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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two integers a and b. Print a+b. Input The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow. Each test case is given as a line of two integers a and b (-1000 ≤ a, b ≤ 1000). Output Print t integers — the required numbers a+b. Example Input 4 1 5 314 15 -99 99 123 987 Output 6 329 0 1110 Submitted Solution: ``` t = int(input()) for _ in range(t): s = '' s = input() a = s.split(" ") print(int(a[0])+int(a[1])) ```
instruction
0
61,628
5
123,256
Yes
output
1
61,628
5
123,257
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two integers a and b. Print a+b. Input The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow. Each test case is given as a line of two integers a and b (-1000 ≤ a, b ≤ 1000). Output Print t integers — the required numbers a+b. Example Input 4 1 5 314 15 -99 99 123 987 Output 6 329 0 1110 Submitted Solution: ``` t = int(input()) for _ in range(t): print(sum(map(int, input().split()))) ```
instruction
0
61,629
5
123,258
Yes
output
1
61,629
5
123,259
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two integers a and b. Print a+b. Input The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow. Each test case is given as a line of two integers a and b (-1000 ≤ a, b ≤ 1000). Output Print t integers — the required numbers a+b. Example Input 4 1 5 314 15 -99 99 123 987 Output 6 329 0 1110 Submitted Solution: ``` k=int(input()) result=[] for i in range(0,k): a,b=input().split() c=int(a)+int(b) result.append(c) for i in result: print(i) ```
instruction
0
61,630
5
123,260
Yes
output
1
61,630
5
123,261
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two integers a and b. Print a+b. Input The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow. Each test case is given as a line of two integers a and b (-1000 ≤ a, b ≤ 1000). Output Print t integers — the required numbers a+b. Example Input 4 1 5 314 15 -99 99 123 987 Output 6 329 0 1110 Submitted Solution: ``` def solve(): n1,k1 = map(int,input().split()) print(n1+k1) tests = int(input()) while tests: tests-=1 print(solve()) ```
instruction
0
61,631
5
123,262
No
output
1
61,631
5
123,263
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two integers a and b. Print a+b. Input The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow. Each test case is given as a line of two integers a and b (-1000 ≤ a, b ≤ 1000). Output Print t integers — the required numbers a+b. Example Input 4 1 5 314 15 -99 99 123 987 Output 6 329 0 1110 Submitted Solution: ``` for _ in range(int(input())): a,b=input().split() print(int(a),int(b)) ```
instruction
0
61,632
5
123,264
No
output
1
61,632
5
123,265
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two integers a and b. Print a+b. Input The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow. Each test case is given as a line of two integers a and b (-1000 ≤ a, b ≤ 1000). Output Print t integers — the required numbers a+b. Example Input 4 1 5 314 15 -99 99 123 987 Output 6 329 0 1110 Submitted Solution: ``` s=int(input()) a,b=map(int,input().split()) print(a+b) ```
instruction
0
61,633
5
123,266
No
output
1
61,633
5
123,267
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two integers a and b. Print a+b. Input The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow. Each test case is given as a line of two integers a and b (-1000 ≤ a, b ≤ 1000). Output Print t integers — the required numbers a+b. Example Input 4 1 5 314 15 -99 99 123 987 Output 6 329 0 1110 Submitted Solution: ``` print(1) ```
instruction
0
61,634
5
123,268
No
output
1
61,634
5
123,269
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an integer m, and a list of n distinct integers between 0 and m - 1. You would like to construct a sequence satisfying the properties: * Each element is an integer between 0 and m - 1, inclusive. * All prefix products of the sequence modulo m are distinct. * No prefix product modulo m appears as an element of the input list. * The length of the sequence is maximized. Construct any sequence satisfying the properties above. Input The first line of input contains two integers n and m (0 ≤ n < m ≤ 200 000) — the number of forbidden prefix products and the modulus. If n is non-zero, the next line of input contains n distinct integers between 0 and m - 1, the forbidden prefix products. If n is zero, this line doesn't exist. Output On the first line, print the number k, denoting the length of your sequence. On the second line, print k space separated integers, denoting your sequence. Examples Input 0 5 Output 5 1 2 4 3 0 Input 3 10 2 9 1 Output 6 3 9 2 9 8 0 Note For the first case, the prefix products of this sequence modulo m are [1, 2, 3, 4, 0]. For the second case, the prefix products of this sequence modulo m are [3, 7, 4, 6, 8, 0]. Submitted Solution: ``` import math def gcdExtended(a, b): # Base Case if a == 0 : return b, 0, 1 gcd, x1, y1 = gcdExtended(b%a, a) # Update x and y using results of recursive # call x = y1 - (b//a) * x1 y = x1 return gcd, x, y def rev_elem(x, m): return (gcdExtended(x, m)[1] + m) % m n, m = map(int, input().split()) a = [] if n > 0: a = [int(i) for i in input().split()] banned = [False] * (m + 5) for i in a: banned[i] = True cycle = [[] for i in range(m + 5)] d, dp, p = [], [], [] for i in range(m): cycle[math.gcd(m, i)].append(i) cycle = [[i for i in j if not banned[i]] for j in cycle] d = [i for i in range(1, m + 1) if m % i == 0] dp = [len(cycle[i]) for i in d] p = [-1 for i in d] ans, lst = -1, -1 for i in range(len(d)): if dp[i] > ans: ans, lst = dp[i], i for j in range(i + 1, len(d)): if d[j] % d[i] != 0 or dp[j] > dp[i] + len(cycle[d[j]]): continue dp[j] = dp[i] + len(cycle[d[j]]) p[j] = i print(ans) pos, dpos, pref = [], [], [] cur = lst while cur != -1: dpos.append(d[cur]) cur = p[cur] dpos.reverse() for i in dpos: pref += cycle[i] cur = 1 for i in pref: ad = 1 if math.gcd(i, m) != math.gcd(cur, m): ad = ((cur * math.gcd(i, m) // math.gcd(cur, math.gcd(i, m))) // cur) % m cur = (cur * ad) % m if i != cur: ad *= (i // math.gcd(i, cur)) * rev_elem(cur // math.gcd(i, cur), m) ad %= m cur = (cur * ad) % m pos.append(ad) print(*pos) ```
instruction
0
61,950
5
123,900
No
output
1
61,950
5
123,901
