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Provide tags and a correct Python 3 solution for this coding contest problem. You are given a sequence of integers of length n and integer number k. You should print any integer number x in the range of [1; 10^9] (i.e. 1 ≀ x ≀ 10^9) such that exactly k elements of given sequence are less than or equal to x. Note that the sequence can contain equal elements. If there is no such x, print "-1" (without quotes). Input The first line of the input contains integer numbers n and k (1 ≀ n ≀ 2 β‹… 10^5, 0 ≀ k ≀ n). The second line of the input contains n integer numbers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” the sequence itself. Output Print any integer number x from range [1; 10^9] such that exactly k elements of given sequence is less or equal to x. If there is no such x, print "-1" (without quotes). Examples Input 7 4 3 7 5 1 10 3 20 Output 6 Input 7 2 3 7 5 1 10 3 20 Output -1 Note In the first example 5 is also a valid answer because the elements with indices [1, 3, 4, 6] is less than or equal to 5 and obviously less than or equal to 6. In the second example you cannot choose any number that only 2 elements of the given sequence will be less than or equal to this number because 3 elements of the given sequence will be also less than or equal to this number.
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Tags: sortings Correct Solution: ``` n,k=map(int,input().split()) t=list(map(int,input().split())) t.sort() t=t[::-1] d={} for i in t: if d.get(i)==None: d[i]=1 else: d[i]+=1 s=0 a=0 while d!={} and s<k: l=d.popitem() s+=l[1] a=l[0] if k==0 and t[-1]!=1: print(1) elif s==k and k!=0: print(a) else: print(-1) ```
output
1
3,066
12
6,133
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a sequence of integers of length n and integer number k. You should print any integer number x in the range of [1; 10^9] (i.e. 1 ≀ x ≀ 10^9) such that exactly k elements of given sequence are less than or equal to x. Note that the sequence can contain equal elements. If there is no such x, print "-1" (without quotes). Input The first line of the input contains integer numbers n and k (1 ≀ n ≀ 2 β‹… 10^5, 0 ≀ k ≀ n). The second line of the input contains n integer numbers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” the sequence itself. Output Print any integer number x from range [1; 10^9] such that exactly k elements of given sequence is less or equal to x. If there is no such x, print "-1" (without quotes). Examples Input 7 4 3 7 5 1 10 3 20 Output 6 Input 7 2 3 7 5 1 10 3 20 Output -1 Note In the first example 5 is also a valid answer because the elements with indices [1, 3, 4, 6] is less than or equal to 5 and obviously less than or equal to 6. In the second example you cannot choose any number that only 2 elements of the given sequence will be less than or equal to this number because 3 elements of the given sequence will be also less than or equal to this number.
instruction
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3,067
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Tags: sortings Correct Solution: ``` import sys input = sys.stdin.readline n, k = map(int, input().split()) a = list(map(int, input().split())) a.sort() if k==0: if a[0]==1: print(-1) else: print(1) elif k<=n-1 and a[k-1]==a[k]: print(-1) else: print(a[k-1]) ```
output
1
3,067
12
6,135
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a sequence of integers of length n and integer number k. You should print any integer number x in the range of [1; 10^9] (i.e. 1 ≀ x ≀ 10^9) such that exactly k elements of given sequence are less than or equal to x. Note that the sequence can contain equal elements. If there is no such x, print "-1" (without quotes). Input The first line of the input contains integer numbers n and k (1 ≀ n ≀ 2 β‹… 10^5, 0 ≀ k ≀ n). The second line of the input contains n integer numbers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” the sequence itself. Output Print any integer number x from range [1; 10^9] such that exactly k elements of given sequence is less or equal to x. If there is no such x, print "-1" (without quotes). Examples Input 7 4 3 7 5 1 10 3 20 Output 6 Input 7 2 3 7 5 1 10 3 20 Output -1 Note In the first example 5 is also a valid answer because the elements with indices [1, 3, 4, 6] is less than or equal to 5 and obviously less than or equal to 6. In the second example you cannot choose any number that only 2 elements of the given sequence will be less than or equal to this number because 3 elements of the given sequence will be also less than or equal to this number. Submitted Solution: ``` def quickSort(alist): quickSortHelper(alist,0,len(alist)-1) def quickSortHelper(alist,first,last): if first<last: splitpoint = partition(alist,first,last) quickSortHelper(alist,first,splitpoint-1) quickSortHelper(alist,splitpoint+1,last) def partition(alist,first,last): pivotvalue = alist[int((first+last)/2)] leftmark = first+1 rightmark = last done = False while not done: while leftmark <= rightmark and alist[leftmark] <= pivotvalue: leftmark = leftmark + 1 while alist[rightmark] >= pivotvalue and rightmark >= leftmark: rightmark = rightmark -1 if rightmark < leftmark: done = True else: temp = alist[leftmark] alist[leftmark] = alist[rightmark] alist[rightmark] = temp temp = alist[first] alist[first] = alist[rightmark] alist[rightmark] = temp return rightmark n,k = map(int,input().split()) alist = [int(x) for x in input().split()] alist.sort() if k==0: if alist[0]==1: print(-1) else: print(alist[0]-1) else: if k==n: print(alist[n-1]) else: if alist[k-1]==alist[k]: print(-1) else: print(alist[k-1]) ```
instruction
0
3,068
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Yes
output
1
3,068
12
6,137
Provide a correct Python 3 solution for this coding contest problem. In this problem, we consider a simple programming language that has only declarations of one- dimensional integer arrays and assignment statements. The problem is to find a bug in the given program. The syntax of this language is given in BNF as follows: <image> where <new line> denotes a new line character (LF). Characters used in a program are alphabetical letters, decimal digits, =, [, ] and new line characters. No other characters appear in a program. A declaration declares an array and specifies its length. Valid indices of an array of length n are integers between 0 and n - 1, inclusive. Note that the array names are case sensitive, i.e. array a and array A are different arrays. The initial value of each element in the declared array is undefined. For example, array a of length 10 and array b of length 5 are declared respectively as follows. a[10] b[5] An expression evaluates to a non-negative integer. A <number> is interpreted as a decimal integer. An <array_name> [<expression>] evaluates to the value of the <expression> -th element of the array. An assignment assigns the value denoted by the right hand side to the array element specified by the left hand side. Examples of assignments are as follows. a[0]=3 a[1]=0 a[2]=a[a[1]] a[a[0]]=a[1] A program is executed from the first line, line by line. You can assume that an array is declared once and only once before any of its element is assigned or referred to. Given a program, you are requested to find the following bugs. * An index of an array is invalid. * An array element that has not been assigned before is referred to in an assignment as an index of array or as the value to be assigned. You can assume that other bugs, such as syntax errors, do not appear. You can also assume that integers represented by <number>s are between 0 and 231 - 1 (= 2147483647), inclusive. Input The input consists of multiple datasets followed by a line which contains only a single '.' (period). Each dataset consists of a program also followed by a line which contains only a single '.' (period). A program does not exceed 1000 lines. Any line does not exceed 80 characters excluding a new line character. Output For each program in the input, you should answer the line number of the assignment in which the first bug appears. The line numbers start with 1 for each program. If the program does not have a bug, you should answer zero. The output should not contain extra characters such as spaces. Example Input a[3] a[0]=a[1] . x[1] x[0]=x[0] . a[0] a[0]=1 . b[2] b[0]=2 b[1]=b[b[0]] b[0]=b[1] . g[2] G[10] g[0]=0 g[1]=G[0] . a[2147483647] a[0]=1 B[2] B[a[0]]=2 a[B[a[0]]]=3 a[2147483646]=a[2] . . Output 2 2 2 3 4 0
instruction
0
3,273
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6,546
"Correct Solution: ``` import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools sys.setrecursionlimit(10**7) inf = 10**20 eps = 1.0 / 10**13 mod = 10**9+7 dd = [(-1,0),(0,1),(1,0),(0,-1)] ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)] def LI(): return [int(x) for x in sys.stdin.readline().split()] def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()] def LF(): return [float(x) for x in sys.stdin.readline().split()] def LS(): return sys.stdin.readline().split() def I(): return int(sys.stdin.readline()) def F(): return float(sys.stdin.readline()) def S(): return input() def pf(s): return print(s, flush=True) def main(): rr = [] def f(n): _a = [n] while 1: s = S() if s == '.': break _a.append(s) _ks = {} _d = {} for _i in range(len(_a)): _s = _a[_i] if '=' in _s: try: exec(_s,_d) for _k in _ks.keys(): # print('_k',_k) _kl = _d[_k].keys() # print('_kl',_kl) if _kl and max(_kl) >= _ks[_k]: # print('mk', _s, _k,_kl) return _i + 1 except: # print('except', _s) # print('_d',_d.keys(),_d['z']) return _i + 1 else: _k = _s.split('[')[0] _n = int(_s.split('[')[1].split(']')[0]) _ks[_k] = _n # print('tg', _k + ' = {}', _n) if _n < 1: continue exec(_k+"={}",_d) return 0 while 1: n = S() if n == '.': break rr.append(f(n)) return '\n'.join(map(str,rr)) print(main()) ```
output
1
3,273
12
6,547
Provide a correct Python 3 solution for this coding contest problem. In this problem, we consider a simple programming language that has only declarations of one- dimensional integer arrays and assignment statements. The problem is to find a bug in the given program. The syntax of this language is given in BNF as follows: <image> where <new line> denotes a new line character (LF). Characters used in a program are alphabetical letters, decimal digits, =, [, ] and new line characters. No other characters appear in a program. A declaration declares an array and specifies its length. Valid indices of an array of length n are integers between 0 and n - 1, inclusive. Note that the array names are case sensitive, i.e. array a and array A are different arrays. The initial value of each element in the declared array is undefined. For example, array a of length 10 and array b of length 5 are declared respectively as follows. a[10] b[5] An expression evaluates to a non-negative integer. A <number> is interpreted as a decimal integer. An <array_name> [<expression>] evaluates to the value of the <expression> -th element of the array. An assignment assigns the value denoted by the right hand side to the array element specified by the left hand side. Examples of assignments are as follows. a[0]=3 a[1]=0 a[2]=a[a[1]] a[a[0]]=a[1] A program is executed from the first line, line by line. You can assume that an array is declared once and only once before any of its element is assigned or referred to. Given a program, you are requested to find the following bugs. * An index of an array is invalid. * An array element that has not been assigned before is referred to in an assignment as an index of array or as the value to be assigned. You can assume that other bugs, such as syntax errors, do not appear. You can also assume that integers represented by <number>s are between 0 and 231 - 1 (= 2147483647), inclusive. Input The input consists of multiple datasets followed by a line which contains only a single '.' (period). Each dataset consists of a program also followed by a line which contains only a single '.' (period). A program does not exceed 1000 lines. Any line does not exceed 80 characters excluding a new line character. Output For each program in the input, you should answer the line number of the assignment in which the first bug appears. The line numbers start with 1 for each program. If the program does not have a bug, you should answer zero. The output should not contain extra characters such as spaces. Example Input a[3] a[0]=a[1] . x[1] x[0]=x[0] . a[0] a[0]=1 . b[2] b[0]=2 b[1]=b[b[0]] b[0]=b[1] . g[2] G[10] g[0]=0 g[1]=G[0] . a[2147483647] a[0]=1 B[2] B[a[0]]=2 a[B[a[0]]]=3 a[2147483646]=a[2] . . Output 2 2 2 3 4 0
instruction
0
3,274
12
6,548
"Correct Solution: ``` import re def get_value(expr, array_size, array): seq = expr.replace(']', '').split('[') seq[-1] = int(seq[-1]) while len(seq) > 1: ind = seq.pop() arr = seq.pop() if arr not in array or ind not in array[arr]: raise KeyError seq.append(array[arr][ind]) return seq[0] def testcase_ends(): array_size = {} array = {} decl_prog = re.compile(r'(\w)\[(\d+)\]') line = input().strip() if line == '.': return True i = 1 while True: if line == '.': print(0) return False if '=' in line: # assignment lhs, rhs = line.split('=') name = lhs[0] try: ind = get_value(lhs[2:-1], array_size, array) value = get_value(rhs, array_size, array) if name not in array or ind >= array_size[name]: raise KeyError array[name][ind] = value except KeyError: print(i) break else: # declaration m = decl_prog.fullmatch(line) assert m is not None name = m.group(1) size = int(m.group(2)) array_size[name] = size array[name] = {} line = input().strip() i += 1 line = input().strip() while line != '.': line = input().strip() return False while not testcase_ends(): pass ```
