Let's denote the type of the $i$-th from the left sushi as $t_i$, where $t_i = 1$ means it is with tuna, and $t_i = 2$ means it is with eel. Arkady does not like tuna, Anna does not like eel. Arkady wants to choose such a continuous subsegment of sushi that it has equal number of sushi of each type and each half of the subsegment has only sushi of one type. For example, subsegment $[2, 2, 2, 1, 1, 1]$ is valid, but subsegment $[1, 2, 1, 2, 1, 2]$ is not, because both halves contain both types of sushi. Find the length of the longest continuous subsegment of sushi Arkady can buy. -----Input----- The first line contains a single integer $n$ ($2 \le n \le 100\,000$) — the number of pieces of sushi. The second line contains $n$ integers $t_1$, $t_2$, ..., $t_n$ ($t_i = 1$, denoting a sushi with tuna or $t_i = 2$, denoting a sushi with eel), representing the types of sushi from left to right. It is guaranteed that there is at least one piece of sushi of each type. Note that it means that there is at least one valid continuous segment. -----Output----- Print a single integer — the maximum length of a valid continuous segment. -----Examples----- Input 7 2 2 2 1 1 2 2 Output 4 Input 6 1 2 1 2 1 2 Output 2 Input 9 2 2 1 1 1 2 2 2 2 Output 6 -----Note----- In the first example Arkady can choose the subsegment $[2, 2, 1, 1]$ or the subsegment $[1, 1, 2, 2]$ with length $4$. In the second example there is no way but to choose one of the subsegments $[2, 1]$ or $[1, 2]$ with length $2$. In the third example Arkady's best choice is the subsegment $[1, 1, 1, 2, 2, 2]$. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Peter got a new snow blower as a New Year present. Of course, Peter decided to try it immediately. After reading the instructions he realized that it does not work like regular snow blowing machines. In order to make it work, you need to tie it to some point that it does not cover, and then switch it on. As a result it will go along a circle around this point and will remove all the snow from its path. Formally, we assume that Peter's machine is a polygon on a plane. Then, after the machine is switched on, it will make a circle around the point to which Peter tied it (this point lies strictly outside the polygon). That is, each of the points lying within or on the border of the polygon will move along the circular trajectory, with the center of the circle at the point to which Peter tied his machine. Peter decided to tie his car to point P and now he is wondering what is the area of the region that will be cleared from snow. Help him. Input The first line of the input contains three integers — the number of vertices of the polygon n (<image>), and coordinates of point P. Each of the next n lines contains two integers — coordinates of the vertices of the polygon in the clockwise or counterclockwise order. It is guaranteed that no three consecutive vertices lie on a common straight line. All the numbers in the input are integers that do not exceed 1 000 000 in their absolute value. Output Print a single real value number — the area of the region that will be cleared. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6. Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>. Examples Input 3 0 0 0 1 -1 2 1 2 Output 12.566370614359172464 Input 4 1 -1 0 0 1 2 2 0 1 1 Output 21.991148575128551812 Note In the first sample snow will be removed from that area: <image> Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Reducing Problems - Bug Fixing #8 Oh no! Timmy's reduce is causing problems, Timmy's goal is to calculate the two teams scores and return the winner but timmy has gotten confused and sometimes teams don't enter their scores, total the scores out of 3! Help timmy fix his program! Return true if team 1 wins or false if team 2 wins! Write your solution by modifying this code: ```python def calculate_total(t1, t2): ``` Your solution should implemented in the function "calculate_total". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Find the minimum area of a square land on which you can place two identical rectangular $a \times b$ houses. The sides of the houses should be parallel to the sides of the desired square land. Formally, You are given two identical rectangles with side lengths $a$ and $b$ ($1 \le a, b \le 100$) — positive integers (you are given just the sizes, but not their positions). Find the square of the minimum area that contains both given rectangles. Rectangles can be rotated (both or just one), moved, but the sides of the rectangles should be parallel to the sides of the desired square. Two rectangles can touch each other (side or corner), but cannot intersect. Rectangles can also touch the sides of the square but must be completely inside it. You can rotate the rectangles. Take a look at the examples for a better understanding. [Image] The picture shows a square that contains red and green rectangles. -----Input----- The first line contains an integer $t$ ($1 \le t \le 10\,000$) —the number of test cases in the input. Then $t$ test cases follow. Each test case is a line containing two integers $a$, $b$ ($1 \le a, b \le 100$) — side lengths of the rectangles. -----Output----- Print $t$ answers to the test cases. Each answer must be a single integer — minimal area of square land, that contains two rectangles with dimensions $a \times b$. -----Example----- Input 8 3 2 4 2 1 1 3 1 4 7 1 3 7 4 100 100 Output 16 16 4 9 64 9 64 40000 -----Note----- Below are the answers for the first two test cases: [Image] [Image] Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Define a "prime prime" number to be a rational number written as one prime number over another prime number: `primeA / primeB` (e.g. `7/31`) Given a whole number `N`, generate the number of "prime prime" rational numbers less than 1, using only prime numbers between `0` and `N` (non inclusive). Return the count of these "prime primes", and the integer part of their sum. ## Example ```python N = 6 # The "prime primes" less than 1 are: 2/3, 2/5, 3/5 # count: 3 2/3 + 2/5 + 3/5 = 1.6667 # integer part: 1 Thus, the function should return 3 and 1. ``` Write your solution by modifying this code: ```python def prime_primes(N): ``` Your solution should implemented in the function "prime_primes". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. There are N integers written on a blackboard. The i-th integer is A_i. Takahashi will repeatedly perform the following operation on these numbers: * Select a pair of integers, A_i and A_j, that have the same parity (that is, both are even or both are odd) and erase them. * Then, write a new integer on the blackboard that is equal to the sum of those integers, A_i+A_j. Determine whether it is possible to have only one integer on the blackboard. Constraints * 2 ≦ N ≦ 10^5 * 1 ≦ A_i ≦ 10^9 * A_i is an integer. Input The input is given from Standard Input in the following format: N A_1 A_2 … A_N Output If it is possible to have only one integer on the blackboard, print `YES`. Otherwise, print `NO`. Examples Input 3 1 2 3 Output YES Input 5 1 2 3 4 5 Output NO Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. problem At IOI Confectionery, rice crackers are baked using the traditional method since the company was founded. This traditional method is to bake the front side for a certain period of time with charcoal, turn it over when the front side is baked, and bake the back side for a certain period of time with charcoal. While keeping this tradition, rice crackers are baked by machine. This machine arranges and bake rice crackers in a rectangular shape with vertical R (1 ≤ R ≤ 10) rows and horizontal C (1 ≤ C ≤ 10000) columns. Normally, it is an automatic operation, and when the front side is baked, the rice crackers are turned over and the back side is baked all at once. One day, when I was baking rice crackers, an earthquake occurred just before turning over the rice crackers, and some rice crackers turned over. Fortunately, the condition of the charcoal fire remained appropriate, but if the front side was baked any more, the baking time set by the tradition since the establishment would be exceeded, and the front side of the rice cracker would be overcooked and could not be shipped as a product. .. Therefore, I hurriedly changed the machine to manual operation and tried to turn over only the rice crackers that had not been turned inside out. This machine can turn over several horizontal rows at the same time and several vertical columns at the same time, but unfortunately it cannot turn over rice crackers one by one. If it takes time to turn it over, the front side of the rice cracker that was not turned over due to the earthquake will be overcooked and cannot be shipped as a product. Therefore, we decided to increase the number of rice crackers that can be baked on both sides without overcooking the front side, that is, the number of "rice crackers that can be shipped". Consider the case where no horizontal rows are flipped, or no vertical columns are flipped. Write a program that outputs the maximum number of rice crackers that can be shipped. Immediately after the earthquake, the rice crackers are in the state shown in the following figure. The black circles represent the state where the front side is burnt, and the white circles represent the state where the back side is burnt. <image> If you turn the first line over, you will see the state shown in the following figure. <image> Furthermore, when the 1st and 5th columns are turned over, the state is as shown in the following