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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. BerPhone X is almost ready for release with n applications being preinstalled on the phone. A category of an application characterizes a genre or a theme of this application (like "game", "business", or "education"). The categories are given as integers between 1 and n, inclusive; the i-th application has category c_i. You can choose m β€” the number of screens and s β€” the size of each screen. You need to fit all n icons of the applications (one icon representing one application) meeting the following requirements: * On each screen, all the icons must belong to applications of the same category (but different screens can contain icons of applications of the same category); * Each screen must be either completely filled with icons (the number of icons on the screen is equal to s) or almost filled with icons (the number of icons is equal to s-1). Your task is to find the minimal possible number of screens m. Input The first line contains an integer t (1 ≀ t ≀ 10 000) β€” the number of test cases in the input. Then t test cases follow. The first line of each test case contains an integer n (1 ≀ n ≀ 2β‹…10^6) β€” the number of the icons. The second line contains n integers c_1, c_2, ..., c_n (1 ≀ c_i ≀ n), where c_i is the category of the i-th application. It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 2β‹…10^6. Output Print t integers β€” the answers to the given test cases in the order they follow in the input. The answer to a test case is an integer m β€” the minimum number of screens on which all n icons can be placed satisfying the given requirements. Example Input 3 11 1 5 1 5 1 5 1 1 1 1 5 6 1 2 2 2 2 1 5 4 3 3 1 2 Output 3 3 4 Note In the first test case of the example, all the icons can be placed on three screens of size 4: a screen with 4 icons of the category 1, a screen with 3 icons of the category 1, and a screen with 4 icons of the category 5. Submitted Solution: ``` import sys import os from io import BytesIO, IOBase from types import GeneratorType from collections import defaultdict BUFSIZE = 8192 import math 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") t=int(input()) for i in range(t): #n=int(input()) #b=list(map(int,input().split())) n=int(input()) c=list(map(int,input().split())) d=defaultdict(lambda:0) for j in c: d[j]+=1 cnt=[] for j in d: cnt.append(d[j]) cnt.sort() mi=cnt[0]+1 ans=float("inf") i=1 while(i<=mi): curr=0 poss=1 for j in cnt: if j>=((i-1)*math.ceil(j/i)): curr+=math.ceil(j/i) else: poss=0 break if poss: ans=min(ans,curr) i+=1 print(ans) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. BerPhone X is almost ready for release with n applications being preinstalled on the phone. A category of an application characterizes a genre or a theme of this application (like "game", "business", or "education"). The categories are given as integers between 1 and n, inclusive; the i-th application has category c_i. You can choose m β€” the number of screens and s β€” the size of each screen. You need to fit all n icons of the applications (one icon representing one application) meeting the following requirements: * On each screen, all the icons must belong to applications of the same category (but different screens can contain icons of applications of the same category); * Each screen must be either completely filled with icons (the number of icons on the screen is equal to s) or almost filled with icons (the number of icons is equal to s-1). Your task is to find the minimal possible number of screens m. Input The first line contains an integer t (1 ≀ t ≀ 10 000) β€” the number of test cases in the input. Then t test cases follow. The first line of each test case contains an integer n (1 ≀ n ≀ 2β‹…10^6) β€” the number of the icons. The second line contains n integers c_1, c_2, ..., c_n (1 ≀ c_i ≀ n), where c_i is the category of the i-th application. It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 2β‹…10^6. Output Print t integers β€” the answers to the given test cases in the order they follow in the input. The answer to a test case is an integer m β€” the minimum number of screens on which all n icons can be placed satisfying the given requirements. Example Input 3 11 1 5 1 5 1 5 1 1 1 1 5 6 1 2 2 2 2 1 5 4 3 3 1 2 Output 3 3 4 Note In the first test case of the example, all the icons can be placed on three screens of size 4: a screen with 4 icons of the category 1, a screen with 3 icons of the category 1, and a screen with 4 icons of the category 5. Submitted Solution: ``` from collections import Counter as CO t=int(input()) for _ in range(t): n=int(input()) arr=list(map(int,input().split())) freq=dict(CO(arr)) l=[] for k in freq: l+=[freq[k]] ls=list(set(l)) fact=[2] for i in ls: for j in range(1,int(i**.5)+1): if(i%j==0): fact+=[j,i//j] fact=list(set(fact)) fact.sort(reverse=True) #print(fact) #print(ls) for i in fact: flag=0 for j in ls: if((i-j%i)<=j//i+1 or j%i==0 ): pass else: #print(i,j) flag=1 break if(flag==0): ans=i break co=0 for j in l: if(j%ans==0): co+=j//ans else: co+=j//ans+1 print(co) ```
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101,330
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output
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. BerPhone X is almost ready for release with n applications being preinstalled on the phone. A category of an application characterizes a genre or a theme of this application (like "game", "business", or "education"). The categories are given as integers between 1 and n, inclusive; the i-th application has category c_i. You can choose m β€” the number of screens and s β€” the size of each screen. You need to fit all n icons of the applications (one icon representing one application) meeting the following requirements: * On each screen, all the icons must belong to applications of the same category (but different screens can contain icons of applications of the same category); * Each screen must be either completely filled with icons (the number of icons on the screen is equal to s) or almost filled with icons (the number of icons is equal to s-1). Your task is to find the minimal possible number of screens m. Input The first line contains an integer t (1 ≀ t ≀ 10 000) β€” the number of test cases in the input. Then t test cases follow. The first line of each test case contains an integer n (1 ≀ n ≀ 2β‹…10^6) β€” the number of the icons. The second line contains n integers c_1, c_2, ..., c_n (1 ≀ c_i ≀ n), where c_i is the category of the i-th application. It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 2β‹…10^6. Output Print t integers β€” the answers to the given test cases in the order they follow in the input. The answer to a test case is an integer m β€” the minimum number of screens on which all n icons can be placed satisfying the given requirements. Example Input 3 11 1 5 1 5 1 5 1 1 1 1 5 6 1 2 2 2 2 1 5 4 3 3 1 2 Output 3 3 4 Note In the first test case of the example, all the icons can be placed on three screens of size 4: a screen with 4 icons of the category 1, a screen with 3 icons of the category 1, and a screen with 4 icons of the category 5. Submitted Solution: ``` from collections import Counter from math import ceil t = int(input()) for _ in range(0,t): n = int(input()) ss = [int(i) for i in input().split()] c = Counter(ss) aa = sorted([int(i) for i in c.values()]) maxx = 10**9+7 check = list(set(sorted(aa))) ll = check[0] if len(check)>=2 and check[1]-check[0] == 1: ll = check[1] for i in range(1,ll+1): val = True pos = [] for ii in aa: if ii%i == 0 or ii%i == i-1: pos.append(ceil(ii/i)) continue else: val = False break if val: maxx = min(maxx,sum(pos)) print(maxx) ```
instruction
0
101,331
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No
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101,331
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. BerPhone X is almost ready for release with n applications being preinstalled on the phone. A category of an application characterizes a genre or a theme of this application (like "game", "business", or "education"). The categories are given as integers between 1 and n, inclusive; the i-th application has category c_i. You can choose m β€” the number of screens and s β€” the size of each screen. You need to fit all n icons of the applications (one icon representing one application) meeting the following requirements: * On each screen, all the icons must belong to applications of the same category (but different screens can contain icons of applications of the same category); * Each screen must be either completely filled with icons (the number of icons on the screen is equal to s) or almost filled with icons (the number of icons is equal to s-1). Your task is to find the minimal possible number of screens m. Input The first line contains an integer t (1 ≀ t ≀ 10 000) β€” the number of test cases in the input. Then t test cases follow. The first line of each test case contains an integer n (1 ≀ n ≀ 2β‹…10^6) β€” the number of the icons. The second line contains n integers c_1, c_2, ..., c_n (1 ≀ c_i ≀ n), where c_i is the category of the i-th application. It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 2β‹…10^6. Output Print t integers β€” the answers to the given test cases in the order they follow in the input. The answer to a test case is an integer m β€” the minimum number of screens on which all n icons can be placed satisfying the given requirements. Example Input 3 11 1 5 1 5 1 5 1 1 1 1 5 6 1 2 2 2 2 1 5 4 3 3 1 2 Output 3 3 4 Note In the first test case of the example, all the icons can be placed on three screens of size 4: a screen with 4 icons of the category 1, a screen with 3 icons of the category 1, and a screen with 4 icons of the category 5. Submitted Solution: ``` def function(lis): lis_item = [] lis_item_freq = [] for i in lis: if i in lis_item: lis_item_freq[lis_item.index(i)] += 1 else: lis_item.append(i) lis_item_freq.append(0) lis_item_freq[lis_item.index(i)] += 1 least_occured = min(lis_item_freq) max_possible = least_occured # it can be least_occured - 1 for i in lis_item_freq: if i%max_possible < max_possible-1 and i%max_possible !=0: #print("yes") max_possible -= 1 if max_possible+1 in lis_item_freq: max_possible += 1 summ = 0 for i in lis_item_freq: summ += i//max_possible if i%max_possible!=0: summ+=1 print(summ) # print(lis_item) # print(lis_item_freq) t = int(input()) for i in range(t): length = int(input()) value = input().split() function(value) ```