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an integer m, and a list of n distinct integers between 0 and m - 1. You would like to construct a sequence satisfying the properties: * Each element is an integer between 0 and m - 1, inclusive. * All prefix products of the sequence modulo m are distinct. * No prefix product modulo m appears as an element of the input list. * The length of the sequence is maximized. Construct any sequence satisfying the properties above. Input The first line of input contains two integers n and m (0 ≤ n < m ≤ 200 000) — the number of forbidden prefix products and the modulus. If n is non-zero, the next line of input contains n distinct integers between 0 and m - 1, the forbidden prefix products. If n is zero, this line doesn't exist. Output On the first line, print the number k, denoting the length of your sequence. On the second line, print k space separated integers, denoting your sequence. Examples Input 0 5 Output 5 1 2 4 3 0 Input 3 10 2 9 1 Output 6 3 9 2 9 8 0 Note For the first case, the prefix products of this sequence modulo m are [1, 2, 3, 4, 0]. For the second case, the prefix products of this sequence modulo m are [3, 7, 4, 6, 8, 0]. Submitted Solution: ``` import math def gcdExtended(a, b): # Base Case if a == 0 : return b, 0, 1 gcd, x1, y1 = gcdExtended(b%a, a) # Update x and y using results of recursive # call x = y1 - (b//a) * x1 y = x1 return gcd, x, y def rev_elem(x, m): return (gcdExtended(x, m)[1] + m) % m n, m = map(int, input().split()) a = [] if n > 0: a = [int(i) for i in input().split()] banned = [False] * (m + 5) for i in a: banned[i] = True cycle = [[] for i in range(m + 5)] d, dp, p = [], [], [] for i in range(m): cycle[math.gcd(m, i)].append(i) cycle = [[i for i in j if not banned[i]] for j in cycle] d = [i for i in range(1, m + 1) if m % i == 0] dp = [len(cycle[i]) for i in d] p = [-1 for i in d] ans, lst = -1, -1 for i in range(len(d)): if dp[i] > ans: ans, lst = dp[i], i for j in range(i + 1, len(d)): if d[j] % d[i] != 0 or dp[j] > dp[i] + len(cycle[d[j]]): continue dp[j] = dp[i] + len(cycle[d[j]]) p[j] = i print(ans) pos, dpos, pref = [], [], [] cur = lst while cur != -1: dpos.append(d[cur]) cur = p[cur] dpos.reverse() for i in dpos: pref += cycle[i] cur = 1 for i in pref: ad = 1 if math.gcd(i, m) != math.gcd(cur, m): ad = ((cur * math.gcd(i, m) // math.gcd(cur, math.gcd(i, m))) // cur) % m cur = (cur * ad) % m ad *= (i // math.gcd(i, m)) * rev_elem(cur // math.gcd(i, m), m) ad %= m cur = (cur * ad) % m pos.append(ad) print(*pos) ```
instruction
0
61,951
5
123,902
No
output
1
61,951
5
123,903
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an integer m, and a list of n distinct integers between 0 and m - 1. You would like to construct a sequence satisfying the properties: * Each element is an integer between 0 and m - 1, inclusive. * All prefix products of the sequence modulo m are distinct. * No prefix product modulo m appears as an element of the input list. * The length of the sequence is maximized. Construct any sequence satisfying the properties above. Input The first line of input contains two integers n and m (0 ≤ n < m ≤ 200 000) — the number of forbidden prefix products and the modulus. If n is non-zero, the next line of input contains n distinct integers between 0 and m - 1, the forbidden prefix products. If n is zero, this line doesn't exist. Output On the first line, print the number k, denoting the length of your sequence. On the second line, print k space separated integers, denoting your sequence. Examples Input 0 5 Output 5 1 2 4 3 0 Input 3 10 2 9 1 Output 6 3 9 2 9 8 0 Note For the first case, the prefix products of this sequence modulo m are [1, 2, 3, 4, 0]. For the second case, the prefix products of this sequence modulo m are [3, 7, 4, 6, 8, 0]. Submitted Solution: ``` def invm(m, n): nn = n x = 0 y = 1 while m != 0: x, y = y, x - (n // m) * y n, m = m, n % m while x < 0: x += nn return x def gcd(m, n): while n: m, n = n, m % n return m n, m = map(int, input().split()) if n: data = set(map(int, input().split())) else: data = set() res = [] cur = 1 gc = 1 while True: gn = None for i in range(gc, m, gc): g = gcd(i,m) if g == gc: if i not in data: next = invm(cur, m) * i % m res.append(next) cur = cur * next % m elif gn is None: gn = g if gn: gc = gn else: break res.append(0) print(len(res)) print(*res) ```
instruction
0
61,952
5
123,904
No
output
1
61,952
5
123,905
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an integer m, and a list of n distinct integers between 0 and m - 1. You would like to construct a sequence satisfying the properties: * Each element is an integer between 0 and m - 1, inclusive. * All prefix products of the sequence modulo m are distinct. * No prefix product modulo m appears as an element of the input list. * The length of the sequence is maximized. Construct any sequence satisfying the properties above. Input The first line of input contains two integers n and m (0 ≤ n < m ≤ 200 000) — the number of forbidden prefix products and the modulus. If n is non-zero, the next line of input contains n distinct integers between 0 and m - 1, the forbidden prefix products. If n is zero, this line doesn't exist. Output On the first line, print the number k, denoting the length of your sequence. On the second line, print k space separated integers, denoting your sequence. Examples Input 0 5 Output 5 1 2 4 3 0 Input 3 10 2 9 1 Output 6 3 9 2 9 8 0 Note For the first case, the prefix products of this sequence modulo m are [1, 2, 3, 4, 0]. For the second case, the prefix products of this sequence modulo m are [3, 7, 4, 6, 8, 0]. Submitted Solution: ``` import math def gcdExtended(a, b): # Base Case if a == 0 : return b, 0, 1 gcd, x1, y1 = gcdExtended(b%a, a) # Update x and y using results of recursive # call x = y1 - (b//a) * x1 y = x1 return gcd, x, y def rev_elem(x, m): return (gcdExtended(x, m)[1] % m + m) % m n, m = map(int, input().split()) a = [] if n > 0: a = [int(i) for i in input().split()] banned = [False] * (m + 5) for i in a: banned[i] = True cycle = [[] for i in range(m + 5)] d, dp, p = [], [], [] for i in range(m): cycle[math.gcd(m, i)].append(i) cycle = [[i for i in j if not banned[i]] for j in cycle] d = [i for i in range(1, m + 1) if m % i == 0] dp = [len(cycle[i]) for i in d] p = [-1 for i in d] ans, lst = -1, -1 for i in range(len(d)): if dp[i] > ans: ans, lst = dp[i], i for j in range(i + 1, len(d)): if d[j] % d[i] != 0 or dp[j] > dp[i] + len(cycle[d[j]]): continue dp[j] = dp[i] + len(cycle[d[j]]) p[j] = i print(ans) pos, dpos, pref = [], [], [] cur = lst while cur != -1: dpos.append(d[cur]) cur = p[cur] dpos.reverse() for i in dpos: pref += cycle[i] cur = 1 for i in pref: ad = 1 if math.gcd(i, m) != math.gcd(cur, m): ad = ((cur * math.gcd(i, m) // math.gcd(cur, math.gcd(i, m))) // cur) % m cur = (cur * ad) % m ad *= i * rev_elem(cur // math.gcd(i, m), m) ad %= m cur = (cur * ad) % m pos.append(ad) print(*pos) ```