output
1
3,274
12
6,549
Provide a correct Python 3 solution for this coding contest problem. In this problem, we consider a simple programming language that has only declarations of one- dimensional integer arrays and assignment statements. The problem is to find a bug in the given program. The syntax of this language is given in BNF as follows: <image> where <new line> denotes a new line character (LF). Characters used in a program are alphabetical letters, decimal digits, =, [, ] and new line characters. No other characters appear in a program. A declaration declares an array and specifies its length. Valid indices of an array of length n are integers between 0 and n - 1, inclusive. Note that the array names are case sensitive, i.e. array a and array A are different arrays. The initial value of each element in the declared array is undefined. For example, array a of length 10 and array b of length 5 are declared respectively as follows. a[10] b[5] An expression evaluates to a non-negative integer. A <number> is interpreted as a decimal integer. An <array_name> [<expression>] evaluates to the value of the <expression> -th element of the array. An assignment assigns the value denoted by the right hand side to the array element specified by the left hand side. Examples of assignments are as follows. a[0]=3 a[1]=0 a[2]=a[a[1]] a[a[0]]=a[1] A program is executed from the first line, line by line. You can assume that an array is declared once and only once before any of its element is assigned or referred to. Given a program, you are requested to find the following bugs. * An index of an array is invalid. * An array element that has not been assigned before is referred to in an assignment as an index of array or as the value to be assigned. You can assume that other bugs, such as syntax errors, do not appear. You can also assume that integers represented by <number>s are between 0 and 231 - 1 (= 2147483647), inclusive. Input The input consists of multiple datasets followed by a line which contains only a single '.' (period). Each dataset consists of a program also followed by a line which contains only a single '.' (period). A program does not exceed 1000 lines. Any line does not exceed 80 characters excluding a new line character. Output For each program in the input, you should answer the line number of the assignment in which the first bug appears. The line numbers start with 1 for each program. If the program does not have a bug, you should answer zero. The output should not contain extra characters such as spaces. Example Input a[3] a[0]=a[1] . x[1] x[0]=x[0] . a[0] a[0]=1 . b[2] b[0]=2 b[1]=b[b[0]] b[0]=b[1] . g[2] G[10] g[0]=0 g[1]=G[0] . a[2147483647] a[0]=1 B[2] B[a[0]]=2 a[B[a[0]]]=3 a[2147483646]=a[2] . . Output 2 2 2 3 4 0
instruction
0
3,275
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6,550
"Correct Solution: ``` class CustomArray: def __init__(self, sz): self.sz = sz self.vals = {} def size(self): return self.sz def assign(self, idx, val): if idx == None or val == None: return False if idx >= self.sz: return False self.vals[idx] = val return True def get(self, idx): if idx == None: return None if idx >= self.sz: return None if idx not in self.vals: return None return self.vals[idx] class Arrays: def __init__(self): self.arrays = {} def declare(self, arrName, sz): if sz == None: return False if arrName in self.arrays: return False self.arrays[arrName] = CustomArray(sz) return True def assign(self, arrName, idx, val): if arrName not in self.arrays: return False return self.arrays[arrName].assign(idx, val) def get(self, arrName, idx): if arrName not in self.arrays: return None return self.arrays[arrName].get(idx) def resolve(expression): global arrays if "[" not in expression: return int(expression) arrName = expression[0] idx = resolve(expression[2:-1]) return arrays.get(arrName, idx) def processAssignment(command): global arrays equalIdx = command.find("=") leftStr = command[:equalIdx] rightStr = command[equalIdx + 1:] leftArrName = leftStr[0] leftIdx = resolve(leftStr[2:-1]) rhs = resolve(rightStr) return arrays.assign(leftArrName, leftIdx, rhs) def processDeclaration(arrStr): global arrays arrName = arrStr[0] sz = int(arrStr[2:-1]) return arrays.declare(arrName, sz) if __name__ == '__main__': while True: commands = [] while True: line = input().strip() if line == '.': break commands.append(line) if len(commands) == 0: break errLine = 0 arrays = Arrays() for i in range(len(commands)): command = commands[i] if "=" in command: result = processAssignment(command) else: result = processDeclaration(command) if not result: errLine = i + 1 break print(errLine) ```
output
1
3,275
12
6,551
Provide a correct Python 3 solution for this coding contest problem. In this problem, we consider a simple programming language that has only declarations of one- dimensional integer arrays and assignment statements. The problem is to find a bug in the given program. The syntax of this language is given in BNF as follows: <image> where <new line> denotes a new line character (LF). Characters used in a program are alphabetical letters, decimal digits, =, [, ] and new line characters. No other characters appear in a program. A declaration declares an array and specifies its length. Valid indices of an array of length n are integers between 0 and n - 1, inclusive. Note that the array names are case sensitive, i.e. array a and array A are different arrays. The initial value of each element in the declared array is undefined. For example, array a of length 10 and array b of length 5 are declared respectively as follows. a[10] b[5] An expression evaluates to a non-negative integer. A <number> is interpreted as a decimal integer. An <array_name> [<expression>] evaluates to the value of the <expression> -th element of the array. An assignment assigns the value denoted by the right hand side to the array element specified by the left hand side. Examples of assignments are as follows. a[0]=3 a[1]=0 a[2]=a[a[1]] a[a[0]]=a[1] A program is executed from the first line, line by line. You can assume that an array is declared once and only once before any of its element is assigned or referred to. Given a program, you are requested to find the following bugs. * An index of an array is invalid. * An array element that has not been assigned before is referred to in an assignment as an index of array or as the value to be assigned. You can assume that other bugs, such as syntax errors, do not appear. You can also assume that integers represented by <number>s are between 0 and 231 - 1 (= 2147483647), inclusive. Input The input consists of multiple datasets followed by a line which contains only a single '.' (period). Each dataset consists of a program also followed by a line which contains only a single '.' (period). A program does not exceed 1000 lines. Any line does not exceed 80 characters excluding a new line character. Output For each program in the input, you should answer the line number of the assignment in which the first bug appears. The line numbers start with 1 for each program. If the program does not have a bug, you should answer zero. The output should not contain extra characters such as spaces. Example Input a[3] a[0]=a[1] . x[1] x[0]=x[0] . a[0] a[0]=1 . b[2] b[0]=2 b[1]=b[b[0]] b[0]=b[1] . g[2] G[10] g[0]=0 g[1]=G[0] . a[2147483647] a[0]=1 B[2] B[a[0]]=2 a[B[a[0]]]=3 a[2147483646]=a[2] . . Output 2 2 2 3 4 0
instruction
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3,276
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"Correct Solution: ``` import re def deref(d, expr): expr = expr.replace(']', '') symb = expr.split('[') symb[-1] = symb[-1] while len(symb) > 1: name, index = symb[-2:] if index not in d[name]: return None symb.pop() symb.pop() symb.append(d[name][index]) return symb[0] def check(s): d = {} dd = {} for i, stmt in enumerate(s, 1): if '=' not in stmt: name = stmt[0] index = stmt[2:-1] d[name] = {} dd[name] = int(index) continue lhs, rhs = stmt.split('=') name = lhs[0] index = lhs[2:-1] index = deref(d, index) value = deref(d, rhs) if index is None or value is None or int(index) >= dd[name]: print(i) return d[name][index] = value print(0) def main(): list_ = [] with open(0) as fin: for line in fin: line = line.strip() if line == '.': if not list_: return 0 check(list_) list_ = [] continue list_.append(line) if __name__ == '__main__': main() ```
output
1
3,276
12
6,553
Provide tags and a correct Python 3 solution for this coding contest problem. Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation. For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2]. The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation. Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque. Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides. Input The first line contains two integers n and q (2 ≀ n ≀ 10^5, 0 ≀ q ≀ 3 β‹… 10^5) β€” the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≀ a_i ≀ 10^9) β€” the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≀ m_j ≀ 10^{18}). Output For each teacher's query, output two numbers A and B β€” the numbers that Valeriy pulls out of the deque for the m_j-th operation. Examples Input 5 3 1 2 3 4 5 1 2 10 Output 1 2 2 3 5 2 Input 2 0 0 0 Output Note Consider all 10 steps for the first test in detail: 1. [1, 2, 3, 4, 5] β€” on the first operation, A and B are 1 and 2, respectively. So, 2 we write to the beginning of the deque, and 1 β€” to the end. We get the following status of the deque: [2, 3, 4, 5, 1]. 2. [2, 3, 4, 5, 1] β‡’ A = 2, B = 3. 3. [3, 4, 5, 1, 2] 4. [4, 5, 1, 2, 3] 5. [5, 1, 2, 3, 4] 6. [5, 2, 3, 4, 1] 7. [5, 3, 4, 1, 2] 8. [5, 4, 1, 2, 3] 9. [5, 1, 2, 3, 4] 10. [5, 2, 3, 4, 1] β‡’ A = 5, B = 2.
instruction
0
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Tags: data structures, implementation Correct Solution: ``` def getN(): return int(input()) def getList(): return list(map(int, input().split())) from collections import deque n, m = getList() nums = getList() mxnum = max(nums) d = deque(nums) qr = [] for i in range(m): qr.append(getN()) log = [] rot = 0 while(True): # print(d) a = d.popleft() b = d.popleft() log.append((a, b)) if a > b: a, b = b, a d.append(a) d.appendleft(b) rot += 1 if b == mxnum: break for q in qr: if q <= rot: print(log[q - 1][0], log[q - 1][1]) else: res = q - rot - 1 print(b, d[res % (n-1) + 1 ]) # print(d) """ 5 10 1 2 5 4 3 1 2 3 4 5 6 7 8 9 10 """ ```
output
1
3,392
12
6,785
Provide tags and a correct Python 3 solution for this coding contest problem. Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation. For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2]. The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation. Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque. Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides. Input The first line contains two integers n and q (2 ≀ n ≀ 10^5, 0 ≀ q ≀ 3 β‹… 10^5) β€” the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≀ a_i ≀ 10^9) β€” the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≀ m_j ≀ 10^{18}). Output For each teacher's query, output two numbers A and B β€” the numbers that Valeriy pulls out of the deque for the m_j-th operation. Examples Input 5 3 1 2 3 4 5 1 2 10 Output 1 2 2 3 5 2 Input 2 0 0 0 Output Note Consider all 10 steps for the first test in detail: 1. [1, 2, 3, 4, 5] β€” on the first operation, A and B are 1 and 2, respectively. So, 2 we write to the beginning of the deque, and 1 β€” to the end. We get the following status of the deque: [2, 3, 4, 5, 1]. 2. [2, 3, 4, 5, 1] β‡’ A = 2, B = 3. 3. [3, 4, 5, 1, 2] 4. [4, 5, 1, 2, 3] 5. [5, 1, 2, 3, 4] 6. [5, 2, 3, 4, 1] 7. [5, 3, 4, 1, 2] 8. [5, 4, 1, 2, 3] 9. [5, 1, 2, 3, 4] 10. [5, 2, 3, 4, 1] β‡’ A = 5, B = 2.
instruction
0
3,393
12
6,786
Tags: data structures, implementation Correct Solution: ``` import sys input=sys.stdin.readline from collections import defaultdict as dc from collections import Counter from bisect import bisect_right, bisect_left import math from operator import itemgetter from heapq import heapify, heappop, heappush n,q=map(int,input().split()) l=list(map(int,input().split())) p=[] t=[] x=l[0] for i in range(1,n): p.append([x,l[i]]) if l[i]>=x: t.append(x) x=l[i] else: t.append(l[i]) t.insert(0,x) #print(x,t,p) for _ in range(q): a=int(input()) if a<=n-1: print(*p[a-1]) else: y=a-n+1 j=y%(n-1) if j==0: j=-1 print(t[0],t[j]) ```
output
1
3,393
12
6,787
Provide tags and a correct Python 3 solution for this coding contest problem. Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation. For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2]. The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation. Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque. Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides. Input The first line contains two integers n and q (2 ≀ n ≀ 10^5, 0 ≀ q ≀ 3 β‹… 10^5) β€” the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≀ a_i ≀ 10^9) β€” the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≀ m_j ≀ 10^{18}). Output For each teacher's query, output two numbers A and B β€” the numbers that Valeriy pulls out of the deque for the m_j-th operation. Examples Input 5 3 1 2 3 4 5 1 2 10 Output 1 2 2 3 5 2 Input 2 0 0 0 Output Note Consider all 10 steps for the first test in detail: 1. [1, 2, 3, 4, 5] β€” on the first operation, A and B are 1 and 2, respectively. So, 2 we write to the beginning of the deque, and 1 β€” to the end. We get the following status of the deque: [2, 3, 4, 5, 1]. 2. [2, 3, 4, 5, 1] β‡’ A = 2, B = 3. 3. [3, 4, 5, 1, 2] 4. [4, 5, 1, 2, 3] 5. [5, 1, 2, 3, 4] 6. [5, 2, 3, 4, 1] 7. [5, 3, 4, 1, 2] 8. [5, 4, 1, 2, 3] 9. [5, 1, 2, 3, 4] 10. [5, 2, 3, 4, 1] β‡’ A = 5, B = 2.