instruction
0
101,332
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202,664
No
output
1
101,332
7
202,665
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. BerPhone X is almost ready for release with n applications being preinstalled on the phone. A category of an application characterizes a genre or a theme of this application (like "game", "business", or "education"). The categories are given as integers between 1 and n, inclusive; the i-th application has category c_i. You can choose m β€” the number of screens and s β€” the size of each screen. You need to fit all n icons of the applications (one icon representing one application) meeting the following requirements: * On each screen, all the icons must belong to applications of the same category (but different screens can contain icons of applications of the same category); * Each screen must be either completely filled with icons (the number of icons on the screen is equal to s) or almost filled with icons (the number of icons is equal to s-1). Your task is to find the minimal possible number of screens m. Input The first line contains an integer t (1 ≀ t ≀ 10 000) β€” the number of test cases in the input. Then t test cases follow. The first line of each test case contains an integer n (1 ≀ n ≀ 2β‹…10^6) β€” the number of the icons. The second line contains n integers c_1, c_2, ..., c_n (1 ≀ c_i ≀ n), where c_i is the category of the i-th application. It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 2β‹…10^6. Output Print t integers β€” the answers to the given test cases in the order they follow in the input. The answer to a test case is an integer m β€” the minimum number of screens on which all n icons can be placed satisfying the given requirements. Example Input 3 11 1 5 1 5 1 5 1 1 1 1 5 6 1 2 2 2 2 1 5 4 3 3 1 2 Output 3 3 4 Note In the first test case of the example, all the icons can be placed on three screens of size 4: a screen with 4 icons of the category 1, a screen with 3 icons of the category 1, and a screen with 4 icons of the category 5. Submitted Solution: ``` from collections import defaultdict as dd t=int(input()) while t: n=int(input()) d=dd(int) l=list(map(int,input().split())) for i in l: d[i]+=1 li=[] for i in d: li.append(d[i]) mx=1000000000000000000 si=li[0] ll=[] mi=10000000000000000000000 for m in range(1,min(li)+1): cou=dd(int) lol=0 lo=0 for i in li: #print(m,i) if(i==1): #print("lol") cou[m]+=1 elif(i%m==0 and m!=1): cou[m]+=i//m else: ex=i%m if(m==1): ex=i//2 cou[m+1]+=ex i-=ex*(m+1) cou[m]+=i//m lol=1 else: if(i//m>=ex): cou[m+1]+=ex i-=ex*(m+1) cou[m]+=i//m lol=1 else: cou[m-1]+=m-ex i-=(m-ex)*(m-1) cou[m]+=i//m lo=1 if((cou[m]+cou[m+1]+cou[m-1])<mi and lol!=lo): mi=(cou[m]+cou[m+1]+cou[m-1]) #print(d,mi) print(mi) t-=1 ```
instruction
0
101,333
7
202,666
No
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Provide tags and a correct Python 3 solution for this coding contest problem. As the boat drifts down the river, a wood full of blossoms shows up on the riverfront. "I've been here once," Mino exclaims with delight, "it's breathtakingly amazing." "What is it like?" "Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?" There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses. The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers. According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers. You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem. Note that you can choose arbitrary n and m under the constraints below, they are not given in the input. Input The first and only line of input contains four space-separated integers a, b, c and d (1 ≀ a, b, c, d ≀ 100) β€” the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively. Output In the first line, output two space-separated integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns in the grid respectively. Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively. In case there are multiple solutions, print any. You can output each letter in either case (upper or lower). Examples Input 5 3 2 1 Output 4 7 DDDDDDD DABACAD DBABACD DDDDDDD Input 50 50 1 1 Output 4 50 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ABABABABABABABABABABABABABABABABABABABABABABABABAB BABABABABABABABABABABABABABABABABABABABABABABABABA DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD Input 1 6 4 5 Output 7 7 DDDDDDD DDDBDBD DDCDCDD DBDADBD DDCDCDD DBDBDDD DDDDDDD Note In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one. <image>
instruction
0
101,776
7
203,552
Tags: constructive algorithms, graphs Correct Solution: ``` a = list(map(int, input().split())) ab = [['A']*25+['B']*25 for i in range(25)] cd = [['C']*25+['D']*25 for i in range(25)] print (50, 50) for i in range(4): a[i] -= 1 si, sj = 26, 26 while a[0] > 0: cd[si-25][sj] = 'A' a[0] -= 1 sj += 2 if sj == 50: sj = 26 si += 2 si, sj = 26, 0 while a[1] > 0: cd[si-25][sj] = 'B' a[1] -= 1 sj += 2 if sj == 26: sj = 0 si += 2 si, sj = 0,0 while a[2] > 0: ab[si][sj] = 'C' a[2] -= 1 sj += 2 if sj == 24: sj = 0 si += 2 si, sj = 0, 26 while a[3] > 0: ab[si][sj] = 'D' a[3] -= 1 sj += 2 if sj == 50: sj = 26 si += 2 for i in ab: print (''.join(i)) for i in cd: print (''.join(i)) ```
output
1
101,776
7
203,553
Provide tags and a correct Python 3 solution for this coding contest problem. As the boat drifts down the river, a wood full of blossoms shows up on the riverfront. "I've been here once," Mino exclaims with delight, "it's breathtakingly amazing." "What is it like?" "Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?" There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses. The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers. According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers. You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem. Note that you can choose arbitrary n and m under the constraints below, they are not given in the input. Input The first and only line of input contains four space-separated integers a, b, c and d (1 ≀ a, b, c, d ≀ 100) β€” the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively. Output In the first line, output two space-separated integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns in the grid respectively. Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively. In case there are multiple solutions, print any. You can output each letter in either case (upper or lower). Examples Input 5 3 2 1 Output 4 7 DDDDDDD DABACAD DBABACD DDDDDDD Input 50 50 1 1 Output 4 50 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ABABABABABABABABABABABABABABABABABABABABABABABABAB BABABABABABABABABABABABABABABABABABABABABABABABABA DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD Input 1 6 4 5 Output 7 7 DDDDDDD DDDBDBD DDCDCDD DBDADBD DDCDCDD DBDBDDD DDDDDDD Note In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one. <image>
instruction
0
101,777
7
203,554
Tags: constructive algorithms, graphs Correct Solution: ``` a = [int(x) - 1 for x in input().split()] n = m = 48 colors = "ABCD" side = n // 2 ans = [[0] * n for _ in range(n)] for i, color in enumerate(colors): for dx in range(side): for dy in range(side): x, y = dx + side * (i & 1), dy + side * (i // 2) ans[x][y] = color new_i = (i + 1) % 4 if 0 < min(dx, dy) and max(dx, dy) < side - 1 and a[new_i] and dx & 1 and dy & 1: ans[x][y] = colors[new_i] a[new_i] -= 1 print(n, m) print(*(''.join(row) for row in ans), sep='\n') ```
output
1
101,777
7
203,555
Provide tags and a correct Python 3 solution for this coding contest problem. As the boat drifts down the river, a wood full of blossoms shows up on the riverfront. "I've been here once," Mino exclaims with delight, "it's breathtakingly amazing." "What is it like?" "Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?" There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses. The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers. According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers. You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem. Note that you can choose arbitrary n and m under the constraints below, they are not given in the input. Input The first and only line of input contains four space-separated integers a, b, c and d (1 ≀ a, b, c, d ≀ 100) β€” the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively. Output In the first line, output two space-separated integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns in the grid respectively. Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively. In case there are multiple solutions, print any. You can output each letter in either case (upper or lower). Examples Input 5 3 2 1 Output 4 7 DDDDDDD DABACAD DBABACD DDDDDDD Input 50 50 1 1 Output 4 50 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ABABABABABABABABABABABABABABABABABABABABABABABABAB BABABABABABABABABABABABABABABABABABABABABABABABABA DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD Input 1 6 4 5 Output 7 7 DDDDDDD DDDBDBD DDCDCDD DBDADBD DDCDCDD DBDBDDD DDDDDDD Note In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one. <image>
instruction
0
101,778
7
203,556
Tags: constructive algorithms, graphs Correct Solution: ``` import sys A,B,C,D = map(int,input().split()) board = [['A']*50 for i in range(33)] for i in range(24,33): for j in range(50): board[i][j] ='B' A -= 1 for i in range(1,24,2): for j in range(1,50,2): # BλŠ” 1개 남겨두기 if B > 1: board[i][j] = 'B' B -= 1 elif C > 0: board[i][j] = 'C' C -= 1 elif D > 0: board[i][j] = 'D' D -= 1 board[23][49] = 'B' for i in range(25,33,2): for j in range(1,50,2): if A > 0: board[i][j] = 'A' A -= 1 sys.stdout.write("33 50\n") for i in range(33): sys.stdout.write(''.join(board[i])) if i != 32: sys.stdout.write('\n') ```
output
1
101,778
7
203,557