figure. In this state, 9 rice crackers can be shipped. <image> input The input consists of multiple datasets. Each dataset is given in the following format. Two integers R and C (1 ≤ R ≤ 10, 1 ≤ C ≤ 10 000) are written on the first line of the input, separated by blanks. The following R line represents the state of the rice cracker immediately after the earthquake. In the (i + 1) line (1 ≤ i ≤ R), C integers ai, 1, ai, 2, ……, ai, C are written separated by blanks, and ai, j are i. It represents the state of the rice cracker in row j. If ai and j are 1, it means that the front side is burnt, and if it is 0, it means that the back side is burnt. When both C and R are 0, it indicates the end of input. The number of data sets does not exceed 5. output For each data set, the maximum number of rice crackers that can be shipped is output on one line. Examples Input 2 5 0 1 0 1 0 1 0 0 0 1 3 6 1 0 0 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 0 0 Output 9 15 Input None Output None Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Everybody in Russia uses Gregorian calendar. In this calendar there are 31 days in January, 28 or 29 days in February (depending on whether the year is leap or not), 31 days in March, 30 days in April, 31 days in May, 30 in June, 31 in July, 31 in August, 30 in September, 31 in October, 30 in November, 31 in December. A year is leap in one of two cases: either its number is divisible by 4, but not divisible by 100, or is divisible by 400. For example, the following years are leap: 2000, 2004, but years 1900 and 2018 are not leap. In this problem you are given n (1 ≤ n ≤ 24) integers a_1, a_2, ..., a_{n}, and you have to check if these integers could be durations in days of n consecutive months, according to Gregorian calendar. Note that these months could belong to several consecutive years. In other words, check if there is a month in some year, such that its duration is a_1 days, duration of the next month is a_2 days, and so on. -----Input----- The first line contains single integer n (1 ≤ n ≤ 24) — the number of integers. The second line contains n integers a_1, a_2, ..., a_{n} (28 ≤ a_{i} ≤ 31) — the numbers you are to check. -----Output----- If there are several consecutive months that fit the sequence, print "YES" (without quotes). Otherwise, print "NO" (without quotes). You can print each letter in arbitrary case (small or large). -----Examples----- Input 4 31 31 30 31 Output Yes Input 2 30 30 Output No Input 5 29 31 30 31 30 Output Yes Input 3 31 28 30 Output No Input 3 31 31 28 Output Yes -----Note----- In the first example the integers can denote months July, August, September and October. In the second example the answer is no, because there are no two consecutive months each having 30 days. In the third example the months are: February (leap year) — March — April – May — June. In the fourth example the number of days in the second month is 28, so this is February. March follows February and has 31 days, but not 30, so the answer is NO. In the fifth example the months are: December — January — February (non-leap year). Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Alice is visiting New York City. To make the trip fun, Alice will take photos of the city skyline and give the set of photos as a present to Bob. However, she wants to find the set of photos with maximum beauty and she needs your help. There are $n$ buildings in the city, the $i$-th of them has positive height $h_i$. All $n$ building heights in the city are different. In addition, each building has a beauty value $b_i$. Note that beauty can be positive or negative, as there are ugly buildings in the city too. A set of photos consists of one or more photos of the buildings in the skyline. Each photo includes one or more buildings in the skyline that form a contiguous segment of indices. Each building needs to be in exactly one photo. This means that if a building does not appear in any photo, or if a building appears in more than one photo, the set of pictures is not valid. The beauty of a photo is equivalent to the beauty $b_i$ of the shortest building in it. The total beauty of a set of photos is the sum of the beauty of all photos in it. Help Alice to find the maximum beauty a valid set of photos can have. -----Input----- The first line contains an integer $n$ ($1 \le n \le 3 \cdot 10^5$), the number of buildings on the skyline. The second line contains $n$ distinct integers $h_1, h_2, \ldots, h_n$ ($1 \le h_i \le n$). The $i$-th number represents the height of building $i$. The third line contains $n$ integers $b_1, b_2, \ldots, b_n$ ($-10^9 \le b_i \le 10^9$). The $i$-th number represents the beauty of building $i$. -----Output----- Print one number representing the maximum beauty Alice can achieve for a valid set of photos of the skyline. -----Examples----- Input 5 1 2 3 5 4 1 5 3 2 4 Output 15 Input 5 1 4 3 2 5 -3 4 -10 2 7 Output 10 Input 2 2 1 -2 -3 Output -3 Input 10 4 7 3 2 5 1 9 10 6 8 -4 40 -46 -8 -16 4 -10 41 12 3 Output 96 -----Note----- In the first example, Alice can achieve maximum beauty by taking five photos, each one containing one building. In the second example, Alice can achieve a maximum beauty of $10$ by taking four pictures: three just containing one building, on buildings $1$, $2$ and $5$, each photo with beauty $-3$, $4$ and $7$ respectively, and another photo containing building $3$ and $4$, with beauty $2$. In the third example, Alice will just take one picture of the whole city. In the fourth example, Alice can take the following pictures to achieve maximum beauty: photos with just one building on buildings $1$, $2$, $8$, $9$, and $10$, and a single photo of buildings $3$, $4$, $5$, $6$, and $7$. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. # Summary: Given a number, `num`, return the shortest amount of `steps` it would take from 1, to land exactly on that number. # Description: A `step` is defined as either: - Adding 1 to the number: `num += 1` - Doubling the number: `num *= 2` You will always start from the number `1` and you will have to return the shortest count of steps it would take to land exactly on that number. `1 <= num <= 10000` Examples: `num == 3` would return `2` steps: ``` 1 -- +1 --> 2: 1 step 2 -- +1 --> 3: 2 steps 2 steps ``` `num == 12` would return `4` steps: ``` 1 -- +1 --> 2: 1 step 2 -- +1 --> 3: 2 steps 3 -- x2 --> 6: 3 steps 6 -- x2 --> 12: 4 steps 4 steps ``` `num == 16` would return `4` steps: ``` 1 -- +1 --> 2: 1 step 2 -- x2 --> 4: 2 steps 4 -- x2 --> 8: 3 steps 8 -- x2 --> 16: 4 steps 4 steps ``` Write your solution by modifying this code: ```python def shortest_steps_to_num(num): ``` Your solution should implemented in the function "shortest_steps_to_num". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7. -----Constraints----- - 1 \leq S \leq 2000 - All values in input are integers. -----Input----- Input is given from Standard Input in the following format: S -----Output----- Print the answer. -----Sample Input----- 7 -----Sample Output----- 3 3 sequences satisfy the condition: \{3,4\}, \{4,3\} and \{7\}. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. A variation of determining leap years, assuming only integers are used and years can be negative and positive. Write a function which will return the days in the year and the year entered in a string. For example 2000, entered as an integer, will return as a string 2000 has 366 days There are a few assumptions we will accept the year 0, even though there is no year 0 in the Gregorian Calendar. Also the basic rule for validating a leap year are as follows Most years that can be divided evenly by 4 are leap years. Exception: Century years are NOT leap years UNLESS they can be evenly divided by 400. So the years 0, -64 and 2016 will return 366 days. Whilst 1974, -10 and 666 will return 365 days. Write your solution by modifying this code: ```python def year_days(year): ``` Your solution should implemented in the function "year_days". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. There is a building with 2N floors, numbered 1, 2, \ldots, 2N from bottom to top. The elevator in this building moved from Floor 1 to Floor 2N just once. On the way, N persons got on and off the elevator. Each person i (1 \leq i \leq N) got on at Floor A_i and off at Floor B_i. Here, 1 \leq A_i < B_i \leq 2N, and just one person got on or off at each floor. Additionally, because of their difficult personalities, the following condition was satisfied: - Let C_i (= B_i - A_i - 1) be the number of times, while Person i were on the elevator, other persons got on or off. Then, the following holds: - If there was a moment when both Person i and Person j were on the elevator, C_i = C_j. We recorded the sequences A and B, but unfortunately, we have lost some of the records. If the record of A_i or B_i is lost, it will be given to you as -1. Additionally, the remaining records may be incorrect. Determine whether there is a pair of A and B that is consistent with the remaining records. -----Constraints----- - 1 \leq N \leq 100 - A_i = -1 or 1 \leq A_i \leq 2N. - B_i = -1 or 1 \leq B_i \leq 2N. - All values in input are integers. -----Input----- Input is given from Standard Input in the following format: N A_1 B_1 A_2 B_2 : A_N B_N -----Output----- If there is a pair of A and B that is consistent with the remaining records, print Yes; otherwise, print No. -----Sample Input----- 3 1 -1 -1 4 -1 6 -----Sample Output----- Yes For example, if B_1 = 3, A_2 = 2, and A_3 = 5, all the requirements are met. In this case, there is a moment when both Person 1 and Person 2 were on the elevator, which is fine since C_1 = C_2 = 1. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Mr. Square is going on a holiday. He wants to bring 2 of his favorite squares with him, so he put them in his rectangle suitcase. Write a function that, given the size of the squares and the suitcase, return whether the squares can fit inside the suitcase. ```Python fit_in(a,b,m,n) a,b are the sizes of the 2 squares m,n are the sizes of the suitcase ``` # Example ```Python fit_in(1,2,3,2) should return True fit_in(1,2,2,1) should return False fit_in(3,2,3,2) should return False fit_in(1,2,1,2) should return False ``` Write your solution by modifying this code: ```python def fit_in(a,b,m,n): ``` Your solution should implemented in the function "fit_in". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Write a function `insertDash(num)`/`InsertDash(int num)` that will insert dashes ('-') between each two odd numbers in num. For example: if num is 454793 the output should be 4547-9-3. Don't count zero as an odd number. Note that the number will always be non-negative (>= 0). Write your solution by modifying this code: ```python def insert_dash(num): ``` Your solution should implemented in the function "insert_dash". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Vasya has recently got a job as a cashier at a local store. His day at work is $L$ minutes long. Vasya has already memorized $n$ regular customers, the $i$-th of which comes after $t_{i}$ minutes after the beginning of the day, and his service consumes $l_{i}$ minutes. It is guaranteed that no customer will arrive while Vasya is servicing another customer. Vasya is a bit lazy, so he likes taking smoke breaks for $a$ minutes each. Those breaks may go one after another, but Vasya must be present at work during all the time periods he must serve regular customers, otherwise one of them may alert his boss. What is the maximum number of breaks Vasya can take during the day? -----Input----- The first line contains three integers $n$, $L$ and $a$ ($0 \le n \le 10^{5}$, $1 \le L \le 10^{9}$, $1 \le a \le L$). The $i$-th of the next $n$ lines contains two integers $t_{i}$ and $l_{i}$ ($0 \le t_{i} \le L - 1$, $1 \le l_{i} \le L$). It is guaranteed that $t_{i} + l_{i} \le t_{i + 1}$ and $t_{n} + l_{n} \le L$. -----Output----- Output one integer — the maximum number of breaks. -----Examples----- Input 2 11 3 0 1 1 1 Output 3 Input 0 5 2 Output 2 Input 1 3 2 1 2 Output 0 -----Note----- In the first sample Vasya can take $3$ breaks starting after $2$, $5$ and $8$ minutes after the beginning of the day. In the second sample Vasya can take $2$ breaks starting after $0$ and $2$ minutes after the beginning of the day. In the third sample Vasya can't take any breaks. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Bridge Removal ICPC islands once had been a popular tourist destination. For nature preservation, however, the government decided to prohibit entrance to the islands, and to remove all the man-made structures there. The hardest part of the project is to remove all the bridges connecting the islands. There are n islands and n-1 bridges. The bridges are built so that all the islands are reachable from all the other islands by crossing one or more bridges. The bridge removal team can choose any island as the starting point, and can repeat either of the following steps. * Move to another island by crossing a bridge that is connected to the current island. * Remove one bridge that is connected to the current island, and stay at the same island after the removal. Of course, a bridge, once removed, cannot be crossed in either direction. Crossing or removing a bridge both takes time proportional to the length of the bridge. Your task is to compute the shortest time necessary for removing all the bridges. Note that the island where the team starts can differ from where the team finishes the work. Input The input consists of at most 100 datasets. Each dataset is formatted as follows. > n > p2 p3 ... pn > d2 d3 ... dn The first integer n (3 ≤ n ≤ 800) is the number of the islands. The islands are numbered from 1 to n. The second line contains n-1 island numbers pi (1 ≤ pi < i), and tells that for each i from 2 to n the island i and the island pi are connected by a bridge. The third line contains n-1 integers di (1 ≤ di ≤ 100,000) each denoting the length of the corresponding bridge. That is, the length of the bridge connecting the island i and pi is di. It takes di units of time to cross the bridge, and also the same units of time to remove it. Note that, with this input format, it is assured that all the islands are reachable each other by crossing one or more bridges. The input ends with a line with a single zero. Output For each dataset, print the minimum time units required to remove all the bridges in a single line. Each line should not have any character other than this number. Sample Input 4 1 2 3 10 20 30 10 1 2 2 1 5 5 1 8 8 10 1 1 20 1 1 30 1 1 3 1 1 1 1 0 Output for the Sample Input 80 136 2 Example Input 4 1 2 3 10 20 30 10 1 2 2 1 5 5 1 8 8 10 1 1 20 1 1 30 1 1 3 1 1 1 1 0 Output 80 136 2 Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Why would we want to stop to only 50 shades of grey? Let's see to how many we can go. Write a function that takes a number n as a parameter and return an array containing n shades of grey in hexadecimal code (`#aaaaaa` for example). The array should be sorted in ascending order starting with `#010101`, `#020202`, etc. (using lower case letters). ```python def shades_of_grey(n): return '''n shades of grey in an array''' ``` As a reminder, the grey color is composed by the same number of red, green and blue: `#010101`, `#aeaeae`, `#555555`, etc. Also, `#000000` and `#ffffff` are not accepted values. When n is negative, just return an empty array. If n is higher than 254, just return an array of 254 elements. Have fun Write your solution by modifying this code: ```python def shades_of_grey(n): ``` Your solution should implemented in the function "shades_of_grey". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You get a "text" and have to shift the vowels by "n" positions to the right. (Negative value for n should shift to the left.) "Position" means the vowel's position if taken as one item in a list of all vowels within the string. A shift by 1 would mean, that every vowel shifts to the place of the next vowel. Shifting over the edges of the text should continue at the other edge. Example: text = "This is a test!" n = 1 output = "Thes is i tast!" text = "This is a test!" n = 3 output = "This as e tist!" If text is null or empty return exactly this value. Vowels are "a,e,i,o,u". Have fun coding it and please don't forget to vote and rank this kata! :-) I have created other katas. Have a look if you like coding and challenges. Write your solution by modifying this code: ```python def vowel_shift(text, n): ``` Your solution should implemented in the function "vowel_shift". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Ari the monster is not an ordinary monster. She is the hidden identity of Super M, the Byteforces’ superhero. Byteforces is a country that consists of n cities, connected by n - 1 bidirectional roads. Every road connects exactly two distinct cities, and the whole road system is designed in a way that one is able to go from any city to any other city using only the given roads. There are m cities being attacked by humans. So Ari... we meant Super M have to immediately go to each of the cities being attacked to scare those bad humans. Super M can pass from one city to another only using the given roads. Moreover, passing through one road takes her exactly one kron - the time unit used in Byteforces. [Image] However, Super M is not on Byteforces now - she is attending a training camp located in a nearby country Codeforces. Fortunately, there is a special device in Codeforces that allows her to instantly teleport from Codeforces to any city of Byteforces. The way back is too long, so for the purpose of this problem teleportation is used exactly once. You are to help Super M, by calculating the city in which she should teleport at the beginning in order to end her job in the minimum time (measured in krons). Also, provide her with this time so she can plan her way back to Codeforces. -----Input----- The first line of the input contains two integers n and m (1 ≤ m ≤ n ≤ 123456) - the number of cities in Byteforces, and the number of cities being attacked respectively. Then follow n - 1 lines, describing the road system. Each line contains two city numbers u_{i} and v_{i} (1 ≤ u_{i}, v_{i} ≤ n) - the ends of the road i. The last line contains m distinct integers - numbers of cities being attacked. These numbers are given in no particular order. -----Output----- First print the number of the city Super M should teleport to. If there are many possible optimal answers, print the one with the lowest city number. Then print the minimum possible time needed to scare all humans in cities being attacked, measured in Krons. Note that the correct answer is always unique. -----Examples----- Input 7 2 1 2 1 3 1 4 3 5 3 6 3 7 2 7 Output 2 3 Input 6 4 1 2 2 3 2 4 4 5 4 6 2 4 5 6 Output 2 4 -----Note----- In the first sample, there are two possibilities to finish the Super M's job in 3 krons. They are: $2 \rightarrow 1 \rightarrow 3 \rightarrow 7$ and $7 \rightarrow 3 \rightarrow 1 \rightarrow 2$. However, you should choose the first one as it starts in the city with the lower number. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. # Task Consider the following operation: We take a positive integer `n` and replace it with the sum of its `prime factors` (if a prime number is presented multiple times in the factorization of `n`, then it's counted the same number of times in the sum). This operation is applied sequentially first to the given number, then to the first result, then to the second result and so on.., until the result remains the same. Given number `n`, find the final result of the operation. # Example For `n = 24`, the output should be `5`. ``` 24 -> (2 + 2 + 2 + 3) = 9 -> (3 + 3) = 6 -> (2 + 3) = 5 -> 5. So the answer for n = 24 is 5.``` # Input/Output - `[input]` integer `n` Constraints: `2 ≤ n ≤ 10000.` - `[output]` an integer Write your solution by modifying this code: ```python def factor_sum(n): ``` Your solution should implemented in the function "factor_sum". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Takahashi recorded his daily life for the last few days as a integer sequence of length 2N, as follows: * a_1, b_1, a_2, b_2, ... , a_N, b_N This means that, starting from a certain time T, he was: * sleeping for exactly a_1 seconds * then awake for exactly b_1 seconds * then sleeping for exactly a_2 seconds * : * then sleeping for exactly a_N seconds * then awake for exactly b_N seconds In this record, he waked up N times. Takahashi is wondering how many times he waked up early during the recorded period. Here, he is said to wake up early if he wakes up between 4:00 AM and 7:00 AM, inclusive. If he wakes up more than once during this period, each of these awakenings is counted as waking up early. Unfortunately, he forgot the time T. Find the maximum possible number of times he waked up early during the recorded period. For your information, a day consists of 86400 seconds, and the length of the period between 4:00 AM and 7:00 AM is 10800 seconds. Constraints * 1 \leq N \leq 10^5 * 1 \leq a_i, b_i \leq 10^5 * a_i and b_i are integers. Input The input is given from Standard Input in the following format: N a_1 b_1 a_2 b_2 : a_N b_N Output Print the maximum possible number of times he waked up early during the recorded period. Examples Input 3 28800 57600 28800 57600 57600 28800 Output 2 Input 10 28800 57600 4800 9600 6000 1200 600 600 300 600 5400 600 6000 5760 6760 2880 6000 12000 9000 600 Output 5 Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given a string s of length n consisting of lowercase English letters. For two given strings s and t, say S is the set of distinct characters of s and T is the set of distinct characters of t. The strings s and t are isomorphic if their lengths are equal and there is a one-to-one mapping (bijection) f between S and T for which f(s_{i}) = t_{i}. Formally: f(s_{i}) = t_{i} for any index i, for any character $x \in S$ there is exactly one character $y \in T$ that f(x) = y, for any character $y \in T$ there is exactly one character $x \in S$ that f(x) = y. For example, the strings "aababc" and "bbcbcz" are isomorphic. Also the strings "aaaww" and "wwwaa" are isomorphic. The following pairs of strings are not isomorphic: "aab" and "bbb", "test" and "best". You have to handle m queries characterized by three integers x, y, len (1 ≤ x, y ≤ n - len + 1). For each query check if two substrings s[x... x + len - 1] and s[y... y + len - 1] are isomorphic. -----Input----- The first line contains two space-separated integers n and m (1 ≤ n ≤ 2·10^5, 1 ≤ m ≤ 2·10^5) — the length of the string s and the number of queries. The second line contains string s consisting of n lowercase English letters. The following m lines contain a single query on each line: x_{i}, y_{i} and len_{i} (1 ≤ x_{i}, y_{i} ≤ n, 1 ≤ len_{i} ≤ n - max(x_{i}, y_{i}) + 1) — the description of the pair of the substrings to check. -----Output----- For each query in a separate line print "YES" if substrings s[x_{i}... x_{i} + len_{i} - 1] and s[y_{i}... y_{i} + len_{i} - 1] are isomorphic and "NO" otherwise. -----Example----- Input 7 4 abacaba 1 1 1 1 4 2 2 1 3 2 4 3 Output YES YES NO YES -----Note----- The queries in the example are following: substrings "a" and "a" are isomorphic: f(a) = a; substrings "ab" and "ca" are isomorphic: f(a) = c, f(b) = a; substrings "bac" and "aba" are not isomorphic since f(b) and f(c) must be equal to a at same time; substrings "bac" and "cab" are isomorphic: f(b) = c, f(a) = a, f(c) = b. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given an array $a$ of length $n$ that has a special condition: every element in this array has at most 7 divisors. Find the length of the shortest non-empty subsequence of this array product of whose elements is a perfect square. A sequence $a$ is a subsequence of an array $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero or all) elements. -----Input----- The first line contains an integer $n$ ($1 \le n \le 10^5$) — the length of $a$. The second line contains $n$ integers $a_1$, $a_2$, $\ldots$, $a_{n}$ ($1 \le a_i \le 10^6$) — the elements of the array $a$. -----Output----- Output the length of the shortest non-empty subsequence of $a$ product of whose elements is a perfect square. If there are several shortest subsequences, you can find any of them. If there's no such subsequence, print "-1". -----Examples----- Input 3 1 4 6 Output 1 Input 4 2 3 6 6 Output 2 Input 3 6 15 10 Output 3 Input 4 2 3 5 7 Output -1 -----Note----- In the first sample, you can choose a subsequence $[1]$. In the second sample, you can choose a subsequence $[6, 6]$. In the third sample, you can choose a subsequence $[6, 15, 10]$. In the fourth sample, there is no such subsequence. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The only difference between easy and hard versions is the constraints. Vova likes pictures with kittens. The news feed in the social network he uses can be represented as an array of $n$ consecutive pictures (with kittens, of course). Vova likes all these pictures, but some are more beautiful than the others: the $i$-th picture has beauty $a_i$. Vova wants to repost exactly $x$ pictures in such a way that: each segment of the news feed of at least $k$ consecutive pictures has at least one picture reposted by Vova; the sum of beauty values of reposted pictures is maximum possible. For example, if $k=1$ then Vova has to repost all the pictures in the news feed. If $k=2$ then Vova can skip some pictures, but between every pair of consecutive pictures Vova has to repost at least one of them. Your task is to calculate the maximum possible sum of values of reposted pictures if Vova follows conditions described above, or say that there is no way to satisfy all conditions. -----Input----- The first line of the input contains three integers $n, k$ and $x$ ($1 \le k, x \le n \le 5000$) — the number of pictures in the news feed, the minimum length of segment with at least one repost in it and the number of pictures Vova is ready to repost. The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$), where $a_i$ is the beauty of the $i$-th picture. -----Output----- Print -1 if there is no way to repost some pictures to satisfy all the conditions in the problem statement. Otherwise print one integer — the maximum sum of values of reposted pictures if Vova follows conditions described in the problem statement. -----Examples----- Input 5 2 3 5 1 3 10 1 Output 18 Input 6 1 5 10 30 30 70 10 10 Output -1 Input 4 3 1 1 100 1 1 Output 100 Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Yet another education system reform has been carried out in Berland recently. The innovations are as follows: An academic year now consists of n days. Each day pupils study exactly one of m subjects, besides, each subject is studied for no more than one day. After the lessons of the i-th subject pupils get the home task that contains no less than ai and no more than bi exercises. Besides, each subject has a special attribute, the complexity (ci). A school can make its own timetable, considering the following conditions are satisfied: * the timetable should contain the subjects in the order of the complexity's strict increasing; * each day, except for the first one, the task should contain either k times more exercises, or more by k compared to the previous day (more formally: let's call the number of home task exercises in the i-th day as xi, then for each i (1 < i ≤ n): either xi = k + xi - 1 or xi = k·xi - 1 must be true); * the total number of exercises in all home tasks should be maximal possible. All limitations are separately set for each school. It turned out that in many cases ai and bi reach 1016 (however, as the Berland Minister of Education is famous for his love to half-measures, the value of bi - ai doesn't exceed 100). That also happened in the Berland School №256. Nevertheless, you as the school's principal still have to work out the timetable for the next academic year... Input The first line contains three integers n, m, k (1 ≤ n ≤ m ≤ 50, 1 ≤ k ≤ 100) which represent the number of days in an academic year, the number of subjects and the k parameter correspondingly. Each of the following m lines contains the description of a subject as three integers ai, bi, ci (1 ≤ ai ≤ bi ≤ 1016, bi - ai ≤ 100, 1 ≤ ci ≤ 100) — two limitations to the number of exercises on the i-th subject and the complexity of the i-th subject, correspondingly. Distinct subjects can have the same complexity. The subjects are numbered with integers from 1 to m. Please do not use the %lld specificator to read or write 64-bit numbers in С++. It is preferred to use the cin stream or the %I64d specificator. Output If no valid solution exists, print the single word "NO" (without the quotes). Otherwise, the first line should contain the word "YES" (without the quotes) and the next n lines should contain any timetable that satisfies all the conditions. The i + 1-th line should contain two positive integers: the number of the subject to study on the i-th day and the number of home task exercises given for this subject. The timetable should contain exactly n subjects. Examples Input 4 5 2 1 10 1 1 10 2 1 10 3 1 20 4 1 100 5 Output YES 2 8 3 10 4 20 5 40 Input 3 4 3 1 3 1 2 4 4 2 3 3 2 2 2 Output NO Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Problem statement AOR Ika got a cabbage with $ N $ leaves. The leaves of this cabbage are numbered $ 1, \ ldots, N $ in order from the outside, and the dirtiness of the $ i $ th leaf is $ D_i $. The larger this value is, the worse the degree of dirt is. AOR Ika-chan decided to use the cabbage leaves for cooking, so she decided to select the dirty leaves to be discarded according to the following procedure. 