instruction
0
3,394
12
6,788
Tags: data structures, implementation Correct Solution: ``` def op(arr,num): for i in range(0,num-1): if arr[0]>arr[1]: z=arr.pop(1) arr.append(z) else: z=arr.pop(0) arr.append(z) print (arr[0],arr[1]) def opmod(arr,num): count=0 while arr[0]!=num: if arr[0]>arr[1]: z=arr.pop(1) arr.append(z) else: z=arr.pop(0) arr.append(z) count=count+1 return count a=input() a=a.split() p,q=int(a[0]),int(a[1]) a=input() arr1=a.split() for i in range(0,p): arr1[i]=int(arr1[i]) s=max(arr1) arr2=[] for i in range(0,q): a=int(input()) arr2.append(a) arr3=[] for j in range(0,p): arr3.append(arr1[j]) rounds=opmod(arr3,s)+1 for i in range(0,q): if arr2[i]<rounds: arr4=[] for j in range(0,p): arr4.append(arr1[j]) op(arr4,arr2[i]) else: rec=(arr2[i]-rounds)%(p-1) print (arr3[0],arr3[1+rec]) ```
output
1
3,394
12
6,789
Provide tags and a correct Python 3 solution for this coding contest problem. Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation. For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2]. The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation. Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque. Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides. Input The first line contains two integers n and q (2 ≀ n ≀ 10^5, 0 ≀ q ≀ 3 β‹… 10^5) β€” the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≀ a_i ≀ 10^9) β€” the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≀ m_j ≀ 10^{18}). Output For each teacher's query, output two numbers A and B β€” the numbers that Valeriy pulls out of the deque for the m_j-th operation. Examples Input 5 3 1 2 3 4 5 1 2 10 Output 1 2 2 3 5 2 Input 2 0 0 0 Output Note Consider all 10 steps for the first test in detail: 1. [1, 2, 3, 4, 5] β€” on the first operation, A and B are 1 and 2, respectively. So, 2 we write to the beginning of the deque, and 1 β€” to the end. We get the following status of the deque: [2, 3, 4, 5, 1]. 2. [2, 3, 4, 5, 1] β‡’ A = 2, B = 3. 3. [3, 4, 5, 1, 2] 4. [4, 5, 1, 2, 3] 5. [5, 1, 2, 3, 4] 6. [5, 2, 3, 4, 1] 7. [5, 3, 4, 1, 2] 8. [5, 4, 1, 2, 3] 9. [5, 1, 2, 3, 4] 10. [5, 2, 3, 4, 1] β‡’ A = 5, B = 2.
instruction
0
3,395
12
6,790
Tags: data structures, implementation Correct Solution: ``` n,k=map(int,input().split()) a=list(map(int,input().split())) mx=max(a) ind=a.index(mx) f=0 s=1 ans=[[] for i in range(ind)] for i in range(ind): ans[i].append(a[f]) ans[i].append(a[s]) if(a[f]>=a[s]): a.append(a[s]) s+=1 else: a.append(a[f]) f=s s+=1 a=a[ind:] #print(a) for i in range(k): m=int(input()) if(m<=ind): print(ans[m-1][0],ans[m-1][1]) else: m-=ind m-=1 m%=(n-1) print(a[0],a[1+m]) ```
output
1
3,395
12
6,791
Provide tags and a correct Python 3 solution for this coding contest problem. Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation. For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2]. The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation. Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque. Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides. Input The first line contains two integers n and q (2 ≀ n ≀ 10^5, 0 ≀ q ≀ 3 β‹… 10^5) β€” the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≀ a_i ≀ 10^9) β€” the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≀ m_j ≀ 10^{18}). Output For each teacher's query, output two numbers A and B β€” the numbers that Valeriy pulls out of the deque for the m_j-th operation. Examples Input 5 3 1 2 3 4 5 1 2 10 Output 1 2 2 3 5 2 Input 2 0 0 0 Output Note Consider all 10 steps for the first test in detail: 1. [1, 2, 3, 4, 5] β€” on the first operation, A and B are 1 and 2, respectively. So, 2 we write to the beginning of the deque, and 1 β€” to the end. We get the following status of the deque: [2, 3, 4, 5, 1]. 2. [2, 3, 4, 5, 1] β‡’ A = 2, B = 3. 3. [3, 4, 5, 1, 2] 4. [4, 5, 1, 2, 3] 5. [5, 1, 2, 3, 4] 6. [5, 2, 3, 4, 1] 7. [5, 3, 4, 1, 2] 8. [5, 4, 1, 2, 3] 9. [5, 1, 2, 3, 4] 10. [5, 2, 3, 4, 1] β‡’ A = 5, B = 2.
instruction
0
3,396
12
6,792
Tags: data structures, implementation Correct Solution: ``` a, b = map(int, input().split()) A = list(map(int, input().split())) A.append(-1) B = [] Z = [] AN = [] x, y = A[0], A[1] for i in range(a - 1): Z.append((x, y)) if x > y: B.append(y) y = A[i + 2] else: B.append(x) x, y = y, A[i + 2] for i in range(b): w = int(input()) if w <= len(Z): AN.append(Z[w - 1]) else: w = w % len(B) AN.append((x, B[w - 1])) for W in AN: print(*W) ```
output
1
3,396
12
6,793
Provide tags and a correct Python 3 solution for this coding contest problem. Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation. For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2]. The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation. Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque. Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides. Input The first line contains two integers n and q (2 ≀ n ≀ 10^5, 0 ≀ q ≀ 3 β‹… 10^5) β€” the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≀ a_i ≀ 10^9) β€” the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≀ m_j ≀ 10^{18}). Output For each teacher's query, output two numbers A and B β€” the numbers that Valeriy pulls out of the deque for the m_j-th operation. Examples Input 5 3 1 2 3 4 5 1 2 10 Output 1 2 2 3 5 2 Input 2 0 0 0 Output Note Consider all 10 steps for the first test in detail: 1. [1, 2, 3, 4, 5] β€” on the first operation, A and B are 1 and 2, respectively. So, 2 we write to the beginning of the deque, and 1 β€” to the end. We get the following status of the deque: [2, 3, 4, 5, 1]. 2. [2, 3, 4, 5, 1] β‡’ A = 2, B = 3. 3. [3, 4, 5, 1, 2] 4. [4, 5, 1, 2, 3] 5. [5, 1, 2, 3, 4] 6. [5, 2, 3, 4, 1] 7. [5, 3, 4, 1, 2] 8. [5, 4, 1, 2, 3] 9. [5, 1, 2, 3, 4] 10. [5, 2, 3, 4, 1] β‡’ A = 5, B = 2.
instruction
0
3,397
12
6,794
Tags: data structures, implementation Correct Solution: ``` n, t = map(int, input().split()) a = list(map(int, input().split())) b, c = [], [] u = a[0] for v in a[1:]: b.append(u) if v > u: u, v = v, u c.append(v) for _ in range(t): x = int(input()) if x < n: print(b[x-1], a[x]) else: print(u, c[(x-1) % (n-1)]) ```
output
1
3,397
12
6,795
Provide tags and a correct Python 3 solution for this coding contest problem. Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation. For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2]. The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation. Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque. Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides. Input The first line contains two integers n and q (2 ≀ n ≀ 10^5, 0 ≀ q ≀ 3 β‹… 10^5) β€” the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≀ a_i ≀ 10^9) β€” the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≀ m_j ≀ 10^{18}). Output For each teacher's query, output two numbers A and B β€” the numbers that Valeriy pulls out of the deque for the m_j-th operation. Examples Input 5 3 1 2 3 4 5 1 2 10 Output 1 2 2 3 5 2 Input 2 0 0 0 Output Note Consider all 10 steps for the first test in detail: 1. [1, 2, 3, 4, 5] β€” on the first operation, A and B are 1 and 2, respectively. So, 2 we write to the beginning of the deque, and 1 β€” to the end. We get the following status of the deque: [2, 3, 4, 5, 1]. 2. [2, 3, 4, 5, 1] β‡’ A = 2, B = 3. 3. [3, 4, 5, 1, 2] 4. [4, 5, 1, 2, 3] 5. [5, 1, 2, 3, 4] 6. [5, 2, 3, 4, 1] 7. [5, 3, 4, 1, 2] 8. [5, 4, 1, 2, 3] 9. [5, 1, 2, 3, 4] 10. [5, 2, 3, 4, 1] β‡’ A = 5, B = 2.
instruction
0
3,398
12
6,796
Tags: data structures, implementation Correct Solution: ``` n, q = map(int,input().split()) l = list(map(int,input().split())) m = max(l) tab = [0] * 2*n for i in range(n): tab[i] = l[i] odp = [[0,0]] * n pocz = 0 kon = n - 1 for j in range(n): A = tab[pocz] B = tab[pocz + 1] odp[j] = [A, B] pocz += 1 kon += 1 tab[pocz] = max(A,B) tab[kon] = min(A,B) for i in range(q): query = int(input()) if query <= n: print(odp[query - 1][0], odp[query - 1][1]) else: print(m, tab[(query-2)%(n-1)+n+1]) ```
output
1
3,398
12
6,797
Provide tags and a correct Python 3 solution for this coding contest problem. Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation. For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2]. The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation. Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque. Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides. Input The first line contains two integers n and q (2 ≀ n ≀ 10^5, 0 ≀ q ≀ 3 β‹… 10^5) β€” the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≀ a_i ≀ 10^9) β€” the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≀ m_j ≀ 10^{18}). Output For each teacher's query, output two numbers A and B β€” the numbers that Valeriy pulls out of the deque for the m_j-th operation. Examples Input 5 3 1 2 3 4 5 1 2 10 Output 1 2 2 3 5 2 Input 2 0 0 0 Output Note Consider all 10 steps for the first test in detail: 1. [1, 2, 3, 4, 5] β€” on the first operation, A and B are 1 and 2, respectively. So, 2 we write to the beginning of the deque, and 1 β€” to the end. We get the following status of the deque: [2, 3, 4, 5, 1]. 2. [2, 3, 4, 5, 1] β‡’ A = 2, B = 3. 3. [3, 4, 5, 1, 2] 4. [4, 5, 1, 2, 3] 5. [5, 1, 2, 3, 4] 6. [5, 2, 3, 4, 1] 7. [5, 3, 4, 1, 2] 8. [5, 4, 1, 2, 3] 9. [5, 1, 2, 3, 4] 10. [5, 2, 3, 4, 1] β‡’ A = 5, B = 2.