instruction
0
61,953
5
123,906
No
output
1
61,953
5
123,907
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a consisting of n integers. You have to process q queries to this array; each query is given as four numbers l, r, x and y, denoting that for every i such that l ≤ i ≤ r and ai = x you have to set ai equal to y. Print the array after all queries are processed. Input The first line contains one integer n (1 ≤ n ≤ 200000) — the size of array a. The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 100) — the elements of array a. The third line contains one integer q (1 ≤ q ≤ 200000) — the number of queries you have to process. Then q lines follow. i-th line contains four integers l, r, x and y denoting i-th query (1 ≤ l ≤ r ≤ n, 1 ≤ x, y ≤ 100). Output Print n integers — elements of array a after all changes are made. Example Input 5 1 2 3 4 5 3 3 5 3 5 1 5 5 1 1 5 1 5 Output 5 2 5 4 5 Submitted Solution: ``` import sys input_ = sys.stdin.read() input_ = input_.split('\n')[:-1] arr = [x for x in input_[1].split()] print(arr) ```
instruction
0
62,006
5
124,012
No
output
1
62,006
5
124,013
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a consisting of n integers. You have to process q queries to this array; each query is given as four numbers l, r, x and y, denoting that for every i such that l ≤ i ≤ r and ai = x you have to set ai equal to y. Print the array after all queries are processed. Input The first line contains one integer n (1 ≤ n ≤ 200000) — the size of array a. The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 100) — the elements of array a. The third line contains one integer q (1 ≤ q ≤ 200000) — the number of queries you have to process. Then q lines follow. i-th line contains four integers l, r, x and y denoting i-th query (1 ≤ l ≤ r ≤ n, 1 ≤ x, y ≤ 100). Output Print n integers — elements of array a after all changes are made. Example Input 5 1 2 3 4 5 3 3 5 3 5 1 5 5 1 1 5 1 5 Output 5 2 5 4 5 Submitted Solution: ``` n = input() arr = list(map(int, input().split())) q = int(input()) for t in range(q): l, r, x, y = map(int, input().split()) for i in range(l-1,r): if(arr[i] == x): arr[i]=y print(arr) ```
instruction
0
62,007
5
124,014
No
output
1
62,007
5
124,015
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a consisting of n integers. You have to process q queries to this array; each query is given as four numbers l, r, x and y, denoting that for every i such that l ≤ i ≤ r and ai = x you have to set ai equal to y. Print the array after all queries are processed. Input The first line contains one integer n (1 ≤ n ≤ 200000) — the size of array a. The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 100) — the elements of array a. The third line contains one integer q (1 ≤ q ≤ 200000) — the number of queries you have to process. Then q lines follow. i-th line contains four integers l, r, x and y denoting i-th query (1 ≤ l ≤ r ≤ n, 1 ≤ x, y ≤ 100). Output Print n integers — elements of array a after all changes are made. Example Input 5 1 2 3 4 5 3 3 5 3 5 1 5 5 1 1 5 1 5 Output 5 2 5 4 5 Submitted Solution: ``` import sys input_ = sys.stdin.readlines() print(input_) ```
instruction
0
62,008
5
124,016
No
output
1
62,008
5
124,017
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a consisting of n integers. You have to process q queries to this array; each query is given as four numbers l, r, x and y, denoting that for every i such that l ≤ i ≤ r and ai = x you have to set ai equal to y. Print the array after all queries are processed. Input The first line contains one integer n (1 ≤ n ≤ 200000) — the size of array a. The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 100) — the elements of array a. The third line contains one integer q (1 ≤ q ≤ 200000) — the number of queries you have to process. Then q lines follow. i-th line contains four integers l, r, x and y denoting i-th query (1 ≤ l ≤ r ≤ n, 1 ≤ x, y ≤ 100). Output Print n integers — elements of array a after all changes are made. Example Input 5 1 2 3 4 5 3 3 5 3 5 1 5 5 1 1 5 1 5 Output 5 2 5 4 5 Submitted Solution: ``` import sys input_ = sys.stdin.read() print(input_) ```
instruction
0
62,009
5
124,018
No
output
1
62,009
5
124,019
Provide a correct Python 3 solution for this coding contest problem. Given is a positive integer N. We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K. * Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K. In how many choices of K will N become 1 in the end? Constraints * 2 \leq N \leq 10^{12} * N is an integer. Input Input is given from Standard Input in the following format: N Output Print the number of choices of K in which N becomes 1 in the end. Examples Input 6 Output 3 Input 3141 Output 13 Input 314159265358 Output 9
instruction
0
62,048
5
124,096
"Correct Solution: ``` def factor(N): arr=[] for i in range(1,int(N**0.5)+1): if(N%i==0): arr.append(i) if(N//i!=i): arr.append(N//i) return arr N=int(input()) li=factor(N) fac=factor(N-1) res=len(fac)-1 for i in range(len(li)): if(li[i]==1): continue tmp=N while(tmp%li[i]==0): tmp//=li[i] if(tmp%li[i]==1): res+=1 print(res) ```
output
1
62,048
5
124,097
Provide a correct Python 3 solution for this coding contest problem. Given is a positive integer N. We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K. * Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K. In how many choices of K will N become 1 in the end? Constraints * 2 \leq N \leq 10^{12} * N is an integer. Input Input is given from Standard Input in the following format: N Output Print the number of choices of K in which N becomes 1 in the end. Examples Input 6 Output 3 Input 3141 Output 13 Input 314159265358 Output 9
instruction
0
62,049
5
124,098