Provide tags and a correct Python 3 solution for this coding contest problem. As the boat drifts down the river, a wood full of blossoms shows up on the riverfront. "I've been here once," Mino exclaims with delight, "it's breathtakingly amazing." "What is it like?" "Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?" There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses. The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers. According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers. You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem. Note that you can choose arbitrary n and m under the constraints below, they are not given in the input. Input The first and only line of input contains four space-separated integers a, b, c and d (1 ≀ a, b, c, d ≀ 100) β€” the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively. Output In the first line, output two space-separated integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns in the grid respectively. Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively. In case there are multiple solutions, print any. You can output each letter in either case (upper or lower). Examples Input 5 3 2 1 Output 4 7 DDDDDDD DABACAD DBABACD DDDDDDD Input 50 50 1 1 Output 4 50 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ABABABABABABABABABABABABABABABABABABABABABABABABAB BABABABABABABABABABABABABABABABABABABABABABABABABA DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD Input 1 6 4 5 Output 7 7 DDDDDDD DDDBDBD DDCDCDD DBDADBD DDCDCDD DBDBDDD DDDDDDD Note In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one. <image>
instruction
0
101,779
7
203,558
Tags: constructive algorithms, graphs Correct Solution: ``` a, b, c, d = map(int, input().split()) res = [['A'] * 50 for i in range(25)] + \ [['B'] * 50 for i in range(25)] a, b = a - 1, b - 1 for i in range(0, 24, 2): for j in range(0, 50, 2): if b > 0: b -= 1 res[i][j] = 'B' elif c > 0: c -= 1 res[i][j] = 'C' elif d > 0: d -= 1 res[i][j] = 'D' if a > 0: a -= 1 res[i + 26][j] = 'A' print(50, 50) for i in res: print(''.join(i)) ```
output
1
101,779
7
203,559
Provide tags and a correct Python 3 solution for this coding contest problem. As the boat drifts down the river, a wood full of blossoms shows up on the riverfront. "I've been here once," Mino exclaims with delight, "it's breathtakingly amazing." "What is it like?" "Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?" There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses. The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers. According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers. You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem. Note that you can choose arbitrary n and m under the constraints below, they are not given in the input. Input The first and only line of input contains four space-separated integers a, b, c and d (1 ≀ a, b, c, d ≀ 100) β€” the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively. Output In the first line, output two space-separated integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns in the grid respectively. Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively. In case there are multiple solutions, print any. You can output each letter in either case (upper or lower). Examples Input 5 3 2 1 Output 4 7 DDDDDDD DABACAD DBABACD DDDDDDD Input 50 50 1 1 Output 4 50 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ABABABABABABABABABABABABABABABABABABABABABABABABAB BABABABABABABABABABABABABABABABABABABABABABABABABA DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD Input 1 6 4 5 Output 7 7 DDDDDDD DDDBDBD DDCDCDD DBDADBD DDCDCDD DBDBDDD DDDDDDD Note In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one. <image>
instruction
0
101,780
7
203,560
Tags: constructive algorithms, graphs Correct Solution: ``` a,b,c,d = map(int,input().split()) if a + b + c + d == 4: print(1,4) print("ABCD") else: print(50,50) ans = [[""]*50 for i in range(50)] if a == 1: for i in range(50): for j in range(50): ans[i][j] = "A" for i in range(0,50,2): for j in range(0,50,2): b -= 1 ans[i][j] = "B" if b == 0: break if b == 0: break for i in range(15,50,2): for j in range(0,50,2): c -= 1 ans[i][j] = "C" if c == 0: break if c == 0: break for i in range(30,50,2): for j in range(0,50,2): d -= 1 ans[i][j] = "D" if d == 0: break if d == 0: break elif b == 1: for i in range(50): for j in range(50): ans[i][j] = "B" for i in range(0,50,2): for j in range(0,50,2): a -= 1 ans[i][j] = "a" if a == 0: break if a == 0: break for i in range(15,50,2): for j in range(0,50,2): c -= 1 ans[i][j] = "C" if c == 0: break if c == 0: break for i in range(30,50,2): for j in range(0,50,2): d -= 1 ans[i][j] = "D" if d == 0: break if d == 0: break else: b -= 1 a -= 1 for i in range(50): for j in range(50): ans[i][j] = "A" for i in range(0,50,2): for j in range(0,50,2): b -= 1 ans[i][j] = "B" if b == 0: break if b == 0: break for i in range(12,50,2): for j in range(0,50,2): c -= 1 ans[i][j] = "C" if c == 0: break if c == 0: break for i in range(24,50,2): for j in range(0,50,2): d -= 1 ans[i][j] = "D" if d == 0: break if d == 0: break for i in range(35,50): for j in range(50): ans[i][j] = "B" for i in range(37,50,2): for j in range(0,50,2): a -= 1 ans[i][j] = "A" if a == 0: break if a == 0: break for i in range(50): for j in range(50): print(ans[i][j],end="") print() ```
output
1
101,780
7
203,561
Provide tags and a correct Python 3 solution for this coding contest problem. As the boat drifts down the river, a wood full of blossoms shows up on the riverfront. "I've been here once," Mino exclaims with delight, "it's breathtakingly amazing." "What is it like?" "Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?" There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses. The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers. According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers. You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem. Note that you can choose arbitrary n and m under the constraints below, they are not given in the input. Input The first and only line of input contains four space-separated integers a, b, c and d (1 ≀ a, b, c, d ≀ 100) β€” the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively. Output In the first line, output two space-separated integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns in the grid respectively. Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively. In case there are multiple solutions, print any. You can output each letter in either case (upper or lower). Examples Input 5 3 2 1 Output 4 7 DDDDDDD DABACAD DBABACD DDDDDDD Input 50 50 1 1 Output 4 50 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ABABABABABABABABABABABABABABABABABABABABABABABABAB BABABABABABABABABABABABABABABABABABABABABABABABABA DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD Input 1 6 4 5 Output 7 7 DDDDDDD DDDBDBD DDCDCDD DBDADBD DDCDCDD DBDBDDD DDDDDDD Note In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one. <image>
instruction
0
101,781
7
203,562
Tags: constructive algorithms, graphs 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**10 mod = 998244353 dd = [(0,-1),(1,0),(0,1),(-1,0)] ddn = [(0,-1),(1,-1),(1,0),(1,1),(0,1),(-1,-1),(-1,0),(-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(): a,b,c,d = LI() r = [['']*50 for _ in range(50)] for i in range(50): for j in range(50): if i < 25: if j < 25: r[i][j] = 'A' else: r[i][j] = 'B' else: if j < 25: r[i][j] = 'C' else: r[i][j] = 'D' for i in range(a-1): j = (i // 12) * 2 k = (i % 12) * 2 r[j][k+26] = 'A' for i in range(b-1): j = (i // 12) * 2 k = (i % 12) * 2 r[j][k] = 'B' for i in range(c-1): j = (i // 12) * 2 k = (i % 12) * 2 r[j+26][k+26] = 'C' for i in range(d-1): j = (i // 12) * 2 k = (i % 12) * 2 r[j+26][k] = 'D' return '50 50\n' + '\n'.join(map(lambda x: ''.join(x), r)) print(main()) ```
output
1
101,781
7
203,563
Provide tags and a correct Python 3 solution for this coding contest problem. As the boat drifts down the river, a wood full of blossoms shows up on the riverfront. "I've been here once," Mino exclaims with delight, "it's breathtakingly amazing." "What is it like?" "Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?" There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses. The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers. According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers. You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem. Note that you can choose arbitrary n and m under the constraints below, they are not given in the input. Input The first and only line of input contains four space-separated integers a, b, c and d (1 ≀ a, b, c, d ≀ 100) β€” the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively. Output In the first line, output two space-separated integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns in the grid respectively. Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively. In case there are multiple solutions, print any. You can output each letter in either case (upper or lower). Examples Input 5 3 2 1 Output 4 7 DDDDDDD DABACAD DBABACD DDDDDDD Input 50 50 1 1 Output 4 50 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ABABABABABABABABABABABABABABABABABABABABABABABABAB BABABABABABABABABABABABABABABABABABABABABABABABABA DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD Input 1 6 4 5 Output 7 7 DDDDDDD DDDBDBD DDCDCDD DBDADBD DDCDCDD DBDBDDD DDDDDDD Note In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one. <image>
instruction
0
101,782
7
203,564
Tags: constructive algorithms, graphs Correct Solution: ``` FIFTY = 50 TWENTY_FIVE = 25 TWELVE = 12 grid = [['X' for _ in range(FIFTY)] for _ in range(FIFTY)] def construct(n, mark, bg, base_i, base_j): for i in range(TWENTY_FIVE): for j in range(TWENTY_FIVE): grid[base_i + i][base_j + j] = bg for i in range(n): grid[base_i + 2 * (i // TWELVE) + 1][base_j + 2 * (i % TWELVE) + 1] = mark def main(): a, b, c, d = map(int, input().split()) construct(a - 1, 'A', 'B', 0, 0) construct(b - 1, 'B', 'C', TWENTY_FIVE, 0) construct(c - 1, 'C', 'D', 0, TWENTY_FIVE) construct(d - 1, 'D', 'A', TWENTY_FIVE, TWENTY_FIVE) print(FIFTY, FIFTY) for row in grid: print(''.join(row)) if __name__ == '__main__': main() ```
output
1
101,782
7
203,565
Provide tags and a correct Python 3 solution for this coding contest problem. As the boat drifts down the river, a wood full of blossoms shows up on the riverfront. "I've been here once," Mino exclaims with delight, "it's breathtakingly amazing." "What is it like?" "Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?" There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses. The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers. According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers. You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem. Note that you can choose arbitrary n and m under the constraints below, they are not given in the input. Input The first and only line of input contains four space-separated integers a, b, c and d (1 ≀ a, b, c, d ≀ 100) β€” the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively. Output In the first line, output two space-separated integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns in the grid respectively. Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively. In case there are multiple solutions, print any. You can output each letter in either case (upper or lower). Examples Input 5 3 2 1 Output 4 7 DDDDDDD DABACAD DBABACD DDDDDDD Input 50 50 1 1 Output 4 50 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ABABABABABABABABABABABABABABABABABABABABABABABABAB BABABABABABABABABABABABABABABABABABABABABABABABABA DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD Input 1 6 4 5 Output 7 7 DDDDDDD DDDBDBD DDCDCDD DBDADBD DDCDCDD DBDBDDD DDDDDDD Note In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one. <image>