instruction
0
3,399
12
6,798
Tags: data structures, implementation Correct Solution: ``` # import sys # input = sys.stdin.readline n,queries = list(map(int,input().split())) l = list(map(int,input().split())) if(queries==0): exit() maxval = max(l) pairs = [] count = 0 f = l[0] secix = 1 while(f!=maxval): # print(l) count+=1 f = l[0] s = l[secix] pairs.append([f,s]) f,s= max(f,s), min(f,s) l[0] = f l.append(s) secix+=1 # print(secix) l = [l[0]]+l[secix:] # print(l) for i in range(n-1): pairs.append([maxval,l[1+i]]) # print(pairs) for m in range(queries): q = int(input()) if(q<=count): print(str(pairs[q-1][0]),str(pairs[q-1][1])) else: q-=(count+1) pos = count+(q%(n-1)) print(str(pairs[pos][0]),str(pairs[pos][1])) ```
output
1
3,399
12
6,799
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation. For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2]. The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation. Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque. Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides. Input The first line contains two integers n and q (2 ≀ n ≀ 10^5, 0 ≀ q ≀ 3 β‹… 10^5) β€” the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≀ a_i ≀ 10^9) β€” the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≀ m_j ≀ 10^{18}). Output For each teacher's query, output two numbers A and B β€” the numbers that Valeriy pulls out of the deque for the m_j-th operation. Examples Input 5 3 1 2 3 4 5 1 2 10 Output 1 2 2 3 5 2 Input 2 0 0 0 Output Note Consider all 10 steps for the first test in detail: 1. [1, 2, 3, 4, 5] β€” on the first operation, A and B are 1 and 2, respectively. So, 2 we write to the beginning of the deque, and 1 β€” to the end. We get the following status of the deque: [2, 3, 4, 5, 1]. 2. [2, 3, 4, 5, 1] β‡’ A = 2, B = 3. 3. [3, 4, 5, 1, 2] 4. [4, 5, 1, 2, 3] 5. [5, 1, 2, 3, 4] 6. [5, 2, 3, 4, 1] 7. [5, 3, 4, 1, 2] 8. [5, 4, 1, 2, 3] 9. [5, 1, 2, 3, 4] 10. [5, 2, 3, 4, 1] β‡’ A = 5, B = 2. Submitted Solution: ``` # !/usr/bin/env python3 # encoding: UTF-8 # Modified: <22/Jun/2019 12:28:28 AM> # βœͺ H4WK3yEδΉ‘ # Mohd. Farhan Tahir # Indian Institute Of Information Technology (IIIT), Gwalior import sys import os from io import IOBase, BytesIO def main(): from collections import deque n, tc = get_ints() arr = get_array() mx = max(arr) q = deque() for i in range(n): q.append(arr[i]) query = 1 dp = [0] * 10**6 while q[0] != mx: f = q.popleft() s = q.popleft() if (f > s): q.appendleft(f) q.append(s) else: q.appendleft(s) q.append(f) dp[query] = (f, s) query += 1 curr = 0 c2 = query while curr != n - 1: #print(q, c2) f = q.popleft() s = q.popleft() q.appendleft(f) q.append(s) dp[c2] = (f, s) curr += 1 c2 += 1 curr = 0 cycle = c2 - query while curr != n - 1: #print(q, c2) f = q.popleft() s = q.popleft() q.appendleft(f) q.append(s) dp[c2] = (f, s) curr += 1 c2 += 1 # print(dp[:10]) #print(cycle, query, c2) # print(dp[:10]) # print(c2) for _ in range(tc): j = int(input()) if j < c2: print(*dp[j]) else: j %= cycle j += cycle #print(j, "j") print(*dp[j]) # print(dp) def get_array(): return list(map(int, sys.stdin.readline().split())) def get_ints(): return map(int, sys.stdin.readline().split()) def input(): return sys.stdin.readline().strip() if __name__ == "__main__": main() ```
instruction
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3,400
12
6,800
Yes
output
1
3,400
12
6,801
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation. For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2]. The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation. Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque. Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides. Input The first line contains two integers n and q (2 ≀ n ≀ 10^5, 0 ≀ q ≀ 3 β‹… 10^5) β€” the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≀ a_i ≀ 10^9) β€” the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≀ m_j ≀ 10^{18}). Output For each teacher's query, output two numbers A and B β€” the numbers that Valeriy pulls out of the deque for the m_j-th operation. Examples Input 5 3 1 2 3 4 5 1 2 10 Output 1 2 2 3 5 2 Input 2 0 0 0 Output Note Consider all 10 steps for the first test in detail: 1. [1, 2, 3, 4, 5] β€” on the first operation, A and B are 1 and 2, respectively. So, 2 we write to the beginning of the deque, and 1 β€” to the end. We get the following status of the deque: [2, 3, 4, 5, 1]. 2. [2, 3, 4, 5, 1] β‡’ A = 2, B = 3. 3. [3, 4, 5, 1, 2] 4. [4, 5, 1, 2, 3] 5. [5, 1, 2, 3, 4] 6. [5, 2, 3, 4, 1] 7. [5, 3, 4, 1, 2] 8. [5, 4, 1, 2, 3] 9. [5, 1, 2, 3, 4] 10. [5, 2, 3, 4, 1] β‡’ A = 5, B = 2. Submitted Solution: ``` from collections import deque n,q=list(map(int,input().split())) a=list(map(int,input().rstrip().split())) a=deque(a) c=[] maxi=max(a) k=a[0] j=0 while(a[0]!=maxi): j+=1 k=a.popleft() h=a.popleft() if k>h: a.appendleft(k) a.append(h) else: a.appendleft(h) a.append(k) c.append((k,h)) for i in range(q): h=int(input())-1 if h<j: print(*c[h]) else: print(maxi,a[(h-j)%(n-1) + 1]) ```
instruction
0
3,401
12
6,802
Yes
output
1
3,401
12
6,803
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation. For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2]. The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation. Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque. Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides. Input The first line contains two integers n and q (2 ≀ n ≀ 10^5, 0 ≀ q ≀ 3 β‹… 10^5) β€” the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≀ a_i ≀ 10^9) β€” the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≀ m_j ≀ 10^{18}). Output For each teacher's query, output two numbers A and B β€” the numbers that Valeriy pulls out of the deque for the m_j-th operation. Examples Input 5 3 1 2 3 4 5 1 2 10 Output 1 2 2 3 5 2 Input 2 0 0 0 Output Note Consider all 10 steps for the first test in detail: 1. [1, 2, 3, 4, 5] β€” on the first operation, A and B are 1 and 2, respectively. So, 2 we write to the beginning of the deque, and 1 β€” to the end. We get the following status of the deque: [2, 3, 4, 5, 1]. 2. [2, 3, 4, 5, 1] β‡’ A = 2, B = 3. 3. [3, 4, 5, 1, 2] 4. [4, 5, 1, 2, 3] 5. [5, 1, 2, 3, 4] 6. [5, 2, 3, 4, 1] 7. [5, 3, 4, 1, 2] 8. [5, 4, 1, 2, 3] 9. [5, 1, 2, 3, 4] 10. [5, 2, 3, 4, 1] β‡’ A = 5, B = 2. Submitted Solution: ``` # @author import sys class CValeriyAndDeque: def solve(self): from collections import deque n, q = [int(item) for item in input().split()] a = [int(item) for item in input().split()] mi = a.index(max(a)) b = deque(a) ans = [(-1, -1)] * mi for i in range(mi): u, v = b.popleft(), b.popleft() ans[i] = (u, v) if u < v: u, v = v, u b.appendleft(u) b.append(v) b = list(b) # print(b) for _ in range(q): m = int(input()) m -= 1 if m >= mi: m -= mi print(b[0], b[1 + m % (n - 1)]) else: print(*ans[m]) solver = CValeriyAndDeque() input = sys.stdin.readline solver.solve() ```
instruction
0
3,402
12
6,804
Yes
output
1
3,402
12
6,805
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation. For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2]. The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation. Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque. Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides. Input The first line contains two integers n and q (2 ≀ n ≀ 10^5, 0 ≀ q ≀ 3 β‹… 10^5) β€” the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≀ a_i ≀ 10^9) β€” the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≀ m_j ≀ 10^{18}). Output For each teacher's query, output two numbers A and B β€” the numbers that Valeriy pulls out of the deque for the m_j-th operation. Examples Input 5 3 1 2 3 4 5 1 2 10 Output 1 2 2 3 5 2 Input 2 0 0 0 Output Note Consider all 10 steps for the first test in detail: 1. [1, 2, 3, 4, 5] β€” on the first operation, A and B are 1 and 2, respectively. So, 2 we write to the beginning of the deque, and 1 β€” to the end. We get the following status of the deque: [2, 3, 4, 5, 1]. 2. [2, 3, 4, 5, 1] β‡’ A = 2, B = 3. 3. [3, 4, 5, 1, 2] 4. [4, 5, 1, 2, 3] 5. [5, 1, 2, 3, 4] 6. [5, 2, 3, 4, 1] 7. [5, 3, 4, 1, 2] 8. [5, 4, 1, 2, 3] 9. [5, 1, 2, 3, 4] 10. [5, 2, 3, 4, 1] β‡’ A = 5, B = 2. Submitted Solution: ``` from collections import deque n, qs = tuple(map(int, input().split())) d = deque(list(map(int, input().split()))) m = max(d) if qs == 0: exit() q = [] for i in range(qs): v = int(input()) q.append([v, i, 'a', 'b']) # print(q) q.sort() # print(q) # print(q[0][0]) i = 0 curv = q[i][0] j = 1 while(d[0] != m): a = d[0] b = d[1] if a > b: d.popleft() d.popleft() d.append(b) d.appendleft(a) else: d.popleft() d.append(a) if curv == j: # print(curv) q[i][2] = a q[i][3] = b i += 1 while i < qs and (q[i][0] == curv): q[i][2] = a q[i][3] = b i += 1 if i == qs: break curv = q[i][0] # print(curv) j += 1 # print(j-1, d) while(i<qs): curv = q[i][0] q[i][2] = m q[i][3] = d[1 + (curv - j)%(n-1)] i += 1 q.sort(key=lambda x: x[1]) for f in range(qs): print(str(q[f][2]) + ' ' +str(q[f][3])) ```
instruction
0
3,403
12
6,806
Yes
output
1
3,403
12
6,807
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation. For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2]. The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation. Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque. Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides. Input The first line contains two integers n and q (2 ≀ n ≀ 10^5, 0 ≀ q ≀ 3 β‹… 10^5) β€” the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≀ a_i ≀ 10^9) β€” the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≀ m_j ≀ 10^{18}). Output For each teacher's query, output two numbers A and B β€” the numbers that Valeriy pulls out of the deque for the m_j-th operation. Examples Input 5 3 1 2 3 4 5 1 2 10 Output 1 2 2 3 5 2 Input 2 0 0 0 Output Note Consider all 10 steps for the first test in detail: 1. [1, 2, 3, 4, 5] β€” on the first operation, A and B are 1 and 2, respectively. So, 2 we write to the beginning of the deque, and 1 β€” to the end. We get the following status of the deque: [2, 3, 4, 5, 1]. 2. [2, 3, 4, 5, 1] β‡’ A = 2, B = 3. 3. [3, 4, 5, 1, 2] 4. [4, 5, 1, 2, 3] 5. [5, 1, 2, 3, 4] 6. [5, 2, 3, 4, 1] 7. [5, 3, 4, 1, 2] 8. [5, 4, 1, 2, 3] 9. [5, 1, 2, 3, 4] 10. [5, 2, 3, 4, 1] β‡’ A = 5, B = 2. Submitted Solution: ``` n,x = map(int, input().split()) m = list(map(int, input().split())) ind = 0 for i in range(n): if(m[ind]<m[i]): ind = i z = m[ind] r = m[0] ans = [] l = [] for i in range(ind): ans.append([r,m[i+1]]) l.append(r) r = m[i+1] for i in range(ind+1, n): l.append(m[i]) #l.reverse() for i in range(x): q = int(input()) if(q<=ind): print(ans[q-1][0], ans[q-1][1]) elif(q>=n): print(z, l[(q-ind-1)%(n-1)]) else: print(z, m[q]) ```
instruction
0
3,404
12
6,808
No
output
1
3,404
12
6,809
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation. For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2]. The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation. Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque. Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides. Input The first line contains two integers n and q (2 ≀ n ≀ 10^5, 0 ≀ q ≀ 3 β‹… 10^5) β€” the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≀ a_i ≀ 10^9) β€” the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≀ m_j ≀ 10^{18}). Output For each teacher's query, output two numbers A and B β€” the numbers that Valeriy pulls out of the deque for the m_j-th operation. Examples Input 5 3 1 2 3 4 5 1 2 10 Output 1 2 2 3 5 2 Input 2 0 0 0 Output Note Consider all 10 steps for the first test in detail: 1. [1, 2, 3, 4, 5] β€” on the first operation, A and B are 1 and 2, respectively. So, 2 we write to the beginning of the deque, and 1 β€” to the end. We get the following status of the deque: [2, 3, 4, 5, 1]. 2. [2, 3, 4, 5, 1] β‡’ A = 2, B = 3. 3. [3, 4, 5, 1, 2] 4. [4, 5, 1, 2, 3] 5. [5, 1, 2, 3, 4] 6. [5, 2, 3, 4, 1] 7. [5, 3, 4, 1, 2] 8. [5, 4, 1, 2, 3] 9. [5, 1, 2, 3, 4] 10. [5, 2, 3, 4, 1] β‡’ A = 5, B = 2. Submitted Solution: ``` class Dek: def __init__(self): self.items = [] def isEmpty(self): return self.items == [] def addFront(self, item): self.items.append(item) def addRear(self, item): self.items.insert(0,item) def removeFront(self): return self.items.pop() def removeRear(self): return self.items.pop(0) def size(self): return len(self.items) def op(self): a = self.removeRear() b = self.removeRear() if a > b: self.addRear(a) self.addFront(b) else: self.addRear(b) self.addFront(a) return (a, b) dek = Dek() n, q = map(int, input().split()) arr = list(map(int, input().split())) for i in range(n): dek.addFront(arr[i]) qs = [] ans = [()]*q for i in range(q): qs.append(int(input())) i = 0 while dek.items[0] != max(dek.items): a, b = dek.op() if i + 1 in qs: for k in range(len(qs)): if qs[k] == i + 1: ans[k] = (a, b) i += 1 for j in qs: if j > i: j -= i num_el = j % (n - 1) if num_el == 0: num_el = n - 1 ans[qs.index(j + i)] = (dek.items[0], dek.items[num_el]) for an in ans: print(*an) ```
instruction
0
3,405
12
6,810
No
output
1
3,405
12
6,811