"Correct Solution: ``` n,a=int(input()),1 for i in range(2,int(n**.5)+1): a+=-~(~-n//i>i)*(~-n%i<1) if n%i<1: m=n while m%i<1:m//=i a+=m%i<2 print(a+(n>2)) ```
output
1
62,049
5
124,099
Provide a correct Python 3 solution for this coding contest problem. Given is a positive integer N. We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K. * Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K. In how many choices of K will N become 1 in the end? Constraints * 2 \leq N \leq 10^{12} * N is an integer. Input Input is given from Standard Input in the following format: N Output Print the number of choices of K in which N becomes 1 in the end. Examples Input 6 Output 3 Input 3141 Output 13 Input 314159265358 Output 9
instruction
0
62,050
5
124,100
"Correct Solution: ``` n = int(input());div=[];ans=[] for i in range(1,int(n**0.5)+2): if n%i == 0: div.append(i);div.append(n//i) for i in div: if i == 1: continue tmp = n while tmp % i == 0: tmp //= i if tmp % i ==1: ans.append(i) n -= 1 for i in range(1,int(n**0.5)+2): if n%i == 0: ans.append(i);ans.append(n//i) print(len(set(ans))-1) ```
output
1
62,050
5
124,101
Provide a correct Python 3 solution for this coding contest problem. Given is a positive integer N. We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K. * Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K. In how many choices of K will N become 1 in the end? Constraints * 2 \leq N \leq 10^{12} * N is an integer. Input Input is given from Standard Input in the following format: N Output Print the number of choices of K in which N becomes 1 in the end. Examples Input 6 Output 3 Input 3141 Output 13 Input 314159265358 Output 9
instruction
0
62,052
5
124,104
"Correct Solution: ``` def check(i): tot=k while(tot%i==0): tot//=i if(tot%i==1): setl.add(i) import math k=int(input()) setl = set() setl.add(k); setl.add(k-1) for x in range(2,int(math.sqrt(k))+1): check(x) check(k//x) if(setl.__contains__(1)): setl.remove(1) print(len(setl)) ```
output
1
62,052
5
124,105
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given is a positive integer N. We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K. * Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K. In how many choices of K will N become 1 in the end? Constraints * 2 \leq N \leq 10^{12} * N is an integer. Input Input is given from Standard Input in the following format: N Output Print the number of choices of K in which N becomes 1 in the end. Examples Input 6 Output 3 Input 3141 Output 13 Input 314159265358 Output 9 Submitted Solution: ``` N = int(input()) ans = set() def check(N, k): if k<2: return False N //= k while N: if (N-1)%k==0: return True if N%k: return False N //= k for k in range(1, int(N**0.5)+1): if (N-1)%k==0: ans.add(k) ans.add((N-1)//k) if N%k==0: if check(N, k): ans.add(k) if check(N, N//k): ans.add(N//k) ans.remove(1) print(len(ans)) ```
instruction
0
62,055
5
124,110
Yes
output
1
62,055
5
124,111
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given is a positive integer N. We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K. * Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K. In how many choices of K will N become 1 in the end? Constraints * 2 \leq N \leq 10^{12} * N is an integer. Input Input is given from Standard Input in the following format: N Output Print the number of choices of K in which N becomes 1 in the end. Examples Input 6 Output 3 Input 3141 Output 13 Input 314159265358 Output 9 Submitted Solution: ``` import math def main(): N = int(input()) cnt = 0 N1 = N - 1 cnt = 2 for i in range(2, int(math.sqrt(N1)) + 1): if N1 % i == 0: cnt += 2 for i in range(2, int(math.sqrt(N)) + 1): if N % i != 0: continue m = N // i n = m while n % i == 0: n //= i if n % i == 1: cnt += 1 n = N // m i = m while n % i == 0: n //= i if n % i == 1: cnt += 1 print(cnt) main() ```
instruction
0
62,059
5
124,118
No
output
1
62,059
5
124,119
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given is a positive integer N. We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K. * Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K. In how many choices of K will N become 1 in the end? Constraints * 2 \leq N \leq 10^{12} * N is an integer. Input Input is given from Standard Input in the following format: N Output Print the number of choices of K in which N becomes 1 in the end. Examples Input 6 Output 3 Input 3141 Output 13 Input 314159265358 Output 9 Submitted Solution: ``` N = int(input()) def check(p): _N = N while _N%p == 0: _N //= p return ((_N-1)%p == 0) or (_N == 1) n = int(N**0.5) P0 = [N] P1 = [N-1] for i in range(2, n+1): if (N-1)%i == 0: P1 += [i, (N-1)//i] if N%i == 0: P0 += [i, N//i] ans = len(P1) for p in P0: ans += check(p) print(ans) ```
instruction
0
62,060
5
124,120
No
output
1
62,060
5
124,121
Provide a correct Python 3 solution for this coding contest problem. A group of people played a game. All players had distinct scores, which are positive integers. Takahashi knows N facts on the players' scores. The i-th fact is as follows: the A_i-th highest score among the players is B_i. Find the maximum possible number of players in the game. Constraints * 1 \leq N \leq 10^5 * 1 \leq A_i \leq 10^9(1\leq i\leq N) * 0 \leq B_i \leq 10^9(1\leq i\leq N) * If i ≠ j, A_i ≠ A_j. * There exists a possible outcome of the game that are consistent with the facts. * All input values are integers. Inputs Input is given from Standard Input in the following format: N A_1 B_1 : A_N B_N Outputs Print the maximum possible number of players in the game. Examples Input 3 4 7 2 9 6 2 Output 8 Input 5 1 10 3 6 5 2 4 4 2 8 Output 7 Input 2 1 1000000000 1000000000 1 Output 1000000001
instruction
0
62,141
5
124,282
"Correct Solution: ``` n = int(input()) AB = [list(map(int,input().split())) for i in range(n)] AB.sort(reverse=True) print(AB[0][0]+AB[0][1]) ```
output
1
62,141
5
124,283
Provide a correct Python 3 solution for this coding contest problem. A group of people played a game. All players had distinct scores, which are positive integers. Takahashi knows N facts on the players' scores. The i-th fact is as follows: the A_i-th highest score among the players is B_i. Find the maximum possible number of players in the game. Constraints * 1 \leq N \leq 10^5 * 1 \leq A_i \leq 10^9(1\leq i\leq N) * 0 \leq B_i \leq 10^9(1\leq i\leq N) * If i ≠ j, A_i ≠ A_j. * There exists a possible outcome of the game that are consistent with the facts. * All input values are integers. Inputs Input is given from Standard Input in the following format: N A_1 B_1 : A_N B_N Outputs Print the maximum possible number of players in the game. Examples Input 3 4 7 2 9 6 2 Output 8 Input 5 1 10 3 6 5 2 4 4 2 8 Output 7 Input 2 1 1000000000 1000000000 1 Output 1000000001