instruction
0
101,783
7
203,566
Tags: constructive algorithms, graphs Correct Solution: ``` a, b, c, d = map(int, input().strip().split()) def fill(s, st, ch, cnt): ri, ci = st, 0 while cnt > 0: s[ri][ci] = ch cnt -= 1 ci += 2 if ci >= 50: ri += 3 ci = 0 dat = dict() dat.update({'A': a, 'B': b, 'C': c, 'D': d}) dat = sorted(dat.items(), key=lambda kv : kv[1]) mf = dat[3] lf = dat[0] res = list() for i in range(30): res.append(list(lf[0] * 50)) for i in range(20): res.append(list(mf[0] * 50)) fill(res, 0, dat[3][0], dat[3][1] - 1) fill(res, 1, dat[2][0], dat[2][1]) fill(res, 2, dat[1][0], dat[1][1]) fill(res, 31, dat[0][0], dat[0][1] - 1) print(50, 50) for e_ in res: print(''.join(map(str, e_))) ```
output
1
101,783
7
203,567
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. As the boat drifts down the river, a wood full of blossoms shows up on the riverfront. "I've been here once," Mino exclaims with delight, "it's breathtakingly amazing." "What is it like?" "Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?" There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses. The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers. According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers. You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem. Note that you can choose arbitrary n and m under the constraints below, they are not given in the input. Input The first and only line of input contains four space-separated integers a, b, c and d (1 ≀ a, b, c, d ≀ 100) β€” the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively. Output In the first line, output two space-separated integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns in the grid respectively. Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively. In case there are multiple solutions, print any. You can output each letter in either case (upper or lower). Examples Input 5 3 2 1 Output 4 7 DDDDDDD DABACAD DBABACD DDDDDDD Input 50 50 1 1 Output 4 50 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ABABABABABABABABABABABABABABABABABABABABABABABABAB BABABABABABABABABABABABABABABABABABABABABABABABABA DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD Input 1 6 4 5 Output 7 7 DDDDDDD DDDBDBD DDCDCDD DBDADBD DDCDCDD DBDBDDD DDDDDDD Note In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one. <image> Submitted Solution: ``` data = input() def main(): counters = [int(x) for x in data.split(' ')] codes = { 0: 'A', 1: 'B', 2: 'C', 3: 'D', } counters[0] -= 1 counters[3] -= 1 completed = [] row = [] for flower in range(1, 4): rows, row = fill_grid(row, 'A', codes[flower], counters[flower]) completed += rows if row: completed.append(''.join(row) + 'A' * (50 - len(row))) completed.append('A' * 50) completed.append('D' * 50) row = [] rows, row = fill_grid(row, 'D', 'A', counters[0]) completed += rows if row: completed.append(''.join(row) + 'D' * (50 - len(row))) completed.append('D' * 50) print('{} 50'.format(len(completed))) for row in completed: print(row) def fill_grid(row, grid, flower, counter): completed = [] while counter > 0: counter -= 1 row.append(flower) row.append(grid) if len(row) == 50: completed.append(''.join(row)) completed.append(''.join([grid] * 50)) row = [] return completed, row if __name__ == '__main__': main() ```
instruction
0
101,784
7
203,568
Yes
output
1
101,784
7
203,569
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. As the boat drifts down the river, a wood full of blossoms shows up on the riverfront. "I've been here once," Mino exclaims with delight, "it's breathtakingly amazing." "What is it like?" "Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?" There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses. The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers. According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers. You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem. Note that you can choose arbitrary n and m under the constraints below, they are not given in the input. Input The first and only line of input contains four space-separated integers a, b, c and d (1 ≀ a, b, c, d ≀ 100) β€” the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively. Output In the first line, output two space-separated integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns in the grid respectively. Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively. In case there are multiple solutions, print any. You can output each letter in either case (upper or lower). Examples Input 5 3 2 1 Output 4 7 DDDDDDD DABACAD DBABACD DDDDDDD Input 50 50 1 1 Output 4 50 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ABABABABABABABABABABABABABABABABABABABABABABABABAB BABABABABABABABABABABABABABABABABABABABABABABABABA DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD Input 1 6 4 5 Output 7 7 DDDDDDD DDDBDBD DDCDCDD DBDADBD DDCDCDD DBDBDDD DDDDDDD Note In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one. <image> Submitted Solution: ``` a,b,c,d=map(int,input().split()) m=[] for i in range(50): m.append([0]*50) for i in range(0,25,2): for j in range(0,25,2): if a==1: break a-=1 m[i][j]='A' if a==1: break for i in range(25): for j in range(25): if m[i][j]==0: m[i][j]='B' for i in range(0,25,2): for j in range(26,50,2): if b==1: break b-=1 m[i][j]='B' if b==1: break for i in range(25): for j in range(25,50): if m[i][j]==0: m[i][j]='C' for i in range(26,50,2): for j in range(25,50,2): if c==1: break c-=1 m[i][j]='C' if c==1: break for i in range(25,50): for j in range(25,50): if m[i][j]==0: m[i][j]='D' for i in range(25,50,2): for j in range(0,24,2): if d==1: break d-=1 m[i][j]='D' if d==1: break for i in range(25,50): for j in range(0,25): if m[i][j]==0: m[i][j]='A' print(50,50) for i in range(50): for j in range(50): print(m[i][j],end="") print() ```
instruction
0
101,785
7
203,570
Yes
output
1
101,785
7
203,571
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. As the boat drifts down the river, a wood full of blossoms shows up on the riverfront. "I've been here once," Mino exclaims with delight, "it's breathtakingly amazing." "What is it like?" "Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?" There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses. The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers. According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers. You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem. Note that you can choose arbitrary n and m under the constraints below, they are not given in the input. Input The first and only line of input contains four space-separated integers a, b, c and d (1 ≀ a, b, c, d ≀ 100) β€” the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively. Output In the first line, output two space-separated integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns in the grid respectively. Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively. In case there are multiple solutions, print any. You can output each letter in either case (upper or lower). Examples Input 5 3 2 1 Output 4 7 DDDDDDD DABACAD DBABACD DDDDDDD Input 50 50 1 1 Output 4 50 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ABABABABABABABABABABABABABABABABABABABABABABABABAB BABABABABABABABABABABABABABABABABABABABABABABABABA DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD Input 1 6 4 5 Output 7 7 DDDDDDD DDDBDBD DDCDCDD DBDADBD DDCDCDD DBDBDDD DDDDDDD Note In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one. <image> Submitted Solution: ``` a,b,c,d=map(int,input().split()) r=[['A' for i in range(50)] for j in range(50)] flag=0 print(50,50) for i in range(0,8,2): for j in range(0,50,2): r[i][j]='D' d-=1 if(d==0): flag=1 break if(flag==1): break flag=0 for i in range(8,16,2): for j in range(0,50,2): r[i][j]='C' c-=1 if(c==0): flag=1 break if(flag==1): break for i in range(49,32,-1): for j in range(50): r[i][j]='B' a-=1 b-=1 flag=0 if(a!=0): for i in range(34,50,2): for j in range(0,50,2): r[i][j]='A' a-=1 if(a==0): flag=1 break if(flag==1): break flag=0 if(b!=0): for i in range(16,50,2): for j in range(0,50,2): r[i][j]='B' b-=1 if(b==0): flag=1 break if(flag==1): break for i in r: for j in i: print(j,end="") print() ```
instruction
0
101,786
7
203,572
Yes
output
1
101,786
7
203,573
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. As the boat drifts down the river, a wood full of blossoms shows up on the riverfront. "I've been here once," Mino exclaims with delight, "it's breathtakingly amazing." "What is it like?" "Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?" There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses. The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers. According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers. You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem. Note that you can choose arbitrary n and m under the constraints below, they are not given in the input. Input The first and only line of input contains four space-separated integers a, b, c and d (1 ≀ a, b, c, d ≀ 100) β€” the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively. Output In the first line, output two space-separated integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns in the grid respectively. Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively. In case there are multiple solutions, print any. You can output each letter in either case (upper or lower). Examples Input 5 3 2 1 Output 4 7 DDDDDDD DABACAD DBABACD DDDDDDD Input 50 50 1 1 Output 4 50 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ABABABABABABABABABABABABABABABABABABABABABABABABAB BABABABABABABABABABABABABABABABABABABABABABABABABA DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD Input 1 6 4 5 Output 7 7 DDDDDDD DDDBDBD DDCDCDD DBDADBD DDCDCDD DBDBDDD DDDDDDD Note In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one. <image> Submitted Solution: ``` a,b,c,d = list(map(int ,input().split())) pole = [] for row in range (40): pole.append(['A']*50) for row in range (10): pole.append(['D']*50) for i in range(b): pole[(i // 25) *2 ][(i %25) *2] = 'B' for i in range(c): pole[ 7 + (i // 25) *2 ][(i %25) *2] = 'C' for i in range(d-1): pole[ 14 + (i // 25) *2 ][(i %25) *2] = 'D' for i in range(a-1): pole[41 + (i // 25) *2 ][(i %25) *2] = 'A' print('50 50') for row in range(50): print(''.join(pole[row])) ```