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation. For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2]. The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation. Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque. Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides. Input The first line contains two integers n and q (2 ≀ n ≀ 10^5, 0 ≀ q ≀ 3 β‹… 10^5) β€” the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≀ a_i ≀ 10^9) β€” the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≀ m_j ≀ 10^{18}). Output For each teacher's query, output two numbers A and B β€” the numbers that Valeriy pulls out of the deque for the m_j-th operation. Examples Input 5 3 1 2 3 4 5 1 2 10 Output 1 2 2 3 5 2 Input 2 0 0 0 Output Note Consider all 10 steps for the first test in detail: 1. [1, 2, 3, 4, 5] β€” on the first operation, A and B are 1 and 2, respectively. So, 2 we write to the beginning of the deque, and 1 β€” to the end. We get the following status of the deque: [2, 3, 4, 5, 1]. 2. [2, 3, 4, 5, 1] β‡’ A = 2, B = 3. 3. [3, 4, 5, 1, 2] 4. [4, 5, 1, 2, 3] 5. [5, 1, 2, 3, 4] 6. [5, 2, 3, 4, 1] 7. [5, 3, 4, 1, 2] 8. [5, 4, 1, 2, 3] 9. [5, 1, 2, 3, 4] 10. [5, 2, 3, 4, 1] β‡’ A = 5, B = 2. Submitted Solution: ``` import collections if __name__ == "__main__": n, q = list(map(int, input().split())) a = collections.deque(map(int, input().split())) maxn = max(a) res = list(range(n)) cnt = 1 while True: if a[0] == maxn: break res[cnt] = [a[0], a[1]] cnt += 1 A = a.popleft() B = a.popleft() if A > B: a.appendleft(A) a.append(B) else: a.appendleft(B) a.append(A) for i in range(q): m = int(input()) if m < cnt: print(res[m][0], res[m][1]) else: print(maxn, int((m - cnt) % (n - 1) + 1)) ```
instruction
0
3,406
12
6,812
No
output
1
3,406
12
6,813
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation. For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2]. The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation. Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque. Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides. Input The first line contains two integers n and q (2 ≀ n ≀ 10^5, 0 ≀ q ≀ 3 β‹… 10^5) β€” the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≀ a_i ≀ 10^9) β€” the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≀ m_j ≀ 10^{18}). Output For each teacher's query, output two numbers A and B β€” the numbers that Valeriy pulls out of the deque for the m_j-th operation. Examples Input 5 3 1 2 3 4 5 1 2 10 Output 1 2 2 3 5 2 Input 2 0 0 0 Output Note Consider all 10 steps for the first test in detail: 1. [1, 2, 3, 4, 5] β€” on the first operation, A and B are 1 and 2, respectively. So, 2 we write to the beginning of the deque, and 1 β€” to the end. We get the following status of the deque: [2, 3, 4, 5, 1]. 2. [2, 3, 4, 5, 1] β‡’ A = 2, B = 3. 3. [3, 4, 5, 1, 2] 4. [4, 5, 1, 2, 3] 5. [5, 1, 2, 3, 4] 6. [5, 2, 3, 4, 1] 7. [5, 3, 4, 1, 2] 8. [5, 4, 1, 2, 3] 9. [5, 1, 2, 3, 4] 10. [5, 2, 3, 4, 1] β‡’ A = 5, B = 2. Submitted Solution: ``` import sys from collections import deque input = sys.stdin.readline n, q = map(int, input().split()) a = list(map(int, input().split())) query = [int(input()) for i in range(q)] max_a = max(a) for i in range(n): if a[i] == max_a: max_ind = i break ans = [0]*(n+1) tmp_max = -1 for i in range(n-1): tmp_max = max(tmp_max, a[i]) ans[i] = [tmp_max, a[i+1]] if a[i+1] == max_a: break a = a[i+1:] + sorted(a[0:i+1]) for j in query: if j - 1 <= i: print(" ".join(map(str, ans[j-1]))) else: print(max_a, a[(j - 2 - i) % (n - 1)+1] ) ```
instruction
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6,814
No
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6,815
Provide tags and a correct Python 3 solution for this coding contest problem. One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers. If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K βŒ‰ bits to store each value. It then takes nk bits to store the whole file. To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≀ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities. Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible. We remind you that 1 byte contains 8 bits. k = ⌈ log_{2} K βŒ‰ is the smallest integer such that K ≀ 2^{k}. In particular, if K = 1, then k = 0. Input The first line contains two integers n and I (1 ≀ n ≀ 4 β‹… 10^{5}, 1 ≀ I ≀ 10^{8}) β€” the length of the array and the size of the disk in bytes, respectively. The next line contains n integers a_{i} (0 ≀ a_{i} ≀ 10^{9}) β€” the array denoting the sound file. Output Print a single integer β€” the minimal possible number of changed elements. Examples Input 6 1 2 1 2 3 4 3 Output 2 Input 6 2 2 1 2 3 4 3 Output 0 Input 6 1 1 1 2 2 3 3 Output 2 Note In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed. In the second example the disk is larger, so the initial file fits it and no changes are required. In the third example we have to change both 1s or both 3s.
instruction
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Tags: sortings, two pointers Correct Solution: ``` import math; n,I = map(int,input().split()); arr = list(map(int,input().split())); k = 8*I//n; K = 2**k; arr.sort(); nd = 1; le = arr[0]; b = [0]; for i in range(1,n): if(arr[i]!=le): le=arr[i]; b.append(i); nd+=1; b.append(n) #print(b); #print(nd); if(K>=nd): print(0); else: maxn = 0; for i in range(K,nd): maxn = max(maxn,(b[i]-b[i-K])); print(n-maxn) ```
output
1
3,408
12
6,817
Provide tags and a correct Python 3 solution for this coding contest problem. One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers. If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K βŒ‰ bits to store each value. It then takes nk bits to store the whole file. To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≀ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities. Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible. We remind you that 1 byte contains 8 bits. k = ⌈ log_{2} K βŒ‰ is the smallest integer such that K ≀ 2^{k}. In particular, if K = 1, then k = 0. Input The first line contains two integers n and I (1 ≀ n ≀ 4 β‹… 10^{5}, 1 ≀ I ≀ 10^{8}) β€” the length of the array and the size of the disk in bytes, respectively. The next line contains n integers a_{i} (0 ≀ a_{i} ≀ 10^{9}) β€” the array denoting the sound file. Output Print a single integer β€” the minimal possible number of changed elements. Examples Input 6 1 2 1 2 3 4 3 Output 2 Input 6 2 2 1 2 3 4 3 Output 0 Input 6 1 1 1 2 2 3 3 Output 2 Note In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed. In the second example the disk is larger, so the initial file fits it and no changes are required. In the third example we have to change both 1s or both 3s.
instruction
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3,409
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Tags: sortings, two pointers Correct Solution: ``` n,l=[int(x) for x in input().split()] a=sorted([int(x) for x in input().split()]) num=len(set(a)) arr=2**((8*l)//n) a.append(10**100) b=[] counter=1 for i in range(1,n+1): if a[i]==a[i-1]: counter+=1 else: b.append(counter) counter=1 pref=[0] for item in b: pref.append(pref[-1]+item) c=max(num-arr,0) lena=len(pref) answer=10**100 for i in range(c+1): answer=min(answer,pref[i]+pref[lena-1]-pref[lena-c+i-1]) print(answer) ```
output
1
3,409
12
6,819
Provide tags and a correct Python 3 solution for this coding contest problem. One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers. If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K βŒ‰ bits to store each value. It then takes nk bits to store the whole file. To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≀ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities. Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible. We remind you that 1 byte contains 8 bits. k = ⌈ log_{2} K βŒ‰ is the smallest integer such that K ≀ 2^{k}. In particular, if K = 1, then k = 0. Input The first line contains two integers n and I (1 ≀ n ≀ 4 β‹… 10^{5}, 1 ≀ I ≀ 10^{8}) β€” the length of the array and the size of the disk in bytes, respectively. The next line contains n integers a_{i} (0 ≀ a_{i} ≀ 10^{9}) β€” the array denoting the sound file. Output Print a single integer β€” the minimal possible number of changed elements. Examples Input 6 1 2 1 2 3 4 3 Output 2 Input 6 2 2 1 2 3 4 3 Output 0 Input 6 1 1 1 2 2 3 3 Output 2 Note In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed. In the second example the disk is larger, so the initial file fits it and no changes are required. In the third example we have to change both 1s or both 3s.
instruction
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3,410
12
6,820
Tags: sortings, two pointers Correct Solution: ``` n, m = map(int, input().split()) a = sorted(map(int, input().split())) b = [0] a += [1 << 30] for i in range(n): if a[i] < a[i+1]: b += [i+1] print(n-max((y-x for x,y in zip(b,b[1<<8*m//n:])),default=n)) ```
output
1
3,410
12
6,821
Provide tags and a correct Python 3 solution for this coding contest problem. One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers. If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K βŒ‰ bits to store each value. It then takes nk bits to store the whole file. To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≀ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities. Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible. We remind you that 1 byte contains 8 bits. k = ⌈ log_{2} K βŒ‰ is the smallest integer such that K ≀ 2^{k}. In particular, if K = 1, then k = 0. Input The first line contains two integers n and I (1 ≀ n ≀ 4 β‹… 10^{5}, 1 ≀ I ≀ 10^{8}) β€” the length of the array and the size of the disk in bytes, respectively. The next line contains n integers a_{i} (0 ≀ a_{i} ≀ 10^{9}) β€” the array denoting the sound file. Output Print a single integer β€” the minimal possible number of changed elements. Examples Input 6 1 2 1 2 3 4 3 Output 2 Input 6 2 2 1 2 3 4 3 Output 0 Input 6 1 1 1 2 2 3 3 Output 2 Note In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed. In the second example the disk is larger, so the initial file fits it and no changes are required. In the third example we have to change both 1s or both 3s.
instruction
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3,411
12
6,822
Tags: sortings, two pointers Correct Solution: ``` from math import log2, ceil n, k = map(int, input().split()) k *= 8 a = sorted(list(map(int, input().split()))) q1, dif = 0, 1 ans = float('inf') for q in range(n): while n*ceil(log2(dif)) <= k and q1 < n: if q1 == n-1 or a[q1] != a[q1+1]: dif += 1 q1 += 1 ans = min(ans, q+n-q1) if q != n-1 and a[q] != a[q+1]: dif -= 1 print(ans) ```
output
1
3,411
12
6,823
Provide tags and a correct Python 3 solution for this coding contest problem. One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers. If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K βŒ‰ bits to store each value. It then takes nk bits to store the whole file. To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≀ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities. Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible. We remind you that 1 byte contains 8 bits. k = ⌈ log_{2} K βŒ‰ is the smallest integer such that K ≀ 2^{k}. In particular, if K = 1, then k = 0. Input The first line contains two integers n and I (1 ≀ n ≀ 4 β‹… 10^{5}, 1 ≀ I ≀ 10^{8}) β€” the length of the array and the size of the disk in bytes, respectively. The next line contains n integers a_{i} (0 ≀ a_{i} ≀ 10^{9}) β€” the array denoting the sound file. Output Print a single integer β€” the minimal possible number of changed elements. Examples Input 6 1 2 1 2 3 4 3 Output 2 Input 6 2 2 1 2 3 4 3 Output 0 Input 6 1 1 1 2 2 3 3 Output 2 Note In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed. In the second example the disk is larger, so the initial file fits it and no changes are required. In the third example we have to change both 1s or both 3s.
instruction
0
3,412
12
6,824
Tags: sortings, two pointers Correct Solution: ``` n,I=map(int,input().split()) I*=8 I //= n arr=list(map(int,input().split())) arr.sort() smen = [0] typs = 1 for i in range(1,n): if arr[i] != arr[i-1]: typs+=1 smen.append(i) smen.append(n) deg = 1 lg = 0 while deg < typs: lg += 1 deg *= 2 if lg == 0 or I >= lg: print(0) else: degi = 2 ** I mon = typs - degi ans = 400001 for x in range(mon+1): now = smen[x] + n - smen[typs-mon+x] if now<ans: ans=now print(ans) ```
output
1
3,412
12
6,825
Provide tags and a correct Python 3 solution for this coding contest problem. One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers. If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K βŒ‰ bits to store each value. It then takes nk bits to store the whole file. To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≀ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities. Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible. We remind you that 1 byte contains 8 bits. k = ⌈ log_{2} K βŒ‰ is the smallest integer such that K ≀ 2^{k}. In particular, if K = 1, then k = 0. Input The first line contains two integers n and I (1 ≀ n ≀ 4 β‹… 10^{5}, 1 ≀ I ≀ 10^{8}) β€” the length of the array and the size of the disk in bytes, respectively. The next line contains n integers a_{i} (0 ≀ a_{i} ≀ 10^{9}) β€” the array denoting the sound file. Output Print a single integer β€” the minimal possible number of changed elements. Examples Input 6 1 2 1 2 3 4 3 Output 2 Input 6 2 2 1 2 3 4 3 Output 0 Input 6 1 1 1 2 2 3 3 Output 2 Note In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed. In the second example the disk is larger, so the initial file fits it and no changes are required. In the third example we have to change both 1s or both 3s.