instruction
0
62,143
5
124,286
"Correct Solution: ``` N = int(input()) AB = [list(map(int, input().split())) for _ in range(N)] sAB = sorted(AB, key=lambda x: - x[0]) print(sum(sAB[0])) ```
output
1
62,143
5
124,287
Provide a correct Python 3 solution for this coding contest problem. A group of people played a game. All players had distinct scores, which are positive integers. Takahashi knows N facts on the players' scores. The i-th fact is as follows: the A_i-th highest score among the players is B_i. Find the maximum possible number of players in the game. Constraints * 1 \leq N \leq 10^5 * 1 \leq A_i \leq 10^9(1\leq i\leq N) * 0 \leq B_i \leq 10^9(1\leq i\leq N) * If i ≠ j, A_i ≠ A_j. * There exists a possible outcome of the game that are consistent with the facts. * All input values are integers. Inputs Input is given from Standard Input in the following format: N A_1 B_1 : A_N B_N Outputs Print the maximum possible number of players in the game. Examples Input 3 4 7 2 9 6 2 Output 8 Input 5 1 10 3 6 5 2 4 4 2 8 Output 7 Input 2 1 1000000000 1000000000 1 Output 1000000001
instruction
0
62,144
5
124,288
"Correct Solution: ``` N=int(input()) maxA=0 minB=10**9 for _ in range(N): A,B=map(int,input().split()) if maxA<A: maxA=A minB=B print(maxA+minB) ```
output
1
62,144
5
124,289
Provide a correct Python 3 solution for this coding contest problem. A group of people played a game. All players had distinct scores, which are positive integers. Takahashi knows N facts on the players' scores. The i-th fact is as follows: the A_i-th highest score among the players is B_i. Find the maximum possible number of players in the game. Constraints * 1 \leq N \leq 10^5 * 1 \leq A_i \leq 10^9(1\leq i\leq N) * 0 \leq B_i \leq 10^9(1\leq i\leq N) * If i ≠ j, A_i ≠ A_j. * There exists a possible outcome of the game that are consistent with the facts. * All input values are integers. Inputs Input is given from Standard Input in the following format: N A_1 B_1 : A_N B_N Outputs Print the maximum possible number of players in the game. Examples Input 3 4 7 2 9 6 2 Output 8 Input 5 1 10 3 6 5 2 4 4 2 8 Output 7 Input 2 1 1000000000 1000000000 1 Output 1000000001
instruction
0
62,145
5
124,290
"Correct Solution: ``` N = int(input()) AB = [list(map(int, input().split())) for _ in range(N)] ab = sorted(AB) print(sum(ab[-1])) ```
output
1
62,145
5
124,291
Provide a correct Python 3 solution for this coding contest problem. A group of people played a game. All players had distinct scores, which are positive integers. Takahashi knows N facts on the players' scores. The i-th fact is as follows: the A_i-th highest score among the players is B_i. Find the maximum possible number of players in the game. Constraints * 1 \leq N \leq 10^5 * 1 \leq A_i \leq 10^9(1\leq i\leq N) * 0 \leq B_i \leq 10^9(1\leq i\leq N) * If i ≠ j, A_i ≠ A_j. * There exists a possible outcome of the game that are consistent with the facts. * All input values are integers. Inputs Input is given from Standard Input in the following format: N A_1 B_1 : A_N B_N Outputs Print the maximum possible number of players in the game. Examples Input 3 4 7 2 9 6 2 Output 8 Input 5 1 10 3 6 5 2 4 4 2 8 Output 7 Input 2 1 1000000000 1000000000 1 Output 1000000001
instruction
0
62,146
5
124,292
"Correct Solution: ``` n = int(input()) a,b = [],[] for i in range(n): aa, bb = map(int, input().split()) a.append(aa) b.append(bb) print (max(a)+min(b)) ```
output
1
62,146
5
124,293
Provide a correct Python 3 solution for this coding contest problem. A group of people played a game. All players had distinct scores, which are positive integers. Takahashi knows N facts on the players' scores. The i-th fact is as follows: the A_i-th highest score among the players is B_i. Find the maximum possible number of players in the game. Constraints * 1 \leq N \leq 10^5 * 1 \leq A_i \leq 10^9(1\leq i\leq N) * 0 \leq B_i \leq 10^9(1\leq i\leq N) * If i ≠ j, A_i ≠ A_j. * There exists a possible outcome of the game that are consistent with the facts. * All input values are integers. Inputs Input is given from Standard Input in the following format: N A_1 B_1 : A_N B_N Outputs Print the maximum possible number of players in the game. Examples Input 3 4 7 2 9 6 2 Output 8 Input 5 1 10 3 6 5 2 4 4 2 8 Output 7 Input 2 1 1000000000 1000000000 1 Output 1000000001
instruction
0
62,147
5
124,294
"Correct Solution: ``` n = int(input()) In = sorted([list(map(int,input().split())) for i in range(n)]) print(In[-1][0]+In[-1][1]) ```
output
1
62,147
5
124,295
Provide a correct Python 3 solution for this coding contest problem. A group of people played a game. All players had distinct scores, which are positive integers. Takahashi knows N facts on the players' scores. The i-th fact is as follows: the A_i-th highest score among the players is B_i. Find the maximum possible number of players in the game. Constraints * 1 \leq N \leq 10^5 * 1 \leq A_i \leq 10^9(1\leq i\leq N) * 0 \leq B_i \leq 10^9(1\leq i\leq N) * If i ≠ j, A_i ≠ A_j. * There exists a possible outcome of the game that are consistent with the facts. * All input values are integers. Inputs Input is given from Standard Input in the following format: N A_1 B_1 : A_N B_N Outputs Print the maximum possible number of players in the game. Examples Input 3 4 7 2 9 6 2 Output 8 Input 5 1 10 3 6 5 2 4 4 2 8 Output 7 Input 2 1 1000000000 1000000000 1 Output 1000000001
instruction
0
62,148
5
124,296
"Correct Solution: ``` N=int(input()) A=[list(map(int,input().split())) for _ in range(N)] AA=sorted(A) print(AA[-1][0]+AA[-1][1]) ```
output
1
62,148
5
124,297