instruction
0
101,787
7
203,574
Yes
output
1
101,787
7
203,575
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. As the boat drifts down the river, a wood full of blossoms shows up on the riverfront. "I've been here once," Mino exclaims with delight, "it's breathtakingly amazing." "What is it like?" "Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?" There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses. The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers. According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers. You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem. Note that you can choose arbitrary n and m under the constraints below, they are not given in the input. Input The first and only line of input contains four space-separated integers a, b, c and d (1 ≀ a, b, c, d ≀ 100) β€” the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively. Output In the first line, output two space-separated integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns in the grid respectively. Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively. In case there are multiple solutions, print any. You can output each letter in either case (upper or lower). Examples Input 5 3 2 1 Output 4 7 DDDDDDD DABACAD DBABACD DDDDDDD Input 50 50 1 1 Output 4 50 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ABABABABABABABABABABABABABABABABABABABABABABABABAB BABABABABABABABABABABABABABABABABABABABABABABABABA DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD Input 1 6 4 5 Output 7 7 DDDDDDD DDDBDBD DDCDCDD DBDADBD DDCDCDD DBDBDDD DDDDDDD Note In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one. <image> Submitted Solution: ``` # https://codeforces.com/problemset/problem/989/C def create(bk, fr, num): a = [[bk for _ in range(50)] for _ in range(12)] flg = True for i in range(0, 12, 2): for j in range(0, 50, 2): if num == 0: flg = False break a[i][j] = fr num -= 1 if flg == False: break return a a, b, c, d = list(map(int, input().split())) a -= 1 b -= 1 c -= 1 d -= 1 ans = [] ans.extend(create('A', 'B', b)) ans.extend(create('B', 'C', c)) ans.extend(create('C', 'D', d)) ans.extend(create('D', 'A', a)) for x in ans: for y in x: print(y, end='') print() ```
instruction
0
101,788
7
203,576
No
output
1
101,788
7
203,577
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. As the boat drifts down the river, a wood full of blossoms shows up on the riverfront. "I've been here once," Mino exclaims with delight, "it's breathtakingly amazing." "What is it like?" "Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?" There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses. The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers. According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers. You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem. Note that you can choose arbitrary n and m under the constraints below, they are not given in the input. Input The first and only line of input contains four space-separated integers a, b, c and d (1 ≀ a, b, c, d ≀ 100) β€” the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively. Output In the first line, output two space-separated integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns in the grid respectively. Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively. In case there are multiple solutions, print any. You can output each letter in either case (upper or lower). Examples Input 5 3 2 1 Output 4 7 DDDDDDD DABACAD DBABACD DDDDDDD Input 50 50 1 1 Output 4 50 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ABABABABABABABABABABABABABABABABABABABABABABABABAB BABABABABABABABABABABABABABABABABABABABABABABABABA DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD Input 1 6 4 5 Output 7 7 DDDDDDD DDDBDBD DDCDCDD DBDADBD DDCDCDD DBDBDDD DDDDDDD Note In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one. <image> Submitted Solution: ``` line = input() flowers = line.split('\n')[0] flowers = flowers.split(' ') a = int(flowers[3]) ind = 3 for i in range(3): if int(flowers[i]) < a: a = int(flowers[i]) ind = i b = int(flowers[3]) index = (ind+2)%4 field = [[0 for x in range(50)] for y in range(50)] def makerect(field,n,index): for i in range(50): for j in range(50): if field[i][j] == 0: field[i][j] = chr(n+65) req = int(flowers[n]) - 1 k = 49 l = 1 while(req > 0): field[k][l] = chr(index + 65) req -= 1 l = l + 2 if(l > 49): l = 1 k = k-2 m = 48 while(m > k-2 and int(flowers[ind]) != 1): for j in range(50): field[m][j] = chr(index+65) m = m - 2 return field def makefield(field,flowers,ind,index): for k in range(4): if k == index: if int(flowers[ind]) == 1: a = int(flowers[k]) else: a = int(flowers[k]) - 1 else: a = int(flowers[k]) j = k i = 0 while a > 0 : field[i][j] = chr(k+65) j = j + 4 a = a - 1 if(j > 49): i = i + 2 j = k return makefield(field,flowers,ind,index) field = makerect(field,ind,index) for i in range(50): for j in range(50): print(field[i][j],end = "") print() ```
instruction
0
101,789
7
203,578
No
output
1
101,789
7
203,579
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. As the boat drifts down the river, a wood full of blossoms shows up on the riverfront. "I've been here once," Mino exclaims with delight, "it's breathtakingly amazing." "What is it like?" "Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?" There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses. The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers. According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers. You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem. Note that you can choose arbitrary n and m under the constraints below, they are not given in the input. Input The first and only line of input contains four space-separated integers a, b, c and d (1 ≀ a, b, c, d ≀ 100) β€” the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively. Output In the first line, output two space-separated integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns in the grid respectively. Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively. In case there are multiple solutions, print any. You can output each letter in either case (upper or lower). Examples Input 5 3 2 1 Output 4 7 DDDDDDD DABACAD DBABACD DDDDDDD Input 50 50 1 1 Output 4 50 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ABABABABABABABABABABABABABABABABABABABABABABABABAB BABABABABABABABABABABABABABABABABABABABABABABABABA DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD Input 1 6 4 5 Output 7 7 DDDDDDD DDDBDBD DDCDCDD DBDADBD DDCDCDD DBDBDDD DDDDDDD Note In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one. <image> Submitted Solution: ``` #input = open('t.txt').readline count = list(map(int, input().split())) flower = 'ABCD' a = [] last = -1 if all(x == 0 for x in count): print('0 0') exit() while True: best = 0 best_count = -1 for i in range(4): if i != last and count[i] > best_count: best = i best_count = count[i] a.append(flower[best]*2) count[best] -= 1 if count[best] == 0: break last = best i = 0 sep = flower[best]*2 while i < 4: pair = flower[i]+flower[best] for j in range(count[i]): a.append(pair) a.append(sep) i += 1 print(str(len(a))+' 2') print('\n'.join(a)) ```
instruction
0
101,790
7
203,580
No
output
1
101,790
7
203,581
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. As the boat drifts down the river, a wood full of blossoms shows up on the riverfront. "I've been here once," Mino exclaims with delight, "it's breathtakingly amazing." "What is it like?" "Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?" There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses. The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers. According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers. You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem. Note that you can choose arbitrary n and m under the constraints below, they are not given in the input. Input The first and only line of input contains four space-separated integers a, b, c and d (1 ≀ a, b, c, d ≀ 100) β€” the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively. Output In the first line, output two space-separated integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns in the grid respectively. Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively. In case there are multiple solutions, print any. You can output each letter in either case (upper or lower). Examples Input 5 3 2 1 Output 4 7 DDDDDDD DABACAD DBABACD DDDDDDD Input 50 50 1 1 Output 4 50 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ABABABABABABABABABABABABABABABABABABABABABABABABAB BABABABABABABABABABABABABABABABABABABABABABABABABA DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD Input 1 6 4 5 Output 7 7 DDDDDDD DDDBDBD DDCDCDD DBDADBD DDCDCDD DBDBDDD DDDDDDD Note In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one. <image> Submitted Solution: ``` a, b, c, d = map(int, input().split()) m = [['D']*50 for i in range(50)] for i in range(a): m[0][i] = 'A' for i in range(b): m[1][i] = 'B' for i in range(c): m[2][i] = 'C' print(50,50) for line in m: print(''.join(line)) ```
instruction
0
101,791
7
203,582
No
output
1
101,791
7
203,583
Provide tags and a correct Python 3 solution for this coding contest problem. You are given n Γ— m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that: 1. All cells in a set have the same color. 2. Every two cells in a set share row or column. Input The first line of input contains integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns correspondingly. The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black. Output Output single integer β€” the number of non-empty sets from the problem description. Examples Input 1 1 0 Output 1 Input 2 3 1 0 1 0 1 0 Output 8 Note In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets.