instruction
0
3,413
12
6,826
Tags: sortings, two pointers Correct Solution: ``` n,I=list(map(int, input().split())) l=list(map(int, input().split())) k=2**(I*8//n) dd={} for x in l: if x in dd: dd[x]+=1 else: dd[x]=1 # print(dd) l=[dd[x] for x in sorted(dd)] # print(l) n=len(l) if k>=n: print(0) else: ss=sum(l[:k]) mxm=ss for i in range(1,n-k+1): ss+=l[i+k-1]-l[i-1] if mxm<ss: mxm=ss print(sum(l)-mxm) ```
output
1
3,413
12
6,827
Provide tags and a correct Python 3 solution for this coding contest problem. One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers. If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K βŒ‰ bits to store each value. It then takes nk bits to store the whole file. To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≀ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities. Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible. We remind you that 1 byte contains 8 bits. k = ⌈ log_{2} K βŒ‰ is the smallest integer such that K ≀ 2^{k}. In particular, if K = 1, then k = 0. Input The first line contains two integers n and I (1 ≀ n ≀ 4 β‹… 10^{5}, 1 ≀ I ≀ 10^{8}) β€” the length of the array and the size of the disk in bytes, respectively. The next line contains n integers a_{i} (0 ≀ a_{i} ≀ 10^{9}) β€” the array denoting the sound file. Output Print a single integer β€” the minimal possible number of changed elements. Examples Input 6 1 2 1 2 3 4 3 Output 2 Input 6 2 2 1 2 3 4 3 Output 0 Input 6 1 1 1 2 2 3 3 Output 2 Note In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed. In the second example the disk is larger, so the initial file fits it and no changes are required. In the third example we have to change both 1s or both 3s.
instruction
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3,414
12
6,828
Tags: sortings, two pointers Correct Solution: ``` from sys import stdin input = stdin.readline from math import floor n, I = [int(i) for i in input().split()] a = [int(i) for i in input().split()] K = 2**(floor(8*I/n)) num_occ = dict() for i in range(n): num_occ[a[i]] = num_occ.get(a[i], 0) + 1 if K >= len(num_occ): print(0) else: sort_keys = sorted(num_occ.keys()) sum_K = [0]*(len(sort_keys)-K+1) acc_K = 0 for i in range(K): acc_K += num_occ[sort_keys[i]] sum_K[0] = acc_K for i in range(K, len(sort_keys)): acc_K += num_occ[sort_keys[i]]-num_occ[sort_keys[i-K]] sum_K[i-K+1] = acc_K print(n-max(sum_K)) ```
output
1
3,414
12
6,829
Provide tags and a correct Python 3 solution for this coding contest problem. One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers. If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K βŒ‰ bits to store each value. It then takes nk bits to store the whole file. To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≀ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities. Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible. We remind you that 1 byte contains 8 bits. k = ⌈ log_{2} K βŒ‰ is the smallest integer such that K ≀ 2^{k}. In particular, if K = 1, then k = 0. Input The first line contains two integers n and I (1 ≀ n ≀ 4 β‹… 10^{5}, 1 ≀ I ≀ 10^{8}) β€” the length of the array and the size of the disk in bytes, respectively. The next line contains n integers a_{i} (0 ≀ a_{i} ≀ 10^{9}) β€” the array denoting the sound file. Output Print a single integer β€” the minimal possible number of changed elements. Examples Input 6 1 2 1 2 3 4 3 Output 2 Input 6 2 2 1 2 3 4 3 Output 0 Input 6 1 1 1 2 2 3 3 Output 2 Note In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed. In the second example the disk is larger, so the initial file fits it and no changes are required. In the third example we have to change both 1s or both 3s.
instruction
0
3,415
12
6,830
Tags: sortings, two pointers Correct Solution: ``` from itertools import accumulate # python template for atcoder1 import sys sys.setrecursionlimit(10**9) input = sys.stdin.readline N, K = map(int, input().split()) A = list(map(int, input().split())) A = sorted(A) L = [] prev = -1 for a in A: if a == prev: L[-1] += 1 else: L.append(1) prev = a max_types = int(2**((8*K)//N)) all_types = len(L) del_types = all_types-max_types if del_types <= 0: ans = 0 else: ans = float('inf') sum_L = N L_acc = [0]+list(accumulate(L)) for i in range(len(L)-max_types): s = L_acc[i+max_types]-L_acc[i] ans = min(ans, sum_L-s) print(ans) ```
output
1
3,415
12
6,831
Provide tags and a correct Python 3 solution for this coding contest problem. Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid. Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid. An operation on array a is: * select an integer k (1 ≀ k ≀ ⌊n/2βŒ‹) * swap the prefix of length k with the suffix of length k For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}. Given the set of test cases, help them determine if each one is valid or invalid. Input The first line contains one integer t (1 ≀ t ≀ 500) β€” the number of test cases. The description of each test case is as follows. The first line of each test case contains a single integer n (1 ≀ n ≀ 500) β€” the size of the arrays. The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” elements of array a. The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≀ b_i ≀ 10^9) β€” elements of array b. Output For each test case, print "Yes" if the given input is valid. Otherwise print "No". You may print the answer in any case. Example Input 5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2 Output yes yes No yes No Note For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1]. For the second test case, a is already equal to b. For the third test case, it is impossible since we cannot obtain 3 in a. For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2]. For the fifth test case, it is impossible to convert a to b.
instruction
0
3,515
12
7,030
Tags: constructive algorithms, implementation, sortings Correct Solution: ``` t = int(input()) for i in range(t): l = int(input()) if l <= 1: g = int(input()) f = int(input()) if g == f: print('Yes') else: print('No') else: a = [] b = [] a = list(map(int, input().split())) b = list(map(int, input().split())) m = [[min(a[0], a[-1]), max(a[0], a[-1])]] flag = 1 for i in range(1, l // 2): m.append([min(a[i], a[l - i - 1]), max(a[i], a[l - i - 1])]) for i in range(l // 2): test = [min(b[i], b[l - i - 1]), max(b[i], b[l - i - 1])] flag = 0 for j in range(len(m)): if test == m[j]: flag = 1 del (m[j]) break if flag == 0: break if flag: if l % 2: if a[l // 2] == b[l // 2]: print('Yes') else: print('No') else: print('Yes') else: print('No') ```
output
1
3,515
12
7,031
Provide tags and a correct Python 3 solution for this coding contest problem. Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid. Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid. An operation on array a is: * select an integer k (1 ≀ k ≀ ⌊n/2βŒ‹) * swap the prefix of length k with the suffix of length k For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}. Given the set of test cases, help them determine if each one is valid or invalid. Input The first line contains one integer t (1 ≀ t ≀ 500) β€” the number of test cases. The description of each test case is as follows. The first line of each test case contains a single integer n (1 ≀ n ≀ 500) β€” the size of the arrays. The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” elements of array a. The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≀ b_i ≀ 10^9) β€” elements of array b. Output For each test case, print "Yes" if the given input is valid. Otherwise print "No". You may print the answer in any case. Example Input 5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2 Output yes yes No yes No Note For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1]. For the second test case, a is already equal to b. For the third test case, it is impossible since we cannot obtain 3 in a. For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2]. For the fifth test case, it is impossible to convert a to b.
instruction
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Tags: constructive algorithms, implementation, sortings Correct Solution: ``` t = int(input()) for _ in range(t): n = int(input()) a = list(map(int, input().split())) b = list(map(int, input().split())) works = True if n % 2: if a[n//2] != b[n//2]: works = False pairsA = [] for i in range(n//2): f = a[i] s = a[n - i - 1] if f > s: f, s = s, f pairsA.append((f,s)) pairsB = [] for i in range(n//2): f = b[i] s = b[n - i - 1] if f > s: f, s = s, f pairsB.append((f,s)) pairsA.sort() pairsB.sort() if works and pairsA == pairsB: print('Yes') else: print('No') ```
output
1
3,516
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7,033
Provide tags and a correct Python 3 solution for this coding contest problem. Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid. Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid. An operation on array a is: * select an integer k (1 ≀ k ≀ ⌊n/2βŒ‹) * swap the prefix of length k with the suffix of length k For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}. Given the set of test cases, help them determine if each one is valid or invalid. Input The first line contains one integer t (1 ≀ t ≀ 500) β€” the number of test cases. The description of each test case is as follows. The first line of each test case contains a single integer n (1 ≀ n ≀ 500) β€” the size of the arrays. The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” elements of array a. The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≀ b_i ≀ 10^9) β€” elements of array b. Output For each test case, print "Yes" if the given input is valid. Otherwise print "No". You may print the answer in any case. Example Input 5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2 Output yes yes No yes No Note For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1]. For the second test case, a is already equal to b. For the third test case, it is impossible since we cannot obtain 3 in a. For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2]. For the fifth test case, it is impossible to convert a to b.
instruction
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Tags: constructive algorithms, implementation, sortings Correct Solution: ``` import sys input=sys.stdin.readline t=int(input()) for _ in range(t): n=int(input()) a=list(map(int,input().split())) b=list(map(int,input().split())) x=sorted(zip(a,reversed(a))) y=sorted(zip(b,reversed(b))) if x==y: print("Yes") else: print("No") ```
output
1
3,517
12
7,035
Provide tags and a correct Python 3 solution for this coding contest problem. Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid. Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid. An operation on array a is: * select an integer k (1 ≀ k ≀ ⌊n/2βŒ‹) * swap the prefix of length k with the suffix of length k For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}. Given the set of test cases, help them determine if each one is valid or invalid. Input The first line contains one integer t (1 ≀ t ≀ 500) β€” the number of test cases. The description of each test case is as follows. The first line of each test case contains a single integer n (1 ≀ n ≀ 500) β€” the size of the arrays. The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” elements of array a. The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≀ b_i ≀ 10^9) β€” elements of array b. Output For each test case, print "Yes" if the given input is valid. Otherwise print "No". You may print the answer in any case. Example Input 5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2 Output yes yes No yes No Note For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1]. For the second test case, a is already equal to b. For the third test case, it is impossible since we cannot obtain 3 in a. For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2]. For the fifth test case, it is impossible to convert a to b.
instruction
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Tags: constructive algorithms, implementation, sortings Correct Solution: ``` def solve(n,a,b,i): if a[n//2]!=b[n//2] and n%2!=0:return 'NO' seta=sorted([[a[i],a[n-1-i]] for i in range(n)]);setb=sorted([[b[i],b[n-i-1]] for i in range(n)]) for i in range(n): if seta[i]!=setb[i]:return 'NO' return 'YES' for _ in range(int(input())):print(solve(int(input()),list(map(int,input().split())),list(map(int,input().split())),0)) ```
output
1
3,518
12
7,037
Provide tags and a correct Python 3 solution for this coding contest problem. Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid. Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid. An operation on array a is: * select an integer k (1 ≀ k ≀ ⌊n/2βŒ‹) * swap the prefix of length k with the suffix of length k For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}. Given the set of test cases, help them determine if each one is valid or invalid. Input The first line contains one integer t (1 ≀ t ≀ 500) β€” the number of test cases. The description of each test case is as follows. The first line of each test case contains a single integer n (1 ≀ n ≀ 500) β€” the size of the arrays. The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” elements of array a. The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≀ b_i ≀ 10^9) β€” elements of array b. Output For each test case, print "Yes" if the given input is valid. Otherwise print "No". You may print the answer in any case. Example Input 5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2 Output yes yes No yes No Note For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1]. For the second test case, a is already equal to b. For the third test case, it is impossible since we cannot obtain 3 in a. For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2]. For the fifth test case, it is impossible to convert a to b.
instruction
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Tags: constructive algorithms, implementation, sortings Correct Solution: ``` import sys input = sys.stdin.readline import math from collections import defaultdict t=int(input()) for i in range(t): n=int(input()) a=[int(i) for i in input().split() if i!='\n'] b=[int(i) for i in input().split() if i!='\n'] dict1,dict2=defaultdict(int),defaultdict(int) freq1,freq2=defaultdict(int),defaultdict(int) for j in range(math.ceil(n/2)): dict1[(min(a[j],a[-j-1]),max(a[-j-1],a[j]))]+=1 dict2[(min(b[-j-1],b[j]),max(b[j],b[-j-1]))]+=1 for j in range(n): freq1[a[j]]+=1 freq2[b[j]]+=1 #print(freq1,freq2) ok=True for j in dict1: for k in j: if freq1[k]!=freq2[k]: ok=False if j not in dict2: ok=False break else: if dict1[j]!=dict2[j]: ok=False break if ok==True: print('Yes') else: print('No') ```
output
1
3,519
12
7,039
Provide tags and a correct Python 3 solution for this coding contest problem. Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid. Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid. An operation on array a is: * select an integer k (1 ≀ k ≀ ⌊n/2βŒ‹) * swap the prefix of length k with the suffix of length k For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}. Given the set of test cases, help them determine if each one is valid or invalid. Input The first line contains one integer t (1 ≀ t ≀ 500) β€” the number of test cases. The description of each test case is as follows. The first line of each test case contains a single integer n (1 ≀ n ≀ 500) β€” the size of the arrays. The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” elements of array a. The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≀ b_i ≀ 10^9) β€” elements of array b. Output For each test case, print "Yes" if the given input is valid. Otherwise print "No". You may print the answer in any case. Example Input 5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2 Output yes yes No yes No Note For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1]. For the second test case, a is already equal to b. For the third test case, it is impossible since we cannot obtain 3 in a. For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2]. For the fifth test case, it is impossible to convert a to b.