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A group of people played a game. All players had distinct scores, which are positive integers. Takahashi knows N facts on the players' scores. The i-th fact is as follows: the A_i-th highest score among the players is B_i. Find the maximum possible number of players in the game. Constraints * 1 \leq N \leq 10^5 * 1 \leq A_i \leq 10^9(1\leq i\leq N) * 0 \leq B_i \leq 10^9(1\leq i\leq N) * If i ≠ j, A_i ≠ A_j. * There exists a possible outcome of the game that are consistent with the facts. * All input values are integers. Inputs Input is given from Standard Input in the following format: N A_1 B_1 : A_N B_N Outputs Print the maximum possible number of players in the game. Examples Input 3 4 7 2 9 6 2 Output 8 Input 5 1 10 3 6 5 2 4 4 2 8 Output 7 Input 2 1 1000000000 1000000000 1 Output 1000000001 Submitted Solution: ``` n=int(input()) a=0 ans=0 for i in range(n): x,y=map(int,input().split()) if a<x: ans=x+y-1 a=x print(ans) ```
instruction
0
62,156
5
124,312
No
output
1
62,156
5
124,313
Provide a correct Python 3 solution for this coding contest problem. Problem Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below. A image of angles Constraints The input satisfies the following conditions. * Angle is expressed in degrees * 0 ≤ θ1, θ2 <360 * θ1 and θ2 are integers * | θ1 − θ2 | ≠ 180 * No input is given that gives the answer [0,0.0001] or [359.999,360) Input The input is given in the following format. θ1 θ2 Output Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001. Examples Input 10 20 Output 15.0 Input 20 350 Output 5.0
instruction
0
62,228
5
124,456
"Correct Solution: ``` a = int(input()) b = int(input()) a = a % 360 b = b % 360 if a > b : a, b = b, a if b - a > 180 : a += 360 t = abs((a - b) / 2) ans = min(a, b) + t ans = ans % 360 print('{:6f}'.format(ans)) ```
output
1
62,228
5
124,457
Provide a correct Python 3 solution for this coding contest problem. Problem Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below. A image of angles Constraints The input satisfies the following conditions. * Angle is expressed in degrees * 0 ≤ θ1, θ2 <360 * θ1 and θ2 are integers * | θ1 − θ2 | ≠ 180 * No input is given that gives the answer [0,0.0001] or [359.999,360) Input The input is given in the following format. θ1 θ2 Output Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001. Examples Input 10 20 Output 15.0 Input 20 350 Output 5.0
instruction
0
62,229
5
124,458
"Correct Solution: ``` a = int(input()) b = int(input()) a, b = min(a, b), max(a, b) if b - a <= 180: print((a+b) / 2) else: print(((a+b+360) % 720) / 2) ```
output
1
62,229
5
124,459
Provide a correct Python 3 solution for this coding contest problem. Problem Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below. A image of angles Constraints The input satisfies the following conditions. * Angle is expressed in degrees * 0 ≤ θ1, θ2 <360 * θ1 and θ2 are integers * | θ1 − θ2 | ≠ 180 * No input is given that gives the answer [0,0.0001] or [359.999,360) Input The input is given in the following format. θ1 θ2 Output Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001. Examples Input 10 20 Output 15.0 Input 20 350 Output 5.0
instruction
0
62,230
5
124,460
"Correct Solution: ``` a, b = int(input()), int(input()) print((a + b) / 2 % 360 if abs (a - b) % 360 < 180 else (a + b + 360) / 2 % 360) ```
output
1
62,230
5
124,461
Provide a correct Python 3 solution for this coding contest problem. Problem Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below. A image of angles Constraints The input satisfies the following conditions. * Angle is expressed in degrees * 0 ≤ θ1, θ2 <360 * θ1 and θ2 are integers * | θ1 − θ2 | ≠ 180 * No input is given that gives the answer [0,0.0001] or [359.999,360) Input The input is given in the following format. θ1 θ2 Output Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001. Examples Input 10 20 Output 15.0 Input 20 350 Output 5.0
instruction
0
62,231
5
124,462
"Correct Solution: ``` s1 = int(input()) s2 = int(input()) a = min(s1,s2) b = max(s1,s2) if b-a>180: print((b+(360-b+a)/2)%360) else: print((a+b)/2) ```
output
1
62,231
5
124,463
Provide a correct Python 3 solution for this coding contest problem. Problem Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below. A image of angles Constraints The input satisfies the following conditions. * Angle is expressed in degrees * 0 ≤ θ1, θ2 <360 * θ1 and θ2 are integers * | θ1 − θ2 | ≠ 180 * No input is given that gives the answer [0,0.0001] or [359.999,360) Input The input is given in the following format. θ1 θ2 Output Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001. Examples Input 10 20 Output 15.0 Input 20 350 Output 5.0
instruction
0
62,232
5
124,464
"Correct Solution: ``` s1 = int(input()) s2 = int(input()) if s1 > s2: s1, s2 = s2, s1 if s2 - s1 < 180: print((s1+s2)/2) elif (s1+s2)/2 +180 < 360: print((s1+s2)/2 +180) else: print((s1 + s2) / 2 - 180) ```
output
1
62,232
5
124,465
Provide a correct Python 3 solution for this coding contest problem. Problem Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below. A image of angles Constraints The input satisfies the following conditions. * Angle is expressed in degrees * 0 ≤ θ1, θ2 <360 * θ1 and θ2 are integers * | θ1 − θ2 | ≠ 180 * No input is given that gives the answer [0,0.0001] or [359.999,360) Input The input is given in the following format. θ1 θ2 Output Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001. Examples Input 10 20 Output 15.0 Input 20 350 Output 5.0
instruction
0
62,234
5
124,468
"Correct Solution: ``` angs = [int(input()), int(input())] angs.sort() if angs[1] - angs[0] > 180: ans = sum(angs) / 2 + 180 if ans >= 360: ans -= 360 print(ans) else: print(sum(angs) / 2) ```
output
1
62,234
5
124,469
Provide a correct Python 3 solution for this coding contest problem. Problem Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below. A image of angles Constraints The input satisfies the following conditions. * Angle is expressed in degrees * 0 ≤ θ1, θ2 <360 * θ1 and θ2 are integers * | θ1 − θ2 | ≠ 180 * No input is given that gives the answer [0,0.0001] or [359.999,360) Input The input is given in the following format. θ1 θ2 Output Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001. Examples Input 10 20 Output 15.0 Input 20 350 Output 5.0
instruction
0
62,235
5
124,470
"Correct Solution: ``` t1 = int(input()) t2 = int(input()) x = (t2-t1)/2 a = x for i in range(-2,3): t = x + i*180 if abs(a) > abs(t): a = t ans = t1+a while ans < 0: ans += 360 while ans > 360: ans -= 360 print(ans) ```
output
1
62,235
5
124,471