instruction
0
102,587
7
205,174
Tags: combinatorics, math Correct Solution: ``` def twopmo(n): return (1<<n)-n-1 n,m = [int(x) for x in input().split()] numzr = [0 for i in range(n)] numzc = [0 for i in range(m)] matrix = [[] for j in range(n)] for i in range(n): matrix[i] = [int(x) for x in input().split()] for i in range(n): for j in range(m): if matrix[i][j]==1: numzc[j]+=1 numzr[i]+=1 ans = n*m for i in range(n): ans = ans + twopmo(numzr[i]) + twopmo(m-numzr[i]) for i in range(m): ans = ans + twopmo(numzc[i]) + twopmo(n-numzc[i]) print(ans) ```
output
1
102,587
7
205,175
Provide tags and a correct Python 3 solution for this coding contest problem. You are given n Γ— m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that: 1. All cells in a set have the same color. 2. Every two cells in a set share row or column. Input The first line of input contains integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns correspondingly. The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black. Output Output single integer β€” the number of non-empty sets from the problem description. Examples Input 1 1 0 Output 1 Input 2 3 1 0 1 0 1 0 Output 8 Note In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets.
instruction
0
102,588
7
205,176
Tags: combinatorics, math Correct Solution: ``` numRows, numCols = [int(i) for i in input().split()] arr = [] total = 0 for _ in range(numRows): arr.append([int(i) for i in input().split()]) for row in range(numRows): numOnes = sum([arr[row][col] for col in range(numCols)]) numZeroes = numCols - numOnes total += (2**numZeroes - 1) + (2**numOnes - 1) for col in range(numCols): numOnes = sum([arr[row][col] for row in range(numRows)]) numZeroes = numRows - numOnes total += (2**numZeroes - 1) + (2**numOnes - 1) total -= numRows * numCols print(total) ```
output
1
102,588
7
205,177
Provide tags and a correct Python 3 solution for this coding contest problem. You are given n Γ— m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that: 1. All cells in a set have the same color. 2. Every two cells in a set share row or column. Input The first line of input contains integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns correspondingly. The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black. Output Output single integer β€” the number of non-empty sets from the problem description. Examples Input 1 1 0 Output 1 Input 2 3 1 0 1 0 1 0 Output 8 Note In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets.
instruction
0
102,589
7
205,178
Tags: combinatorics, math Correct Solution: ``` n, m = map(int, input().split()) a = [list(map(int, input().split())) for i in range(n)] col = [[0, 0] for i in range(m)] row = [[0, 0] for i in range(n)] for i in range(n): summa = sum(a[i]) row[i] = [summa, m - summa] for i in range(m): summa = 0 for j in range(n): summa += a[j][i] col[i] = [summa, n - summa] res = 0 for i in row: res += (2 ** i[0]) + (2 ** i[1]) - 2 for i in col: res += (2 ** i[0]) + (2 ** i[1]) - 2 res -= n *m print(res) ```
output
1
102,589
7
205,179
Provide tags and a correct Python 3 solution for this coding contest problem. You are given n Γ— m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that: 1. All cells in a set have the same color. 2. Every two cells in a set share row or column. Input The first line of input contains integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns correspondingly. The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black. Output Output single integer β€” the number of non-empty sets from the problem description. Examples Input 1 1 0 Output 1 Input 2 3 1 0 1 0 1 0 Output 8 Note In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets.
instruction
0
102,590
7
205,180
Tags: combinatorics, math Correct Solution: ``` #B. Rectangles #Problem number 844: Rectangles n,m = [int(i) for i in input().split()] #each element of the row and of the column will contain a pair ('number_of_whites', 'number_of_blacks') rows = [[0,0] for i in range(n)] columns = [[0,0] for i in range(m)] #read row by row for i in range(n): row = [int(element) for element in input().split()] for j in range(m): if row[j] == 0: #white rows[i][0] += 1 columns[j][0] += 1 else: rows[i][1] += 1 columns[j][1] += 1 #count individual sets number_of_sets = n*m for count in rows: if count[0] > 0: number_of_sets += 2**count[0] - 1 - count[0] #total number of subsets - empty subset - individual subsets(counted since the beginning) if count[1] > 0: number_of_sets += 2**count[1] - 1 - count[1] for count in columns: if count[0] > 0: number_of_sets += 2**count[0] - 1 - count[0] #total number of subsets - empty subset - individual subsets(counted since the beginning) if count[1] > 0: number_of_sets += 2**count[1] - 1 - count[1] print(number_of_sets) ```
output
1
102,590
7
205,181
Provide tags and a correct Python 3 solution for this coding contest problem. You are given n Γ— m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that: 1. All cells in a set have the same color. 2. Every two cells in a set share row or column. Input The first line of input contains integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns correspondingly. The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black. Output Output single integer β€” the number of non-empty sets from the problem description. Examples Input 1 1 0 Output 1 Input 2 3 1 0 1 0 1 0 Output 8 Note In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets.
instruction
0
102,591
7
205,182
Tags: combinatorics, math Correct Solution: ``` n, m = [int(x) for x in input().split()] l = [] for i in range(n): temp = list(map(int, input().split())) l.append(temp) s = n * m for i in range(n): c0 = 0 c1 = 0 for j in range(m): if l[i][j] == 0: c0 += 1 else: c1 += 1 s += ((2 ** c0) - 1 - c0) s += ((2 ** c1) - 1 - c1) for i in range(m): c0 = 0 c1 = 0 for j in range(n): if l[j][i] == 0: c0 += 1 else: c1 += 1 s += ((2 ** c0) - 1 - c0) s += ((2 ** c1) - 1 - c1) print(s) ```
output
1
102,591
7
205,183
Provide tags and a correct Python 3 solution for this coding contest problem. You are given n Γ— m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that: 1. All cells in a set have the same color. 2. Every two cells in a set share row or column. Input The first line of input contains integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns correspondingly. The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black. Output Output single integer β€” the number of non-empty sets from the problem description. Examples Input 1 1 0 Output 1 Input 2 3 1 0 1 0 1 0 Output 8 Note In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets.
instruction
0
102,592
7
205,184
Tags: combinatorics, math Correct Solution: ``` h, w = map(int, input().split()) grid = [] ans = 0 for i in range(h): grid.append(input().split()) for i in range(h): whiterun = 0 blackrun = 0 for x in range(w): if grid[i][x] == '0': ans += 2**whiterun whiterun += 1 else: ans += 2**blackrun blackrun += 1 for i in range(w): whiterun = 0 blackrun = 0 for x in range(h): if grid[x][i] == '0': ans += (2**whiterun)-1 whiterun += 1 else: ans += (2**blackrun)-1 blackrun += 1 print(ans) ```
output
1
102,592
7
205,185
Provide tags and a correct Python 3 solution for this coding contest problem. You are given n Γ— m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that: 1. All cells in a set have the same color. 2. Every two cells in a set share row or column. Input The first line of input contains integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns correspondingly. The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black. Output Output single integer β€” the number of non-empty sets from the problem description. Examples Input 1 1 0 Output 1 Input 2 3 1 0 1 0 1 0 Output 8 Note In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets.
instruction
0
102,593
7
205,186
Tags: combinatorics, math Correct Solution: ``` import sys input = sys.stdin.readline def solve(): n, m = map(int, input().split()) a = [list(map(int, input().split())) for i in range(n)] r = 0 for i in a: c = i.count(0) r += 2**c - 1 + 2**(m - c) - 1 for i in range(m): c = 0 for j in range(n): c += a[j][i] == 0 r += 2**c - 1 + 2**(n - c) - 1 print(r - n * m) solve() ```
output
1
102,593
7
205,187
Provide tags and a correct Python 3 solution for this coding contest problem. You are given n Γ— m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that: 1. All cells in a set have the same color. 2. Every two cells in a set share row or column. Input The first line of input contains integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns correspondingly. The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black. Output Output single integer β€” the number of non-empty sets from the problem description. Examples Input 1 1 0 Output 1 Input 2 3 1 0 1 0 1 0 Output 8 Note In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets.