instruction
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Tags: constructive algorithms, implementation, sortings Correct Solution: ``` t=int(input()) for _ in range(t): q,f=lambda:list(map(int,input().split())),lambda x:sorted(zip(x,x[::-1])) q(),print(['no','yes'][f(q())==f(q())]) ```
output
1
3,520
12
7,041
Provide tags and a correct Python 3 solution for this coding contest problem. Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid. Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid. An operation on array a is: * select an integer k (1 ≀ k ≀ ⌊n/2βŒ‹) * swap the prefix of length k with the suffix of length k For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}. Given the set of test cases, help them determine if each one is valid or invalid. Input The first line contains one integer t (1 ≀ t ≀ 500) β€” the number of test cases. The description of each test case is as follows. The first line of each test case contains a single integer n (1 ≀ n ≀ 500) β€” the size of the arrays. The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” elements of array a. The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≀ b_i ≀ 10^9) β€” elements of array b. Output For each test case, print "Yes" if the given input is valid. Otherwise print "No". You may print the answer in any case. Example Input 5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2 Output yes yes No yes No Note For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1]. For the second test case, a is already equal to b. For the third test case, it is impossible since we cannot obtain 3 in a. For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2]. For the fifth test case, it is impossible to convert a to b.
instruction
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Tags: constructive algorithms, implementation, sortings Correct Solution: ``` for _ in range(int(input())): n = int(input()) a = tuple(map(int, input().split())) b = tuple(map(int, input().split())) if sorted(zip(a, reversed(a))) == sorted(zip(b, reversed(b))): print("Yes") else: print("No") ```
output
1
3,521
12
7,043
Provide tags and a correct Python 3 solution for this coding contest problem. Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid. Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid. An operation on array a is: * select an integer k (1 ≀ k ≀ ⌊n/2βŒ‹) * swap the prefix of length k with the suffix of length k For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}. Given the set of test cases, help them determine if each one is valid or invalid. Input The first line contains one integer t (1 ≀ t ≀ 500) β€” the number of test cases. The description of each test case is as follows. The first line of each test case contains a single integer n (1 ≀ n ≀ 500) β€” the size of the arrays. The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” elements of array a. The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≀ b_i ≀ 10^9) β€” elements of array b. Output For each test case, print "Yes" if the given input is valid. Otherwise print "No". You may print the answer in any case. Example Input 5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2 Output yes yes No yes No Note For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1]. For the second test case, a is already equal to b. For the third test case, it is impossible since we cannot obtain 3 in a. For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2]. For the fifth test case, it is impossible to convert a to b.
instruction
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Tags: constructive algorithms, implementation, sortings Correct Solution: ``` # by the authority of GOD author: manhar singh sachdev # import os,sys from io import BytesIO, IOBase def solve(n,a,b): if n%2: if a[n//2]!=b[n//2]: return 'NO' ar1,ar2 = [],[] for i in range(n//2): ar1.append(sorted([a[i],a[-1-i]])) ar2.append(sorted([b[i],b[-1-i]])) if sorted(ar1) == sorted(ar2): return 'YES' else: return 'NO' def main(): for _ in range(int(input())): n = int(input()) a = list(map(int,input().split())) b = list(map(int,input().split())) print(solve(n,a,b)) #Fast IO Region BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") if __name__ == '__main__': main() ```
output
1
3,522
12
7,045
Provide tags and a correct Python 2 solution for this coding contest problem. Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid. Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid. An operation on array a is: * select an integer k (1 ≀ k ≀ ⌊n/2βŒ‹) * swap the prefix of length k with the suffix of length k For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}. Given the set of test cases, help them determine if each one is valid or invalid. Input The first line contains one integer t (1 ≀ t ≀ 500) β€” the number of test cases. The description of each test case is as follows. The first line of each test case contains a single integer n (1 ≀ n ≀ 500) β€” the size of the arrays. The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” elements of array a. The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≀ b_i ≀ 10^9) β€” elements of array b. Output For each test case, print "Yes" if the given input is valid. Otherwise print "No". You may print the answer in any case. Example Input 5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2 Output yes yes No yes No Note For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1]. For the second test case, a is already equal to b. For the third test case, it is impossible since we cannot obtain 3 in a. For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2]. For the fifth test case, it is impossible to convert a to b.
instruction
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Tags: constructive algorithms, implementation, sortings Correct Solution: ``` from sys import stdin, stdout from collections import Counter, defaultdict def ni(): return int(raw_input()) def li(): return list(map(int,raw_input().split())) def pn(n): stdout.write(str(n)+'\n') def pa(arr): pr(' '.join(map(str,arr))+'\n') # fast read function for total integer input def inp(): # this function returns whole input of # space/line seperated integers # Use Ctrl+D to flush stdin. return (map(int,stdin.read().split())) range = xrange # not for python 3.0+ """ def fun(l): ans=0 for i in l: ans|=i return ans """ # main code for t in range(ni()): n=ni() l1=li() l2=li() a1=[] a2=[] for i in range(n/2): a1.append((min(l1[i],l1[n-1-i]),max(l1[i],l1[n-1-i]))) a2.append((min(l2[i],l2[n-1-i]),max(l2[i],l2[n-1-i]))) a1.sort() a2.sort() f=0 if n%2 and (l1[n/2]!=l2[n/2]): f=1 if f or a1!=a2: stdout.write('No\n') else: stdout.write('Yes\n') ```
output
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3,523
12
7,047
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid. Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid. An operation on array a is: * select an integer k (1 ≀ k ≀ ⌊n/2βŒ‹) * swap the prefix of length k with the suffix of length k For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}. Given the set of test cases, help them determine if each one is valid or invalid. Input The first line contains one integer t (1 ≀ t ≀ 500) β€” the number of test cases. The description of each test case is as follows. The first line of each test case contains a single integer n (1 ≀ n ≀ 500) β€” the size of the arrays. The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” elements of array a. The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≀ b_i ≀ 10^9) β€” elements of array b. Output For each test case, print "Yes" if the given input is valid. Otherwise print "No". You may print the answer in any case. Example Input 5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2 Output yes yes No yes No Note For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1]. For the second test case, a is already equal to b. For the third test case, it is impossible since we cannot obtain 3 in a. For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2]. For the fifth test case, it is impossible to convert a to b. Submitted Solution: ``` import os import sys from io import BytesIO, IOBase # region fastio BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # ------------------------------ from math import factorial, ceil from collections import Counter, defaultdict, deque from heapq import heapify, heappop, heappush def RL(): return map(int, sys.stdin.readline().rstrip().split()) def RLL(): return list(map(int, sys.stdin.readline().rstrip().split())) def N(): return int(input()) def comb(n, m): return factorial(n) / (factorial(m) * factorial(n - m)) if n >= m else 0 def perm(n, m): return factorial(n) // (factorial(n - m)) if n >= m else 0 def mdis(x1, y1, x2, y2): return abs(x1 - x2) + abs(y1 - y2) mod = 998244353 INF = float('inf') # ------------------------------ def main(): for _ in range(N()): n = N() arra = RLL() arrb = RLL() ca = Counter(arra) cb = Counter(arrb) if (n%2==1 and arra[n//2]!=arrb[n//2]) or ca!=cb: print("No") else: reca = [] recb = [] for i in range(ceil(n/2)): pa = sorted([arra[i], arra[n-1-i]]) pb = sorted([arrb[i], arrb[n-1-i]]) reca.append(pa) recb.append(pb) # print(reca) # print(recb) print('yes' if sorted(reca)==sorted(recb) else 'No') if __name__ == "__main__": main() ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid. Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid. An operation on array a is: * select an integer k (1 ≀ k ≀ ⌊n/2βŒ‹) * swap the prefix of length k with the suffix of length k For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}. Given the set of test cases, help them determine if each one is valid or invalid. Input The first line contains one integer t (1 ≀ t ≀ 500) β€” the number of test cases. The description of each test case is as follows. The first line of each test case contains a single integer n (1 ≀ n ≀ 500) β€” the size of the arrays. The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” elements of array a. The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≀ b_i ≀ 10^9) β€” elements of array b. Output For each test case, print "Yes" if the given input is valid. Otherwise print "No". You may print the answer in any case. Example Input 5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2 Output yes yes No yes No Note For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1]. For the second test case, a is already equal to b. For the third test case, it is impossible since we cannot obtain 3 in a. For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2]. For the fifth test case, it is impossible to convert a to b. Submitted Solution: ``` import sys INF = 10**20 MOD = 10**9 + 7 I = lambda:list(map(int,input().split())) from math import gcd from math import ceil from collections import defaultdict as dd, Counter from bisect import bisect_left as bl, bisect_right as br def solve(): n, = I() a = I() b = I() if n % 2 and a[n // 2] != b[n // 2]: print('No') return pairs = dd(int) bpair = dd(int) for i in range(n // 2): x, y = a[i], a[n - i - 1] if x > y: x, y = y, x pairs[(x, y)] += 1 x, y = b[i], b[n - i - 1] if x > y: x, y = y, x bpair[(x, y)] += 1 for i in pairs: if pairs[i] != bpair[i]: print('No') return print('Yes') t, = I() while t: t -= 1 solve() ```
instruction
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Yes
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid. Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid. An operation on array a is: * select an integer k (1 ≀ k ≀ ⌊n/2βŒ‹) * swap the prefix of length k with the suffix of length k For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}. Given the set of test cases, help them determine if each one is valid or invalid. Input The first line contains one integer t (1 ≀ t ≀ 500) β€” the number of test cases. The description of each test case is as follows. The first line of each test case contains a single integer n (1 ≀ n ≀ 500) β€” the size of the arrays. The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” elements of array a. The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≀ b_i ≀ 10^9) β€” elements of array b. Output For each test case, print "Yes" if the given input is valid. Otherwise print "No". You may print the answer in any case. Example Input 5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2 Output yes yes No yes No Note For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1]. For the second test case, a is already equal to b. For the third test case, it is impossible since we cannot obtain 3 in a. For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2]. For the fifth test case, it is impossible to convert a to b. Submitted Solution: ``` t = int(input()) for _ in range(t): n = int(input()) a = list(map(int, input().split())) b = list(map(int, input().split())) paira = [] for i in range((n+1)//2): paira.append(tuple(sorted([a[i], a[~i]]))) pairb = [] for i in range((n+1)//2): pairb.append(tuple(sorted([b[i], b[~i]]))) paira.sort() pairb.sort() if paira == pairb: print("Yes") else: print("No") ```
instruction
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3,526
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Yes
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3,526
12
7,053