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Problem Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below. A image of angles Constraints The input satisfies the following conditions. * Angle is expressed in degrees * 0 ≤ θ1, θ2 <360 * θ1 and θ2 are integers * | θ1 − θ2 | ≠ 180 * No input is given that gives the answer [0,0.0001] or [359.999,360) Input The input is given in the following format. θ1 θ2 Output Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001. Examples Input 10 20 Output 15.0 Input 20 350 Output 5.0 Submitted Solution: ``` a,b=int(input()),int(input()) print((a+b+360*(abs(a-b)>180))/2%360) ```
instruction
0
62,236
5
124,472
Yes
output
1
62,236
5
124,473
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Problem Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below. A image of angles Constraints The input satisfies the following conditions. * Angle is expressed in degrees * 0 ≤ θ1, θ2 <360 * θ1 and θ2 are integers * | θ1 − θ2 | ≠ 180 * No input is given that gives the answer [0,0.0001] or [359.999,360) Input The input is given in the following format. θ1 θ2 Output Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001. Examples Input 10 20 Output 15.0 Input 20 350 Output 5.0 Submitted Solution: ``` a = float(input()) b = float(input()) if a>b: a,b=b,a ansa = (a+b)/2 ta = abs(a-ansa) if ansa<0: ansa+=360.0 ansb = (a+b-360)/2 tb = abs(a-ansb) if ansb<0: ansb+=360.0 if ta<tb: print(ansa) else: print(ansb) ```
instruction
0
62,237
5
124,474
Yes
output
1
62,237
5
124,475
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Problem Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below. A image of angles Constraints The input satisfies the following conditions. * Angle is expressed in degrees * 0 ≤ θ1, θ2 <360 * θ1 and θ2 are integers * | θ1 − θ2 | ≠ 180 * No input is given that gives the answer [0,0.0001] or [359.999,360) Input The input is given in the following format. θ1 θ2 Output Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001. Examples Input 10 20 Output 15.0 Input 20 350 Output 5.0 Submitted Solution: ``` t1 = int(input()) t2 = int(input()) if not t1 < t2: t1, t2 = t2, t1 if t2 - t1 <= 180: print((t2 + t1)/2) else: print(((t2 + t1 + 360) % 720)/2) ```
instruction
0
62,238
5
124,476
Yes
output
1
62,238
5
124,477
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Problem Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below. A image of angles Constraints The input satisfies the following conditions. * Angle is expressed in degrees * 0 ≤ θ1, θ2 <360 * θ1 and θ2 are integers * | θ1 − θ2 | ≠ 180 * No input is given that gives the answer [0,0.0001] or [359.999,360) Input The input is given in the following format. θ1 θ2 Output Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001. Examples Input 10 20 Output 15.0 Input 20 350 Output 5.0 Submitted Solution: ``` a=int(input()) b=int(input()) if (a+b)/2<180: print((a+b)/2) else: print(((a+b)/2)-180) ```
instruction
0
62,239
5
124,478
No
output
1
62,239
5
124,479
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Problem Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below. A image of angles Constraints The input satisfies the following conditions. * Angle is expressed in degrees * 0 ≤ θ1, θ2 <360 * θ1 and θ2 are integers * | θ1 − θ2 | ≠ 180 * No input is given that gives the answer [0,0.0001] or [359.999,360) Input The input is given in the following format. θ1 θ2 Output Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001. Examples Input 10 20 Output 15.0 Input 20 350 Output 5.0 Submitted Solution: ``` a = float(input()) b = float(input()) #if a>b: a,b=b,a ansa = (a+b)/2 ta = abs(a-ansa) if ansa<0: ansa+=360.0 ansb = (a+b-360)/2 tb = abs(a-ansb) if ansb<0: ansb+=360.0 if ta<tb: print(ansa) else: print(ansb) ```
instruction
0
62,240
5
124,480
No
output
1
62,240
5
124,481
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Problem Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below. A image of angles Constraints The input satisfies the following conditions. * Angle is expressed in degrees * 0 ≤ θ1, θ2 <360 * θ1 and θ2 are integers * | θ1 − θ2 | ≠ 180 * No input is given that gives the answer [0,0.0001] or [359.999,360) Input The input is given in the following format. θ1 θ2 Output Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001. Examples Input 10 20 Output 15.0 Input 20 350 Output 5.0 Submitted Solution: ``` s1 = int(input()) s2 = int(input()) d = s1 - s2 if abs(d) >= 180: s1 = min(360-s1, s1) s2 = min(360-s2, s2) if s1 >= s2: print(abs(s1-s2)/2) else: print(360-abs(s1-s2)/2) else: print(abs(d)/2 + min(s1, s2)) ```
instruction
0
62,241
5
124,482
No
output
1
62,241
5
124,483
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Problem Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below. A image of angles Constraints The input satisfies the following conditions. * Angle is expressed in degrees * 0 ≤ θ1, θ2 <360 * θ1 and θ2 are integers * | θ1 − θ2 | ≠ 180 * No input is given that gives the answer [0,0.0001] or [359.999,360) Input The input is given in the following format. θ1 θ2 Output Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001. Examples Input 10 20 Output 15.0 Input 20 350 Output 5.0 Submitted Solution: ``` a=int(input()) b=int(input()) if a+b<360: print((a+b)/2) else: print(((a+b)/2)-180) ```
instruction
0
62,242
5
124,484
No
output
1
62,242
5
124,485
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive integer n greater or equal to 2. For every pair of integers a and b (2 ≤ |a|, |b| ≤ n), you can transform a into b if and only if there exists an integer x such that 1 < |x| and (a ⋅ x = b or b ⋅ x = a), where |x| denotes the absolute value of x. After such a transformation, your score increases by |x| points and you are not allowed to transform a into b nor b into a anymore. Initially, you have a score of 0. You can start at any integer and transform it as many times as you like. What is the maximum score you can achieve? Input A single line contains a single integer n (2 ≤ n ≤ 100 000) — the given integer described above. Output Print an only integer — the maximum score that can be achieved with the transformations. If it is not possible to perform even a single transformation for all possible starting integers, print 0. Examples Input 4 Output 8 Input 6 Output 28 Input 2 Output 0 Note In the first example, the transformations are 2 → 4 → (-2) → (-4) → 2. In the third example, it is impossible to perform even a single transformation.