instruction
0
102,594
7
205,188
Tags: combinatorics, math Correct Solution: ``` (n,m)=map(int,input().split()); l=[]; for i in range(n): ll=list(map(int,input().split())); l.append(ll); s=0; for x in l: c1=x.count(1); c0=x.count(0); s=s+2**c1+2**c0-2; for i in range(m): c0=0; c1=0; for j in range(n): if(l[j][i]==0): c0+=1; if(l[j][i]==1): c1+=1; s=s+2**c0+2**c1-2; s=s-m*n; print(s); ```
output
1
102,594
7
205,189
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given n Γ— m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that: 1. All cells in a set have the same color. 2. Every two cells in a set share row or column. Input The first line of input contains integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns correspondingly. The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black. Output Output single integer β€” the number of non-empty sets from the problem description. Examples Input 1 1 0 Output 1 Input 2 3 1 0 1 0 1 0 Output 8 Note In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets. Submitted Solution: ``` n, m = map(int, input().split()) g, v = [list(map(int, input().split())) for i in range(n)], -n * m for si in map(sum, g): v += 2 ** si - 1 + 2 ** (m - si) - 1 for sj in (sum(g[i][j] for i in range(n)) for j in range(m)): v += 2 ** sj - 1 + 2 ** (n - sj) - 1 print(v) ```
instruction
0
102,595
7
205,190
Yes
output
1
102,595
7
205,191
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given n Γ— m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that: 1. All cells in a set have the same color. 2. Every two cells in a set share row or column. Input The first line of input contains integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns correspondingly. The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black. Output Output single integer β€” the number of non-empty sets from the problem description. Examples Input 1 1 0 Output 1 Input 2 3 1 0 1 0 1 0 Output 8 Note In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets. Submitted Solution: ``` import math def choose(n, k): return math.factorial(n) / (math.factorial(k) * math.factorial(n - k)) class CodeforcesTask844BSolution: def __init__(self): self.result = '' self.n_m = [] self.board = [] def read_input(self): self.n_m = [int(x) for x in input().split(" ")] for x in range(self.n_m[0]): self.board.append([int(x) for x in input().split(" ")]) def process_task(self): white_row_sums = [sum(row) for row in self.board] black_row_sums = [self.n_m[1] - row for row in white_row_sums] white_col_sums = [0] * self.n_m[1] for x in range(self.n_m[1]): for y in range(self.n_m[0]): white_col_sums[x] += self.board[y][x] black_col_sums = [self.n_m[0] - row for row in white_col_sums] subsets = white_row_sums + black_row_sums + white_col_sums + black_col_sums sub_cnt = 0 for ss in subsets: sub_cnt += 2 ** ss - 1 self.result = str(int(sub_cnt - self.n_m[0] * self.n_m[1])) def get_result(self): return self.result if __name__ == "__main__": Solution = CodeforcesTask844BSolution() Solution.read_input() Solution.process_task() print(Solution.get_result()) ```
instruction
0
102,596
7
205,192
Yes
output
1
102,596
7
205,193
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given n Γ— m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that: 1. All cells in a set have the same color. 2. Every two cells in a set share row or column. Input The first line of input contains integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns correspondingly. The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black. Output Output single integer β€” the number of non-empty sets from the problem description. Examples Input 1 1 0 Output 1 Input 2 3 1 0 1 0 1 0 Output 8 Note In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets. Submitted Solution: ``` a = input().split() n,m = int(a[0]), int(a[1]) c1 = [0]*m r =0 for i in range(n): k = list(map(int,input().split())) s1=0 for j in range(m): if(k[j]==1): s1+=1 c1[j]+=1 r += 2**s1 + 2**(m-s1) - 2 for i in c1: r+= 2**i + 2**(n-i) - 2 r-=(n*m) print(r) ```
instruction
0
102,597
7
205,194
Yes
output
1
102,597
7
205,195
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given n Γ— m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that: 1. All cells in a set have the same color. 2. Every two cells in a set share row or column. Input The first line of input contains integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns correspondingly. The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black. Output Output single integer β€” the number of non-empty sets from the problem description. Examples Input 1 1 0 Output 1 Input 2 3 1 0 1 0 1 0 Output 8 Note In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets. Submitted Solution: ``` import sys inf = float('inf') ip = lambda : sys.stdin.readline().rstrip() split = lambda : ip().split(' ') ip1 = lambda : map(int,split()) arr = lambda : list(ip1()) arr1 = lambda n : [arr() for _ in range(n)] mod = 998244353 n,m=ip1() a=arr1(n) ans=n*m for i in range(n): ct=0 for j in range(m): if a[i][j]: ct+=1 ct2=m-ct ans += 2**ct + 2**ct2 - 2 - ct-ct2 for j in range(m): ct=0 for i in range(n): if a[i][j]: ct+=1 ct2=n-ct ans += 2**ct + 2**ct2 - 2-ct-ct2 print(ans) ```
instruction
0
102,598
7
205,196
Yes
output
1
102,598
7
205,197
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given n Γ— m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that: 1. All cells in a set have the same color. 2. Every two cells in a set share row or column. Input The first line of input contains integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns correspondingly. The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black. Output Output single integer β€” the number of non-empty sets from the problem description. Examples Input 1 1 0 Output 1 Input 2 3 1 0 1 0 1 0 Output 8 Note In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets. Submitted Solution: ``` n,m = map(int, input().split()) grid = [] for i in range(n): row = [int(x) for x in input().split()] grid.append(row) numCells = n * m whiteRow = [] blackRow = [] whiteCol = [] blackCol = [] for row in grid: whiteRow.append(len([x for x in row if x == 0])) blackRow.append(len([x for x in row if x == 1])) for i in range(m): col = [row[i] for row in grid] whiteCol.append(len([x for x in col if x == 0])) blackCol.append(len([x for x in col if x == 1])) total = 0 x1 = [x for x in whiteRow if x >= 2] x2 = [x for x in whiteCol if x >= 2] x3 = [x for x in blackRow if x >= 2] x4 = [x for x in blackCol if x >= 2] print(numCells + len(x1)+ len(x2) + len(x3) + len(x4)) ```
instruction
0
102,599
7
205,198
No
output
1
102,599
7
205,199
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given n Γ— m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that: 1. All cells in a set have the same color. 2. Every two cells in a set share row or column. Input The first line of input contains integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns correspondingly. The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black. Output Output single integer β€” the number of non-empty sets from the problem description. Examples Input 1 1 0 Output 1 Input 2 3 1 0 1 0 1 0 Output 8 Note In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets. Submitted Solution: ``` n, m = map(int, input().split()) matrix = [list(map(int, input().split())) for _ in range(n)] result = n * m for i in range(n): if matrix[i].count(0): result += matrix[i].count(0) - 1 if matrix[i].count(1): result += matrix[i].count(1) - 1 for i in range(m): zero_counter, one_counter = 0, 0 for j in range(n): if matrix[j][i] == 0: zero_counter += 1 else: one_counter += 1 if zero_counter: result += zero_counter - 1 if one_counter: result += one_counter - 1 print(result) ```
instruction
0
102,600
7
205,200
No
output
1
102,600
7
205,201
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given n Γ— m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that: 1. All cells in a set have the same color. 2. Every two cells in a set share row or column. Input The first line of input contains integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns correspondingly. The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black. Output Output single integer β€” the number of non-empty sets from the problem description. Examples Input 1 1 0 Output 1 Input 2 3 1 0 1 0 1 0 Output 8 Note In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets. Submitted Solution: ``` import math def choose(n, k): return math.factorial(n) / (math.factorial(k) * math.factorial(n - k)) class CodeforcesTask844BSolution: def __init__(self): self.result = '' self.n_m = [] self.board = [] def read_input(self): self.n_m = [int(x) for x in input().split(" ")] for x in range(self.n_m[0]): self.board.append([int(x) for x in input().split(" ")]) def process_task(self): white_row_sums = [sum(row) for row in self.board] black_row_sums = [self.n_m[1] - row for row in white_row_sums] white_col_sums = [0] * self.n_m[1] for x in range(self.n_m[1]): for y in range(self.n_m[0]): white_col_sums[x] += self.board[y][x] black_col_sums = [self.n_m[0] - row for row in white_col_sums] subsets = white_row_sums + black_row_sums + white_col_sums + black_col_sums sub_cnt = 0 for ss in subsets: for x in range(2, ss + 1): sub_cnt += choose(ss, x) self.result = str(int(sub_cnt + self.n_m[0] * self.n_m[1])) def get_result(self): return self.result if __name__ == "__main__": Solution = CodeforcesTask844BSolution() Solution.read_input() Solution.process_task() print(Solution.get_result()) ```
instruction
0
102,601
7
205,202
No
output
1
102,601
7
205,203