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid. Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid. An operation on array a is: * select an integer k (1 ≀ k ≀ ⌊n/2βŒ‹) * swap the prefix of length k with the suffix of length k For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}. Given the set of test cases, help them determine if each one is valid or invalid. Input The first line contains one integer t (1 ≀ t ≀ 500) β€” the number of test cases. The description of each test case is as follows. The first line of each test case contains a single integer n (1 ≀ n ≀ 500) β€” the size of the arrays. The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” elements of array a. The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≀ b_i ≀ 10^9) β€” elements of array b. Output For each test case, print "Yes" if the given input is valid. Otherwise print "No". You may print the answer in any case. Example Input 5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2 Output yes yes No yes No Note For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1]. For the second test case, a is already equal to b. For the third test case, it is impossible since we cannot obtain 3 in a. For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2]. For the fifth test case, it is impossible to convert a to b. Submitted Solution: ``` # from math import factorial as fac from collections import defaultdict # from copy import deepcopy import sys, math f = None try: f = open('q1.input', 'r') except IOError: f = sys.stdin if 'xrange' in dir(__builtins__): range = xrange # print(f.readline()) sys.setrecursionlimit(10**2) def print_case_iterable(case_num, iterable): print("Case #{}: {}".format(case_num," ".join(map(str,iterable)))) def print_case_number(case_num, iterable): print("Case #{}: {}".format(case_num,iterable)) def print_iterable(A): print (' '.join(A)) def read_int(): return int(f.readline().strip()) def read_int_array(): return [int(x) for x in f.readline().strip().split(" ")] def rns(): a = [x for x in f.readline().split(" ")] return int(a[0]), a[1].strip() def read_string(): return list(f.readline().strip()) def ri(): return int(f.readline().strip()) def ria(): return [int(x) for x in f.readline().strip().split(" ")] def rns(): a = [x for x in f.readline().split(" ")] return int(a[0]), a[1].strip() def rs(): return list(f.readline().strip()) def bi(x): return bin(x)[2:] from collections import deque import math NUMBER = 10**9 + 7 # NUMBER = 998244353 def factorial(n) : M = NUMBER f = 1 for i in range(1, n + 1): f = (f * i) % M # Now f never can # exceed 10^9+7 return f def mult(a,b): return (a * b) % NUMBER def minus(a , b): return (a - b) % NUMBER def plus(a , b): return (a + b) % NUMBER def egcd(a, b): if a == 0: return (b, 0, 1) else: g, y, x = egcd(b % a, a) return (g, x - (b // a) * y, y) def modinv(a): m = NUMBER g, x, y = egcd(a, m) if g != 1: raise Exception('modular inverse does not exist') else: return x % m def choose(n,k): if n < k: assert false return mult(factorial(n), modinv(mult(factorial(k),factorial(n-k)))) from collections import deque, defaultdict import heapq def solution(a,b,n): da = defaultdict(int) db = defaultdict(int) for i in range(n//2): da[frozenset([a[i], a[n-1-i]])]+=1 db[frozenset([b[i], b[n-1-i]])]+=1 if n % 2: if a[n//2] != b[n//2]: return "No" for x in da: if db[x] != da[x]: return "No" return "Yes" def main(): T = ri() for i in range(T): n = ri() a = ria() b = ria() x = solution(a,b,n) if 'xrange' not in dir(__builtins__): print(x) else: print >>output,str(x)# "Case #"+str(i+1)+':', if 'xrange' in dir(__builtins__): print(output.getvalue()) output.close() if 'xrange' in dir(__builtins__): import cStringIO output = cStringIO.StringIO() #example usage: # for l in res: # print >>output, str(len(l)) + ' ' + ' '.join(l) if __name__ == '__main__': main() ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid. Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid. An operation on array a is: * select an integer k (1 ≀ k ≀ ⌊n/2βŒ‹) * swap the prefix of length k with the suffix of length k For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}. Given the set of test cases, help them determine if each one is valid or invalid. Input The first line contains one integer t (1 ≀ t ≀ 500) β€” the number of test cases. The description of each test case is as follows. The first line of each test case contains a single integer n (1 ≀ n ≀ 500) β€” the size of the arrays. The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” elements of array a. The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≀ b_i ≀ 10^9) β€” elements of array b. Output For each test case, print "Yes" if the given input is valid. Otherwise print "No". You may print the answer in any case. Example Input 5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2 Output yes yes No yes No Note For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1]. For the second test case, a is already equal to b. For the third test case, it is impossible since we cannot obtain 3 in a. For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2]. For the fifth test case, it is impossible to convert a to b. Submitted Solution: ``` # your code goes here from collections import defaultdict t = int(input()) for _ in range(t): n = int(input()) a = list(map(int,input().split())) b = list(map(int,input().split())) possible = 1 pairs = defaultdict(int) if n%2 == 1 and a[n//2] != b[n//2]: possible = 0 for i in range(n//2): x,y = min(a[i],a[n-i-1]),max(a[i],a[n-i-1]) pairs[(x,y)] += 1 for j in range(n//2): x,y = min(a[j],a[n-j-1]),max(a[j],a[n-j-1]) if pairs[(x,y)] <= 0: possible = 0 pairs[(x,y)] -= 1 print("yes") if possible else print("No") ```
instruction
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3,528
12
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No
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid. Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid. An operation on array a is: * select an integer k (1 ≀ k ≀ ⌊n/2βŒ‹) * swap the prefix of length k with the suffix of length k For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}. Given the set of test cases, help them determine if each one is valid or invalid. Input The first line contains one integer t (1 ≀ t ≀ 500) β€” the number of test cases. The description of each test case is as follows. The first line of each test case contains a single integer n (1 ≀ n ≀ 500) β€” the size of the arrays. The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” elements of array a. The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≀ b_i ≀ 10^9) β€” elements of array b. Output For each test case, print "Yes" if the given input is valid. Otherwise print "No". You may print the answer in any case. Example Input 5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2 Output yes yes No yes No Note For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1]. For the second test case, a is already equal to b. For the third test case, it is impossible since we cannot obtain 3 in a. For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2]. For the fifth test case, it is impossible to convert a to b. Submitted Solution: ``` import sys, os, io def rs(): return sys.stdin.readline().rstrip() def ri(): return int(sys.stdin.readline()) def ria(): return list(map(int, sys.stdin.readline().split())) def ws(s): sys.stdout.write(s + '\n') def wi(n): sys.stdout.write(str(n) + '\n') def wia(a): sys.stdout.write(' '.join([str(x) for x in a]) + '\n') from collections import Counter def solve(n, a, b): ca = Counter(a) cb = Counter(b) return ca == cb and (n % 2 == 0 or n % 2 == 1 and a[n//2] == b[n//2]) def main(): for _ in range(ri()): n = ri() a = ria() b = ria() ws('Yes' if solve(n, a, b) else 'No') if __name__ == '__main__': main() ```
instruction
0
3,529
12
7,058
No
output
1
3,529
12
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid. Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid. An operation on array a is: * select an integer k (1 ≀ k ≀ ⌊n/2βŒ‹) * swap the prefix of length k with the suffix of length k For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}. Given the set of test cases, help them determine if each one is valid or invalid. Input The first line contains one integer t (1 ≀ t ≀ 500) β€” the number of test cases. The description of each test case is as follows. The first line of each test case contains a single integer n (1 ≀ n ≀ 500) β€” the size of the arrays. The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” elements of array a. The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≀ b_i ≀ 10^9) β€” elements of array b. Output For each test case, print "Yes" if the given input is valid. Otherwise print "No". You may print the answer in any case. Example Input 5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2 Output yes yes No yes No Note For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1]. For the second test case, a is already equal to b. For the third test case, it is impossible since we cannot obtain 3 in a. For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2]. For the fifth test case, it is impossible to convert a to b. Submitted Solution: ``` for _ in range(int(input())): n = int(input()) a = list(map(int, input().split())) b = list(map(int, input().split())) if sorted(a) != sorted(b): print('NO') continue c = {} for i in range(n): if a[i] not in c: c[a[i]] = [a[n - i - 1]] else: c[a[i]] += [a[n - i - 1]] if a[n - i - 1] not in c: c[a[n - i - 1]] = [a[i]] else: c[a[n - i - 1]] += [a[i]] for i in range(n): if b[n - i - 1] not in c[b[i]]: print('NO') break else: print('YES') ```
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3,530
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No
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12
7,061
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid. Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid. An operation on array a is: * select an integer k (1 ≀ k ≀ ⌊n/2βŒ‹) * swap the prefix of length k with the suffix of length k For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}. Given the set of test cases, help them determine if each one is valid or invalid. Input The first line contains one integer t (1 ≀ t ≀ 500) β€” the number of test cases. The description of each test case is as follows. The first line of each test case contains a single integer n (1 ≀ n ≀ 500) β€” the size of the arrays. The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” elements of array a. The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≀ b_i ≀ 10^9) β€” elements of array b. Output For each test case, print "Yes" if the given input is valid. Otherwise print "No". You may print the answer in any case. Example Input 5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2 Output yes yes No yes No Note For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1]. For the second test case, a is already equal to b. For the third test case, it is impossible since we cannot obtain 3 in a. For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2]. For the fifth test case, it is impossible to convert a to b. Submitted Solution: ``` import sys import string import math import bisect as bi from collections import defaultdict as dd input=sys.stdin.readline def cin(): return map(int,sin().split()) def ain(): return list(map(int,sin().split())) def sin(): return input() def inin(): return int(input()) def pref(a,n): pre=[0]*n pre[0]=a[0] for i in range(1,n): pre[i]=a[i]+pre[i-1] return pre ##dp1=[1]*100 ##dp1[0]=2 ##for i in range(1,100): ## dp1[i]=dp1[i-1]*2 ##pre=pref(dp1,100) for i in range(inin()): n=inin() a=ain() b=ain() if(a==b): print('yes') elif(sorted(a)==sorted(b)): if(n%2==1 and a[n//2]!=b[n//2]): print('no') else: l=[] l1=[] for i in range(n//2): l+=(max(a[i],a[n-i-1]),min(a[i],a[n-i-1])) l1+=(max(b[i],b[n-i-1]),min(b[i],b[n-i-1])) l.sort() l1.sort() if(l==l1): print('yes') else: print('no') else: print('no') ```
instruction
0
3,531
12
7,062
No
output
1
3,531
12
7,063
Evaluate the correctness of the submitted Python 2 solution to the coding contest problem. Provide a "Yes" or "No" response. Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid. Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid. An operation on array a is: * select an integer k (1 ≀ k ≀ ⌊n/2βŒ‹) * swap the prefix of length k with the suffix of length k For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}. Given the set of test cases, help them determine if each one is valid or invalid. Input The first line contains one integer t (1 ≀ t ≀ 500) β€” the number of test cases. The description of each test case is as follows. The first line of each test case contains a single integer n (1 ≀ n ≀ 500) β€” the size of the arrays. The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≀ a_i ≀ 10^9) β€” elements of array a. The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≀ b_i ≀ 10^9) β€” elements of array b. Output For each test case, print "Yes" if the given input is valid. Otherwise print "No". You may print the answer in any case. Example Input 5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2 Output yes yes No yes No Note For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1]. For the second test case, a is already equal to b. For the third test case, it is impossible since we cannot obtain 3 in a. For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2]. For the fifth test case, it is impossible to convert a to b. Submitted Solution: ``` from sys import stdin, stdout from collections import Counter, defaultdict def ni(): return int(raw_input()) def li(): return list(map(int,raw_input().split())) def pn(n): stdout.write(str(n)+'\n') def pa(arr): pr(' '.join(map(str,arr))+'\n') # fast read function for total integer input def inp(): # this function returns whole input of # space/line seperated integers # Use Ctrl+D to flush stdin. return (map(int,stdin.read().split())) range = xrange # not for python 3.0+ """ def fun(l): ans=0 for i in l: ans|=i return ans """ # main code for t in range(ni()): n=ni() l1=li() l2=li() d=Counter() for i in range(n/2): d[l1[i]]=l1[n-1-i] d[l1[n-1-i]]=l1[i] f=0 for i in range(n/2): if d[l2[i]]!=l2[n-1-i] or d[l2[n-1-i]]!=l2[i]: f=1 break if n%2: if l1[(n/2)]!=l2[(n/2)]: f=1 if f: stdout.write('No\n') else: stdout.write('Yes\n') ```
instruction
0
3,532
12
7,064
No
output
1
3,532
12
7,065
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a permutation a consisting of n numbers 1, 2, ..., n (a permutation is an array in which each element from 1 to n occurs exactly once). You can perform the following operation: choose some subarray (contiguous subsegment) of a and rearrange the elements in it in any way you want. But this operation cannot be applied to the whole array. For example, if a = [2, 1, 4, 5, 3] and we want to apply the operation to the subarray a[2, 4] (the subarray containing all elements from the 2-nd to the 4-th), then after the operation, the array can become a = [2, 5, 1, 4, 3] or, for example, a = [2, 1, 5, 4, 3]. Your task is to calculate the minimum number of operations described above to sort the permutation a in ascending order. Input The first line contains a single integer t (1 ≀ t ≀ 2000) β€” the number of test cases. The first line of the test case contains a single integer n (3 ≀ n ≀ 50) β€” the number of elements in the permutation. The second line of the test case contains n distinct integers from 1 to n β€” the given permutation a. Output For each test case, output a single integer β€” the minimum number of operations described above to sort the array a in ascending order. Example Input 3 4 1 3 2 4 3 1 2 3 5 2 1 4 5 3 Output 1 0 2 Note In the explanations, a[i, j] defines the subarray of a that starts from the i-th element and ends with the j-th element. In the first test case of the example, you can select the subarray a[2, 3] and swap the elements in it. In the second test case of the example, the permutation is already sorted, so you don't need to apply any operations. In the third test case of the example, you can select the subarray a[3, 5] and reorder the elements in it so a becomes [2, 1, 3, 4, 5], and then select the subarray a[1, 2] and swap the elements in it, so a becomes [1, 2, 3, 4, 5].
instruction
0
3,619
12
7,238
Tags: constructive algorithms, greedy Correct Solution: ``` for t in range(int(input())): N = int(input()) arr = list(map(int,input().split())) if arr == sorted(arr): print(0) elif arr[0] == 1 or arr[-1] == N: print(1) elif arr[0] == N and arr[-1] == 1: print(3) else: print(2) ```
output
1
3,619
12
7,239