instruction
0
62,293
5
124,586
Tags: dfs and similar, graphs, implementation, math Correct Solution: ``` import sys input=sys.stdin.readline n=int(input()) print(sum([sum([k//j for k in range(2*j,n+1,j)]) for j in range(2,n+1)])*4) ```
output
1
62,293
5
124,587
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive integer n greater or equal to 2. For every pair of integers a and b (2 ≤ |a|, |b| ≤ n), you can transform a into b if and only if there exists an integer x such that 1 < |x| and (a ⋅ x = b or b ⋅ x = a), where |x| denotes the absolute value of x. After such a transformation, your score increases by |x| points and you are not allowed to transform a into b nor b into a anymore. Initially, you have a score of 0. You can start at any integer and transform it as many times as you like. What is the maximum score you can achieve? Input A single line contains a single integer n (2 ≤ n ≤ 100 000) — the given integer described above. Output Print an only integer — the maximum score that can be achieved with the transformations. If it is not possible to perform even a single transformation for all possible starting integers, print 0. Examples Input 4 Output 8 Input 6 Output 28 Input 2 Output 0 Note In the first example, the transformations are 2 → 4 → (-2) → (-4) → 2. In the third example, it is impossible to perform even a single transformation.
instruction
0
62,295
5
124,590
Tags: dfs and similar, graphs, implementation, math Correct Solution: ``` n = int(input()) sum = 0 for i in range(2, n + 1): j = 2 while(j * i <= n): sum += i j += 1 print(4 * sum) ```
output
1
62,295
5
124,591
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive integer n greater or equal to 2. For every pair of integers a and b (2 ≤ |a|, |b| ≤ n), you can transform a into b if and only if there exists an integer x such that 1 < |x| and (a ⋅ x = b or b ⋅ x = a), where |x| denotes the absolute value of x. After such a transformation, your score increases by |x| points and you are not allowed to transform a into b nor b into a anymore. Initially, you have a score of 0. You can start at any integer and transform it as many times as you like. What is the maximum score you can achieve? Input A single line contains a single integer n (2 ≤ n ≤ 100 000) — the given integer described above. Output Print an only integer — the maximum score that can be achieved with the transformations. If it is not possible to perform even a single transformation for all possible starting integers, print 0. Examples Input 4 Output 8 Input 6 Output 28 Input 2 Output 0 Note In the first example, the transformations are 2 → 4 → (-2) → (-4) → 2. In the third example, it is impossible to perform even a single transformation.
instruction
0
62,296
5
124,592
Tags: dfs and similar, graphs, implementation, math Correct Solution: ``` n=int(input()) ans=0 for i in range(2,n+1): j=2 lead=2*i while(lead<=n): ans+=4*j j+=1 lead+=i print(ans) ```
output
1
62,296
5
124,593
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive integer n greater or equal to 2. For every pair of integers a and b (2 ≤ |a|, |b| ≤ n), you can transform a into b if and only if there exists an integer x such that 1 < |x| and (a ⋅ x = b or b ⋅ x = a), where |x| denotes the absolute value of x. After such a transformation, your score increases by |x| points and you are not allowed to transform a into b nor b into a anymore. Initially, you have a score of 0. You can start at any integer and transform it as many times as you like. What is the maximum score you can achieve? Input A single line contains a single integer n (2 ≤ n ≤ 100 000) — the given integer described above. Output Print an only integer — the maximum score that can be achieved with the transformations. If it is not possible to perform even a single transformation for all possible starting integers, print 0. Examples Input 4 Output 8 Input 6 Output 28 Input 2 Output 0 Note In the first example, the transformations are 2 → 4 → (-2) → (-4) → 2. In the third example, it is impossible to perform even a single transformation.
instruction
0
62,297
5
124,594
Tags: dfs and similar, graphs, implementation, math Correct Solution: ``` import sys input=sys.stdin.readline n=int(input()) ans=0 for i in range(2,n+1): for j in range(i+i,n+1,i): ans+=j//i print(4*ans) ```
output
1
62,297
5
124,595
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive integer n greater or equal to 2. For every pair of integers a and b (2 ≤ |a|, |b| ≤ n), you can transform a into b if and only if there exists an integer x such that 1 < |x| and (a ⋅ x = b or b ⋅ x = a), where |x| denotes the absolute value of x. After such a transformation, your score increases by |x| points and you are not allowed to transform a into b nor b into a anymore. Initially, you have a score of 0. You can start at any integer and transform it as many times as you like. What is the maximum score you can achieve? Input A single line contains a single integer n (2 ≤ n ≤ 100 000) — the given integer described above. Output Print an only integer — the maximum score that can be achieved with the transformations. If it is not possible to perform even a single transformation for all possible starting integers, print 0. Examples Input 4 Output 8 Input 6 Output 28 Input 2 Output 0 Note In the first example, the transformations are 2 → 4 → (-2) → (-4) → 2. In the third example, it is impossible to perform even a single transformation.
instruction
0
62,298
5
124,596
Tags: dfs and similar, graphs, implementation, math Correct Solution: ``` n = int(input()) print(sum([(n//i -1)*i*4 for i in range(2,n+1)])) ```
output
1
62,298
5
124,597
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive integer n greater or equal to 2. For every pair of integers a and b (2 ≤ |a|, |b| ≤ n), you can transform a into b if and only if there exists an integer x such that 1 < |x| and (a ⋅ x = b or b ⋅ x = a), where |x| denotes the absolute value of x. After such a transformation, your score increases by |x| points and you are not allowed to transform a into b nor b into a anymore. Initially, you have a score of 0. You can start at any integer and transform it as many times as you like. What is the maximum score you can achieve? Input A single line contains a single integer n (2 ≤ n ≤ 100 000) — the given integer described above. Output Print an only integer — the maximum score that can be achieved with the transformations. If it is not possible to perform even a single transformation for all possible starting integers, print 0. Examples Input 4 Output 8 Input 6 Output 28 Input 2 Output 0 Note In the first example, the transformations are 2 → 4 → (-2) → (-4) → 2. In the third example, it is impossible to perform even a single transformation.
instruction
0
62,299
5
124,598
Tags: dfs and similar, graphs, implementation, math Correct Solution: ``` n = int(input()) ans = 0 for i in range(2,n//2+1): x = n // i ans += ( x * (x+1) // 2 - 1 ) * 4 print(ans) ```
output
1
62,299
5
124,599