1. Initialize the discard candidates to empty. 2. Focus on the outermost leaves that have not yet been examined. If all the items have been checked, the process ends. 3. If the leaf is dirty for $ A $ or more, add it to the discard candidate and return to 2. Otherwise it ends. However, as a result of this operation, I noticed that the number of leaves that can be used for cooking may be extremely reduced. Therefore, I decided to reconsider the leaves to be discarded after the above operation and perform the following operations. 1. If there are less than $ M $ leaves that are not candidates for disposal, proceed to 2. Otherwise it ends. 2. Focus on the innermost leaf that has not been examined yet among the leaves that are candidates for disposal. If there are no leaves that are candidates for disposal, the process ends. 3. If the leaf is less than $ B $, remove it from the discard candidates and return to 2. Otherwise, discard all the leaves remaining in the discard candidates and finish. When you perform these operations, find the number of leaves to be finally discarded. Input constraints $ 1 \ leq N \ leq 1000 $ $ 0 \ leq M \ leq N $ $ 1 \ leq A \ leq B \ leq 1000 $ $ 1 \ leq D_ {i} \ leq 1000 $ sample Sample input 1 5 3 6 9 9 7 5 3 1 Sample output 1 2 Discard the first and second sheets. Sample input 2 5 3 6 9 5 4 3 2 1 Sample output 2 0 Do not throw away from the first piece. Sample input 3 5 3 6 9 10 8 6 4 2 Sample output 3 1 I tried to throw away the third one, but I reconsidered and decided not to throw away the second and third ones. Sample input 4 5 3 6 9 5 10 8 6 4 Sample output 4 0 AOR Ika doesn't know that the second piece is dirty. Sample input 5 5 0 6 9 9 9 8 8 7 Sample output 5 Five I don't mind throwing everything away. input $ N \ M \ A \ B $ $ D_ {1} \ D_ {2} \ \ cdots \ D_ {N} $ output Output the number of leaves to be finally thrown away. Example Input 5 3 6 9 9 7 5 3 1 Output 2 Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. She catched the thrown coin that draws parabolic curve with her sparkling fingers. She is an ESPer. Yes, she is an electro-master who has the third strongest power among more than one million ESPers in the city. Being flicked by her thumb, the coin is accelerated by electromagnetic force and is shot as Fleming's right-hand rule. Even if she holds back the initial velocity of the coin exceeds three times of the speed of sound. The coin that is shot in such velocity is heated because of air friction and adiabatic compression. As a result coin melts and shines in orange. This is her special ability, called railgun. The strength of railgun can make a hole of two meters in diameter on a concrete wall. She had defeated criminals such as post office robberies and bank robberies in the city with her ability. And today, she decided to destroy a laboratory that is suspected to making some inhumane experiments on human body. Only her railgun can shoot it. The railgun with a coin cannot destroy the laboratory because of lack of power. Since she have found a powered-suit nearby, so she decided to use it as a projectile. However, in this case it is difficult to take sight properly because the suit is much bigger and heavier than coins. Therefore she only can shoot the suit with certain velocity vector from her current position. Depending on the position of the laboratory, her railgun may not hit it and become a firework. Therefore she asked cooperation to the strongest ESPer in the city. He can change direction of a moving object as one of uncountable application of his ESP. Let's consider a 2-dimensional plane where the laboratory is on the origin (0, 0). She shoots a projectile from P = (px, py) with velocity vector V = (vx, vy). His ESP makes a virtual wall of radius R (= 1.0) centered on the origin. When projectile collides with the wall, it is reflected so that incident angle will be equal to reflection angle. Range of railgun is limited to D, because air friction decreases velocity of projectile and heat may melts projectile completely. Under these conditions, please write a program that judges if the railgun hits the laboratory. Size of the laboratory and the suit is ignorablly small. After the railgun is shot, it is allowed to pass through P again. Constraints * Judge data never include dataset where the answer is (D - 1.0e-3) or bigger. * 0.0001 ≤ \|V\| ≤ 0.9999 * 0.0001 ≤ \|P\| ≤ 0.9999 * D ≤ 50 Input Input consists of several datasets. The first line of each dataset contains a real number D. Next line contains 4 real numbers, which means px, py, vx, vy, respectively. Input terminates when D = 0. Output For each dataset, if the railgun hits, output the distance it moved until hits. Otherwise output 'impossible' (without quotes). You can print any number of digits and answer with an error less than 1.0e-6 will be accepted. Example Input 10.0 0.5 0.0 -0.2 0.0 1.0 0.1 0.0 0.2 0.2 0 Output 0.50000000 impossible Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The HR manager was disappointed again. The last applicant failed the interview the same way as 24 previous ones. "Do I give such a hard task?" — the HR manager thought. "Just raise number 5 to the power of n and get last two digits of the number. Yes, of course, n can be rather big, and one cannot find the power using a calculator, but we need people who are able to think, not just follow the instructions." Could you pass the interview in the machine vision company in IT City? -----Input----- The only line of the input contains a single integer n (2 ≤ n ≤ 2·10^18) — the power in which you need to raise number 5. -----Output----- Output the last two digits of 5^{n} without spaces between them. -----Examples----- Input 2 Output 25 Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Recently a serious bug has been found in the FOS code. The head of the F company wants to find the culprit and punish him. For that, he set up an organizational meeting, the issue is: who's bugged the code? Each of the n coders on the meeting said: 'I know for sure that either x or y did it!' The head of the company decided to choose two suspects and invite them to his office. Naturally, he should consider the coders' opinions. That's why the head wants to make such a choice that at least p of n coders agreed with it. A coder agrees with the choice of two suspects if at least one of the two people that he named at the meeting was chosen as a suspect. In how many ways can the head of F choose two suspects? Note that even if some coder was chosen as a suspect, he can agree with the head's choice if he named the other chosen coder at the meeting. -----Input----- The first line contains integers n and p (3 ≤ n ≤ 3·10^5; 0 ≤ p ≤ n) — the number of coders in the F company and the minimum number of agreed people. Each of the next n lines contains two integers x_{i}, y_{i} (1 ≤ x_{i}, y_{i} ≤ n) — the numbers of coders named by the i-th coder. It is guaranteed that x_{i} ≠ i, y_{i} ≠ i, x_{i} ≠ y_{i}. -----Output----- Print a single integer –– the number of possible two-suspect sets. Note that the order of the suspects doesn't matter, that is, sets (1, 2) и (2, 1) are considered identical. -----Examples----- Input 4 2 2 3 1 4 1 4 2 1 Output 6 Input 8 6 5 6 5 7 5 8 6 2 2 1 7 3 1 3 1 4 Output 1 Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. A `Nice array` is defined to be an array where for every value `n` in the array, there is also an element `n-1` or `n+1` in the array. example: ``` [2,10,9,3] is Nice array because 2=3-1 10=9+1 3=2+1 9=10-1 ``` Write a function named `isNice`/`IsNice` that returns `true` if its array argument is a Nice array, else `false`. You should also return `false` if `input` array has `no` elements. Write your solution by modifying this code: ```python def is_nice(arr): ``` Your solution should implemented in the function "is_nice". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The only difference between the easy and the hard versions is constraints. A subsequence is a string that can be derived from another string by deleting some or no symbols without changing the order of the remaining symbols. Characters to be deleted are not required to go successively, there can be any gaps between them. For example, for the string "abaca" the following strings are subsequences: "abaca", "aba", "aaa", "a" and "" (empty string). But the following strings are not subsequences: "aabaca", "cb" and "bcaa". You are given a string $s$ consisting of $n$ lowercase Latin letters. In one move you can take any subsequence $t$ of the given string and add it to the set $S$. The set $S$ can't contain duplicates. This move costs $n - \|t\|$, where $\|t\|$ is the length of the added subsequence (i.e. the price equals to the number of the deleted characters). Your task is to find out the minimum possible total cost to obtain a set $S$ of size $k$ or report that it is impossible to do so. -----Input----- The first line of the input contains two integers $n$ and $k$ ($1 \le n \le 100, 1 \le k \le 10^{12}$) — the length of the string and the size of the set, correspondingly. The second line of the input contains a string $s$ consisting of $n$ lowercase Latin letters. -----Output----- Print one integer — if it is impossible to obtain the set $S$ of size $k$, print -1. Otherwise, print the minimum possible total cost to do it. -----Examples----- Input 4 5 asdf Output 4 Input 5 6 aaaaa Output 15 Input 5 7 aaaaa Output -1 Input 10 100 ajihiushda Output 233 -----Note----- In the first example we can generate $S$ = { "asdf", "asd", "adf", "asf", "sdf" }. The cost of the first element in $S$ is $0$ and the cost of the others is $1$. So the total cost of $S$ is $4$. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. C: Only one subsequence --Unique Subsequence- problem One day Ebi-chan noticed that a text string T of length n and a pattern string P (m \ leq n) of length m were placed on the desk. Ebi-chan loves the "only one subsequence" that appears in strings, so she immediately began investigating whether P was the only subsequence of T. The property that P is the only subsequence of T is expressed as follows: Now write the i-th character of the string X as X_i. * A sequence of length m S = (s_1, ..., s_m) (where s_1 <s_2 <... <s_m) and for each i (i = 1, ..., m) T_ {s_i} The sequence S with = P_i is uniquely determined. For several hours after starting the investigation, Ebi-chan was staring at the string, but it seems that she was tired because the string was too long. If you couldn't see it, you decided to help Ebi-chan. For Ebi-chan, write a program that outputs “yes” if P is only one subsequence of T, and “no” otherwise. Input format T P The first line is given the text string T. The second line is given the pattern string P. Constraint * 1 \ leq \| P \| \ leq \| T \| \ leq 5 \ times 10 ^ 5 * T and P are composed of lowercase letters ‘a’-’z’. Output format Print “yes” if P is a single subsequence of T, otherwise “no” on one line. Input example 1 aizucamp azu Output example 1 yes Input example 2 abracadabra rada Output example 2 no Input example 3 hokkaido dekai Output example 3 no Example Input aizucamp azu Output yes Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Suppose you are given a string $s$ of length $n$ consisting of lowercase English letters. You need to compress it using the smallest possible number of coins. To compress the string, you have to represent $s$ as a concatenation of several non-empty strings: $s = t_{1} t_{2} \ldots t_{k}$. The $i$-th of these strings should be encoded with one of the two ways: if $\|t_{i}\| = 1$, meaning that the current string consists of a single character, you can encode it paying $a$ coins; if $t_{i}$ is a substring of $t_{1} t_{2} \ldots t_{i - 1}$, then you can encode it paying $b$ coins. A string $x$ is a substring of a string $y$ if $x$ can be obtained from $y$ by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. So your task is to calculate the minimum possible number of coins you need to spend in order to compress the given string $s$. -----Input----- The first line contains three positive integers, separated by spaces: $n$, $a$ and $b$ ($1 \leq n, a, b \leq 5000$) — the length of the string, the cost to compress a one-character string and the cost to compress a string that appeared before. The second line contains a single string $s$, consisting of $n$ lowercase English letters. -----Output----- Output a single integer — the smallest possible number of coins you need to spend to compress $s$. -----Examples----- Input 3 3 1 aba Output 7 Input 4 1 1 abcd Output 4 Input 4 10 1 aaaa Output 12 -----Note----- In the first sample case, you can set $t_{1} =$ 'a', $t_{2} =$ 'b', $t_{3} =$ 'a' and pay $3 + 3 + 1 = 7$ coins, since $t_{3}$ is a substring of $t_{1}t_{2}$. In the second sample, you just need to compress every character by itself. In the third sample, you set $t_{1} = t_{2} =$ 'a', $t_{3} =$ 'aa' and pay $10 + 1 + 1 = 12$ coins, since $t_{2}$ is a substring of $t_{1}$ and $t_{3}$ is a substring of $t_{1} t_{2}$. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The statement of this problem is the same as the statement of problem C2. The only difference is that, in problem C1, $n$ is always even, and in C2, $n$ is always odd. You are given a regular polygon with $2 \cdot n$ vertices (it's convex and has equal sides and equal angles) and all its sides have length $1$. Let's name it as $2n$-gon. Your task is to find the square of the minimum size such that you can embed $2n$-gon in the square. Embedding $2n$-gon in the square means that you need to place $2n$-gon in the square in such way that each point which lies inside or on a border of $2n$-gon should also lie inside or on a border of the square. You can rotate $2n$-gon and/or the square. -----Input----- The first line contains a single integer $T$ ($1 \le T \le 200$) — the number of test cases. Next $T$ lines contain descriptions of test cases — one per line. Each line contains single even integer $n$ ($2 \le n \le 200$). Don't forget you need to embed $2n$-gon, not an $n$-gon. -----Output----- Print $T$ real numbers — one per test case. For each test case, print the minimum length of a side of the square $2n$-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed $10^{-6}$. -----Example----- Input 3 2 4 200 Output 1.000000000 2.414213562 127.321336469 Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The central dogma of molecular biology is that DNA is transcribed into RNA, which is then tranlsated into protein. RNA, like DNA, is a long strand of nucleic acids held together by a sugar backbone (ribose in this case). Each segment of three bases is called a codon. Molecular machines called ribosomes translate the RNA codons into amino acid chains, called polypeptides which are then folded into a protein. Protein sequences are easily visualized in much the same way that DNA and RNA are, as large strings of letters. An important thing to note is that the 'Stop' codons do not encode for a specific amino acid. Their only function is to stop translation of the protein, as such they are not incorporated into the polypeptide chain. 'Stop' codons should not be in the final protein sequence. To save a you a lot of unnecessary (and boring) typing the keys and values for your amino acid dictionary are provided. Given a string of RNA, create a funciton which translates the RNA into its protein sequence. Note: the test cases will always produce a valid string. ```python protein('UGCGAUGAAUGGGCUCGCUCC') returns 'CDEWARS' ``` Included as test cases is a real world example! The last example test case encodes for a protein called green fluorescent protein; once spliced into the genome of another organism, proteins like GFP allow biologists to visualize cellular processes! Amino Acid Dictionary ---------------------- ```python # Phenylalanine 'UUC':'F', 'UUU':'F', # Leucine 'UUA':'L', 'UUG':'L', 'CUU':'L', 'CUC':'L','CUA':'L','CUG':'L', # Isoleucine 'AUU':'I', 'AUC':'I', 'AUA':'I', # Methionine 'AUG':'M', # Valine 'GUU':'V', 'GUC':'V', 'GUA':'V', 'GUG':'V', # Serine 'UCU':'S', 'UCC':'S', 'UCA':'S', 'UCG':'S', 'AGU':'S', 'AGC':'S', # Proline 'CCU':'P', 'CCC':'P', 'CCA':'P', 'CCG':'P', # Threonine 'ACU':'T', 'ACC':'T', 'ACA':'T', 'ACG':'T', # Alanine 'GCU':'A', 'GCC':'A', 'GCA':'A', 'GCG':'A', # Tyrosine 'UAU':'Y', 'UAC':'Y', # Histidine 'CAU':'H', 'CAC':'H', # Glutamine 'CAA':'Q', 'CAG':'Q', # Asparagine 'AAU':'N', 'AAC':'N', # Lysine 'AAA':'K', 'AAG':'K', # Aspartic Acid 'GAU':'D', 'GAC':'D', # Glutamic Acid 'GAA':'E', 'GAG':'E', # Cystine 'UGU':'C', 'UGC':'C', # Tryptophan 'UGG':'W', # Arginine 'CGU':'R', 'CGC':'R', 'CGA':'R', 'CGG':'R', 'AGA':'R', 'AGG':'R', # Glycine 'GGU':'G', 'GGC':'G', 'GGA':'G', 'GGG':'G', # Stop codon 'UAA':'Stop', 'UGA':'Stop', 'UAG':'Stop' ``` Write your solution by modifying this code: ```python def protein(rna): ``` Your solution should implemented in the function "protein". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. We have a grid of squares with N rows and M columns. Let (i, j) denote the square at the i-th row from the top and j-th column from the left. We will choose K of the squares and put a piece on each of them. If we place the K pieces on squares (x_1, y_1), (x_2, y_2), ..., and (x_K, y_K), the cost of this arrangement is computed as: \sum_{i=1}^{K-1} \sum_{j=i+1}^K (\|x_i - x_j\| + \|y_i - y_j\|) Find the sum of the costs of all possible arrangements of the pieces. Since this value can be tremendous, print it modulo 10^9+7. We consider two arrangements of the pieces different if and only if there is a square that contains a piece in one of the arrangements but not in the other. -----Constraints----- - 2 \leq N \times M \leq 2 \times 10^5 - 2 \leq K \leq N \times M - All values in input are integers. -----Input----- Input is given from Standard Input in the following format: N M K -----Output----- Print the sum of the costs of all possible arrangements of the pieces, modulo 10^9+7. -----Sample Input----- 2 2 2 -----Sample Output----- 8 There are six possible arrangements of the pieces, as follows: - ((1,1),(1,2)), with the cost \|1-1\|+\|1-2\| = 1 - ((1,1),(2,1)), with the cost \|1-2\|+\|1-1\| = 1 - ((1,1),(2,2)), with the cost \|1-2\|+\|1-2\| = 2 - ((1,2),(2,1)), with the cost \|1-2\|+\|2-1\| = 2 - ((1,2),(2,2)), with the cost \|1-2\|+\|2-2\| = 1 - ((2,1),(2,2)), with the cost \|2-2\|+\|1-2\| = 1 The sum of these costs is 8. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Given two integers `a` and `b`, which can be positive or negative, find the sum of all the numbers between including them too and return it. If the two numbers are equal return `a` or `b`. Note: `a` and `b` are not ordered! ## Examples ```python get_sum(1, 0) == 1 // 1 + 0 = 1 get_sum(1, 2) == 3 // 1 + 2 = 3 get_sum(0, 1) == 1 // 0 + 1 = 1 get_sum(1, 1) == 1 // 1 Since both are same get_sum(-1, 0) == -1 // -1 + 0 = -1 get_sum(-1, 2) == 2 // -1 + 0 + 1 + 2 = 2 ``` ```C get_sum(1, 0) == 1 // 1 + 0 = 1 get_sum(1, 2) == 3 // 1 + 2 = 3 get_sum(0, 1) == 1 // 0 + 1 = 1 get_sum(1, 1) == 1 // 1 Since both are same get_sum(-1, 0) == -1 // -1 + 0 = -1 get_sum(-1, 2) == 2 // -1 + 0 + 1 + 2 = 2 ``` Write your solution by modifying this code: ```python def get_sum(a,b): ``` Your solution should implemented in the function "get_sum". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Given a number, write a function to output its reverse digits. (e.g. given 123 the answer is 321) Numbers should preserve their sign; i.e. a negative number should still be negative when reversed. ### Examples ``` 123 -> 321 -456 -> -654 1000 -> 1 ``` Write your solution by modifying this code: ```python def reverse_number(n): ``` Your solution should implemented in the function "reverse_number". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. "Point reflection" or "point symmetry" is a basic concept in geometry where a given point, P, at a given position relative to a mid-point, Q has a corresponding point, P1, which is the same distance from Q but in the opposite direction. ## Task Given two points P and Q, output the symmetric point of point P about Q. Each argument is a two-element array of integers representing the point's X and Y coordinates. Output should be in the same format, giving the X and Y coordinates of point P1. You do not have to validate the input. This kata was inspired by the Hackerrank challenge [Find Point](https://www.hackerrank.com/challenges/find-point) Write your solution by modifying this code: ```python def symmetric_point(p, q): ``` Your solution should implemented in the function "symmetric_point". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Mad scientist Mike has just finished constructing a new device to search for extraterrestrial intelligence! He was in such a hurry to launch it for the first time that he plugged in the power wires without giving it a proper glance and started experimenting right away. After a while Mike observed that the wires ended up entangled and now have to be untangled again. The device is powered by two wires "plus" and "minus". The wires run along the floor from the wall (on the left) to the device (on the right). Both the wall and the device have two contacts in them on the same level, into which the wires are plugged in some order. The wires are considered entangled if there are one or more places where one wire runs above the other one. For example, the picture below has four such places (top view): [Image] Mike knows the sequence in which the wires run above each other. Mike also noticed that on the left side, the "plus" wire is always plugged into the top contact (as seen on the picture). He would like to untangle the wires without unplugging them and without moving the device. Determine if it is possible to do that. A wire can be freely moved and stretched on the floor, but cannot be cut. To understand the problem better please read the notes to the test samples. -----Input----- The single line of the input contains a sequence of characters "+" and "-" of length n (1 ≤ n ≤ 100000). The i-th (1 ≤ i ≤ n) position of the sequence contains the character "+", if on the i-th step from the wall the "plus" wire runs above the "minus" wire, and the character "-" otherwise. -----Output----- Print either "Yes" (without the quotes) if the wires can be untangled or "No" (without the quotes) if the wires cannot be untangled. -----Examples----- Input -++- Output Yes Input +- Output No Input ++ Output Yes Input - Output No -----Note----- The first testcase corresponds to the picture in the statement. To untangle the wires, one can first move the "plus" wire lower, thus eliminating the two crosses in the middle, and then draw it under the "minus" wire, eliminating also the remaining two crosses. In the second testcase the "plus" wire makes one full revolution around the "minus" wire. Thus the wires cannot be untangled: [Image] In the third testcase the "plus" wire simply runs above the "minus" wire twice in sequence. The wires can be untangled by lifting "plus" and moving it higher: [Image] In the fourth testcase the "minus" wire runs above the "plus" wire once. The wires cannot be untangled without moving the device itself: [Image] Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Vasya is studying number theory. He has denoted a function f(a, b) such that: f(a, 0) = 0; f(a, b) = 1 + f(a, b - gcd(a, b)), where gcd(a, b) is the greatest common divisor of a and b. Vasya has two numbers x and y, and he wants to calculate f(x, y). He tried to do it by himself, but found out that calculating this function the way he wants to do that might take very long time. So he decided to ask you to implement a program that will calculate this function swiftly. -----Input----- The first line contains two integer numbers x and y (1 ≤ x, y ≤ 10^12). -----Output----- Print f(x, y). -----Examples----- Input 3 5 Output 3 Input 6 3 Output 1 Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The tycoon of a winery empire in Mondstadt, unmatched in every possible way. A thinker in the Knights of Favonius with an exotic appearance. This time, the brothers are dealing with a strange piece of wood marked with their names. This plank of wood can be represented as a string of n characters. Each character is either a 'D' or a 'K'. You want to make some number of cuts (possibly 0) on this string, partitioning it into several contiguous pieces, each with length at least 1. Both brothers act with dignity, so they want to split the wood as evenly as possible. They want to know the maximum number of pieces you can split the wood into such that the ratios of the number of occurrences of 'D' to the number of occurrences of 'K' in each chunk are the same. Kaeya, the curious thinker, is interested in the solution for multiple scenarios. He wants to know the answer for every prefix of the given string. Help him to solve this problem! For a string we define a ratio as a:b where 'D' appears in it a times, and 'K' appears b times. Note that a or b can equal 0, but not both. Ratios a:b and c:d are considered equal if and only if a⋅ d = b⋅ c. For example, for the string 'DDD' the ratio will be 3:0, for 'DKD' — 2:1, for 'DKK' — 1:2, and for 'KKKKDD' — 2:4. Note that the ratios of the latter two strings are equal to each other, but they are not equal to the ratios of the first two strings. Input Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 1000). Description of the test cases follows. The first line of each test case contains an integer n (1 ≤ n ≤ 5 ⋅ 10^5) — the length of the wood. The second line of each test case contains a string s of length n. Every character of s will be either 'D' or 'K'. It is guaranteed that the sum of n over all test cases does not exceed 5 ⋅ 10^5. Output For each test case, output n space separated integers. The i-th of these numbers should equal the answer for the prefix s_{1},s_{2},...,s_{i}. Example Input 5 3 DDK 6 DDDDDD 4 DKDK 1 D 9 DKDKDDDDK Output 1 2 1 1 2 3 4 5 6 1 1 1 2 1 1 1 1 2 1 2 1 1 3 Note For the first test case, there is no way to partition 'D' or 'DDK' into more than one block with equal ratios of numbers of 'D' and 'K', while you can split 'DD' into 'D' and 'D'. For the second test case, you can split each prefix of length i into i blocks 'D'. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. A competitive eater, Alice is scheduling some practices for an eating contest on a magical calendar. The calendar is unusual because a week contains not necessarily $7$ days! In detail, she can choose any integer $k$ which satisfies $1 \leq k \leq r$, and set $k$ days as the number of days in a week. Alice is going to paint some $n$ consecutive days on this calendar. On this calendar, dates are written from the left cell to the right cell in a week. If a date reaches the last day of a week, the next day's cell is the leftmost cell in the next (under) row. She wants to make all of the painted cells to be connected by side. It means, that for any two painted cells there should exist at least one sequence of painted cells, started in one of these cells, and ended in another, such that any two consecutive cells in this sequence are connected by side. Alice is considering the shape of the painted cells. Two shapes are the same if there exists a way to make them exactly overlapped using only parallel moves, parallel to the calendar's sides. For example, in the picture, a week has $4$ days and Alice paints $5$ consecutive days. [1] and [2] are different shapes, but [1] and [3] are equal shapes. [Image] Alice wants to know how many possible shapes exists if she set how many days a week has and choose consecutive $n$ days and paints them in calendar started in one of the days of the week. As was said before, she considers only shapes, there all cells are connected by side. -----Input----- The input consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 1000$) — the number of test cases. Next $t$ lines contain descriptions of test cases. For each test case, the only line contains two integers $n$, $r$ ($1 \le n \le 10^9, 1 \le r \le 10^9$). -----Output----- For each test case, print a single integer — the answer to the problem. Please note, that the answer for some test cases won't fit into $32$-bit integer type, so you should use at least $64$-bit integer type in your programming language. -----Example----- Input 5 3 4 3 2 3 1 13 7 1010000 9999999 Output 4 3 1 28 510049495001 -----Note----- In the first test case, Alice can set $1,2,3$ or $4$ days as the number of days in a week. There are $6$ possible paintings shown in the picture, but there are only $4$ different shapes. So, the answer is $4$. Notice that the last example in the picture is an invalid painting because all cells are not connected by sides. [Image] In the last test case, be careful with the overflow issue, described in the output format. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. A string is called bracket sequence if it does not contain any characters other than "(" and ")". A bracket sequence is called regular if it it is possible to obtain correct arithmetic expression by inserting characters "+" and "1" into this sequence. For example, "", "(())" and "()()" are regular bracket sequences; "))" and ")((" are bracket sequences (but not regular ones), and "(a)" and "(1)+(1)" are not bracket sequences at all. You have a number of strings; each string is a bracket sequence of length $2$. So, overall you have $cnt_1$ strings "((", $cnt_2$ strings "()", $cnt_3$ strings ")(" and $cnt_4$ strings "))". You want to write all these strings in some order, one after another; after that, you will get a long bracket sequence of length $2(cnt_1 + cnt_2 + cnt_3 + cnt_4)$. You wonder: is it possible to choose some order of the strings you have such that you will get a regular bracket sequence? Note that you may not remove any characters or strings, and you may not add anything either. -----Input----- The input consists of four lines, $i$-th of them contains one integer $cnt_i$ ($0 \le cnt_i \le 10^9$). -----Output----- Print one integer: $1$ if it is possible to form a regular bracket sequence by choosing the correct order of the given strings, $0$ otherwise. -----Examples----- Input 3 1 4 3 Output 1 Input 0 0 0 0 Output 1 Input 1 2 3 4 Output 0 -----Note----- In the first example it is possible to construct a string "(())()(()((()()()())))", which is a regular bracket sequence. In the second example it is possible to construct a string "", which is a regular bracket sequence. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Given an array of 4 integers ```[a,b,c,d]``` representing two points ```(a, b)``` and ```(c, d)```, return a string representation of the slope of the line joining these two points. For an undefined slope (division by 0), return ```undefined``` . Note that the "undefined" is case-sensitive. ``` a:x1 b:y1 c:x2 d:y2 ``` Assume that ```[a,b,c,d]``` and the answer are all integers (no floating numbers!). Slope: Write your solution by modifying this code: ```python def find_slope(points): ``` Your solution should implemented in the function "find_slope". The i Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Masha has three sticks of length $a$, $b$ and $c$ centimeters respectively. In one minute Masha can pick one arbitrary stick and increase its length by one centimeter. She is not allowed to break sticks. What is the minimum number of minutes she needs to spend increasing the stick's length in order to be able to assemble a triangle of positive area. Sticks should be used as triangle's sides (one stick for one side) and their endpoints should be located at triangle's vertices. -----Input----- The only line contains tree integers $a$, $b$ and $c$ ($1 \leq a, b, c \leq 100$) — the lengths of sticks Masha possesses. -----Output----- Print a single integer — the minimum number of minutes that Masha needs to spend in order to be able to make the triangle of positive area from her sticks. -----Examples----- Input 3 4 5 Output 0 Input 2 5 3 Output 1 Input 100 10 10 Output 81 -----Note----- In the first example, Masha can make a triangle from the sticks without increasing the length of any of them. In the second example, Masha can't make a triangle of positive area from the sticks she has at the beginning, but she can spend one minute to increase the length $2$ centimeter stick by one and after that form a triangle with sides $3$, $3$ and $5$ centimeters. In the third example, Masha can take $33$ minutes to increase one of the $10$ centimeters sticks by $33$ centimeters, and after that take $48$ minutes to increase another $10$ centimeters stick by $48$ centimeters. This way she can form a triangle with lengths $43$, $58$ and $100$ centimeters in $81$ minutes. One can show that it is impossible to get a valid triangle faster. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Let's call two strings $s$ and $t$ anagrams of each other if it is possible to rearrange symbols in the string $s$ to get a string, equal to $t$. Let's consider two strings $s$ and $t$ which are anagrams of each other. We say that $t$ is a reducible anagram of $s$ if there exists an integer $k \ge 2$ and $2k$ non-empty strings $s_1, t_1, s_2, t_2, \dots, s_k, t_k$ that satisfy the following conditions: If we write the strings $s_1, s_2, \dots, s_k$ in order, the resulting string will be equal to $s$; If we write the strings $t_1, t_2, \dots, t_k$ in order, the resulting string will be equal to $t$; For all integers $i$ between $1$ and $k$ inclusive, $s_i$ and $t_i$ are anagrams of each other. If such strings don't exist, then $t$ is said to be an irreducible anagram of $s$. Note that these notions are only defined when $s$ and $t$ are anagrams of each other. For example, consider the string $s = $ "gamegame". Then the string $t = $ "megamage" is a reducible anagram of $s$, we may choose for example $s_1 = $ "game", $s_2 = $ "gam", $s_3 = $ "e" and $t_1 = $ "mega", $t_2 = $ "mag", $t_3 = $ "e": [Image] On the other hand, we can prove that $t = $ "memegaga" is an irreducible anagram of $s$. You will be given a string $s$ and $q$ queries, represented by two integers $1 \le l \le r \le \|s\|$ (where $\|s\|$ is equal to the length of the string $s$). For each query, you should find if the substring of $s$ formed by characters from the $l$-th to the $r$-th has at least one irreducible anagram. -----Input----- The first line contains a string $s$, consisting of lowercase English characters ($1 \le \|s\| \le 2 \cdot 10^5$). The second line contains a single integer $q$ ($1 \le q \le 10^5$) — the number of queries. Each of the following $q$ lines contain two integers $l$ and $r$ ($1 \le l \le r \le \|s\|$), representing a query for the substring of $s$ formed by characters from the $l$-th to the $r$-th. -----Output----- For each query, print a single line containing "Yes" (without quotes) if the corresponding substring has at least one irreducible anagram, and a single line containing "No" (without quotes) otherwise. -----Examples----- Input aaaaa 3 1 1 2 4 5 5 Output Yes No Yes Input aabbbbbbc 6 1 2 2 4 2 2 1 9 5 7 3 5 Output No Yes Yes Yes No No -----Note----- In the first sample, in the first and third queries, the substring is "a", which has itself as an irreducible anagram since two or more non-empty strings cannot be put together to obtain "a". On the other hand, in the second query, the substring is "aaa", which has no irreducible anagrams: its only anagram is itself, and we may choose $s_1 = $ "a", $s_2 = $ "aa", $t_1 = $ "a", $t_2 = $ "aa" to show that it is a reducible anagram. In the second query of the second sample, the substring is "abb", which has, for example, "bba" as an irreducible anagram. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. HQ9+ is a joke programming language which has only four one-character instructions: * "H" prints "Hello, World!", * "Q" prints the source code of the program itself, * "9" prints the lyrics of "99 Bottles of Beer" song, * "+" increments the value stored in the internal accumulator. Instructions "H" and "Q" are case-sensitive and must be uppercase. The characters of the program which are not instructions are ignored. You are given a program written in HQ9+. You have to figure out whether executing this program will produce any output. Input The input will consist of a single line p which will give a program in HQ9+. String p will contain between 1 and 100 characters, inclusive. ASCII-code of each character of p will be between 33 (exclamation mark) and 126 (tilde), inclusive. Output Output "YES", if executing the program will produce any output, and "NO" otherwise. Examples Input Hi! Output YES Input Codeforces Output NO Note In the first case the program contains only one instruction — "H", which prints "Hello, World!". In the second case none of the program characters are language instructions. Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.

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