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given n Γ— m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that: 1. All cells in a set have the same color. 2. Every two cells in a set share row or column. Input The first line of input contains integers n and m (1 ≀ n, m ≀ 50) β€” the number of rows and the number of columns correspondingly. The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black. Output Output single integer β€” the number of non-empty sets from the problem description. Examples Input 1 1 0 Output 1 Input 2 3 1 0 1 0 1 0 Output 8 Note In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets. Submitted Solution: ``` n,m = list(map(int,input().split())) ans = 0 c1,c0 = 0,0 for i in range(n): arr = list(map(int,input().split())) c1 = arr.count(1) c0 = m-c1 ans+=((2**c1)-1) ans+=((2**c0)-1) print(ans) ```
instruction
0
102,602
7
205,204
No
output
1
102,602
7
205,205
Provide tags and a correct Python 3 solution for this coding contest problem. The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive. Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that: 1. for every i: b_i and g_i are integers between 1 and k, inclusive; 2. there are no two completely identical pairs, i.e. no two indices i, j (i β‰  j) such that b_i = b_j and g_i = g_j at the same time; 3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β‰  g_i for every i; 4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β‰  b_{i + 1} and g_i β‰  g_{i + 1} hold. Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second): Bad color choosing: * (1, 2), (2, 3), (3, 2), (1, 2) β€” contradiction with the second rule (there are equal pairs); * (2, 3), (1, 1), (3, 2), (1, 3) β€” contradiction with the third rule (there is a pair with costumes of the same color); * (1, 2), (2, 3), (1, 3), (2, 1) β€” contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same). Good color choosing: * (1, 2), (2, 1), (1, 3), (3, 1); * (1, 2), (3, 1), (2, 3), (3, 2); * (3, 1), (1, 2), (2, 3), (3, 2). You have to find any suitable color choosing or say that no suitable choosing exists. Input The only line of the input contains two integers n and k (2 ≀ n, k ≀ 2 β‹… 10^5) β€” the number of pairs and the number of colors. Output If it is impossible to find any suitable colors choosing, print "NO". Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β€” colors of costumes of man and woman in the i-th pair, respectively. You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable. Examples Input 4 3 Output YES 3 1 1 3 3 2 2 3 Input 10 4 Output YES 2 1 1 3 4 2 3 4 4 3 3 2 2 4 4 1 1 4 3 1 Input 13 4 Output NO
instruction
0
102,924
7
205,848
Tags: constructive algorithms, implementation Correct Solution: ``` n, k = map(int, input().split()) i = 1 if k*(k-1) < n: print("NO") else: print("YES") l = 0 j = 0 while l < n//2: l += 1 j += 1 if i == j: j += 1 if j > k: i += 1 j = i+1 print(i,j) print(j,i) j += 1 if i == j: j += 1 if j > k: i += 1 j = i+1 if n % 2 == 1: print(i, j) ```
output
1
102,924
7
205,849
Provide tags and a correct Python 3 solution for this coding contest problem. The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive. Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that: 1. for every i: b_i and g_i are integers between 1 and k, inclusive; 2. there are no two completely identical pairs, i.e. no two indices i, j (i β‰  j) such that b_i = b_j and g_i = g_j at the same time; 3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β‰  g_i for every i; 4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β‰  b_{i + 1} and g_i β‰  g_{i + 1} hold. Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second): Bad color choosing: * (1, 2), (2, 3), (3, 2), (1, 2) β€” contradiction with the second rule (there are equal pairs); * (2, 3), (1, 1), (3, 2), (1, 3) β€” contradiction with the third rule (there is a pair with costumes of the same color); * (1, 2), (2, 3), (1, 3), (2, 1) β€” contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same). Good color choosing: * (1, 2), (2, 1), (1, 3), (3, 1); * (1, 2), (3, 1), (2, 3), (3, 2); * (3, 1), (1, 2), (2, 3), (3, 2). You have to find any suitable color choosing or say that no suitable choosing exists. Input The only line of the input contains two integers n and k (2 ≀ n, k ≀ 2 β‹… 10^5) β€” the number of pairs and the number of colors. Output If it is impossible to find any suitable colors choosing, print "NO". Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β€” colors of costumes of man and woman in the i-th pair, respectively. You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable. Examples Input 4 3 Output YES 3 1 1 3 3 2 2 3 Input 10 4 Output YES 2 1 1 3 4 2 3 4 4 3 3 2 2 4 4 1 1 4 3 1 Input 13 4 Output NO
instruction
0
102,925
7
205,850
Tags: constructive algorithms, implementation Correct Solution: ``` from collections import * from math import * k,n = map(int,input().split()) K = k ans = [] for i in range(1,n+1): for j in range(i+1,n+1): if(k <= 0): break ans.append([i,j]) ans.append([j,i]) k -= 2 if(len(ans) >= K): print("YES") for i in range(K): print(*ans[i]) else: print("NO") ```
output
1
102,925
7
205,851
Provide tags and a correct Python 3 solution for this coding contest problem. The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive. Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that: 1. for every i: b_i and g_i are integers between 1 and k, inclusive; 2. there are no two completely identical pairs, i.e. no two indices i, j (i β‰  j) such that b_i = b_j and g_i = g_j at the same time; 3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β‰  g_i for every i; 4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β‰  b_{i + 1} and g_i β‰  g_{i + 1} hold. Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second): Bad color choosing: * (1, 2), (2, 3), (3, 2), (1, 2) β€” contradiction with the second rule (there are equal pairs); * (2, 3), (1, 1), (3, 2), (1, 3) β€” contradiction with the third rule (there is a pair with costumes of the same color); * (1, 2), (2, 3), (1, 3), (2, 1) β€” contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same). Good color choosing: * (1, 2), (2, 1), (1, 3), (3, 1); * (1, 2), (3, 1), (2, 3), (3, 2); * (3, 1), (1, 2), (2, 3), (3, 2). You have to find any suitable color choosing or say that no suitable choosing exists. Input The only line of the input contains two integers n and k (2 ≀ n, k ≀ 2 β‹… 10^5) β€” the number of pairs and the number of colors. Output If it is impossible to find any suitable colors choosing, print "NO". Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β€” colors of costumes of man and woman in the i-th pair, respectively. You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable. Examples Input 4 3 Output YES 3 1 1 3 3 2 2 3 Input 10 4 Output YES 2 1 1 3 4 2 3 4 4 3 3 2 2 4 4 1 1 4 3 1 Input 13 4 Output NO
instruction
0
102,926
7
205,852
Tags: constructive algorithms, implementation Correct Solution: ``` m,k = map(int,input().strip().split()) maxp = k*(k-1) mp = {} if m>maxp: print("NO") else: l = 1 h = 2 print("YES") i = 0 while i<m: if str(l)+" "+str(h) not in mp: print(l,h) i+=1 if i>=m: break print(h,l) i+=1 mp[str(l)+" "+str(h)] = 1 mp[str(h)+" "+str(l)] = 1 h+=1 if h==l: h+=1 if h>k: h = 1 l+=1 ```
output
1
102,926
7
205,853
Provide tags and a correct Python 3 solution for this coding contest problem. The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive. Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that: 1. for every i: b_i and g_i are integers between 1 and k, inclusive; 2. there are no two completely identical pairs, i.e. no two indices i, j (i β‰  j) such that b_i = b_j and g_i = g_j at the same time; 3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β‰  g_i for every i; 4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β‰  b_{i + 1} and g_i β‰  g_{i + 1} hold. Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second): Bad color choosing: * (1, 2), (2, 3), (3, 2), (1, 2) β€” contradiction with the second rule (there are equal pairs); * (2, 3), (1, 1), (3, 2), (1, 3) β€” contradiction with the third rule (there is a pair with costumes of the same color); * (1, 2), (2, 3), (1, 3), (2, 1) β€” contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same). Good color choosing: * (1, 2), (2, 1), (1, 3), (3, 1); * (1, 2), (3, 1), (2, 3), (3, 2); * (3, 1), (1, 2), (2, 3), (3, 2). You have to find any suitable color choosing or say that no suitable choosing exists. Input The only line of the input contains two integers n and k (2 ≀ n, k ≀ 2 β‹… 10^5) β€” the number of pairs and the number of colors. Output If it is impossible to find any suitable colors choosing, print "NO". Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β€” colors of costumes of man and woman in the i-th pair, respectively. You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable. Examples Input 4 3 Output YES 3 1 1 3 3 2 2 3 Input 10 4 Output YES 2 1 1 3 4 2 3 4 4 3 3 2 2 4 4 1 1 4 3 1 Input 13 4 Output NO
instruction
0
102,927
7
205,854
Tags: constructive algorithms, implementation Correct Solution: ``` n,k=map(int,input().split()) if(n>(k*(k-1))): print('NO') else: print('YES') arr=[0]*(k+1) for i in range(1,k): arr[i]=i+1 arr[-1]=1 ansarr=[] count=0 index=1 while(count<n): ansarr.append(index) ansarr.append(arr[index]) arr[index]+=1 if(arr[index]>k): arr[index]=1 index+=1 count+=1 if(index>k): index=1 print(*ansarr) ```
output
1
102,927
7
205,855
Provide tags and a correct Python 3 solution for this coding contest problem. The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive. Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that: 1. for every i: b_i and g_i are integers between 1 and k, inclusive; 2. there are no two completely identical pairs, i.e. no two indices i, j (i β‰  j) such that b_i = b_j and g_i = g_j at the same time; 3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β‰  g_i for every i; 4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β‰  b_{i + 1} and g_i β‰  g_{i + 1} hold. Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second): Bad color choosing: * (1, 2), (2, 3), (3, 2), (1, 2) β€” contradiction with the second rule (there are equal pairs); * (2, 3), (1, 1), (3, 2), (1, 3) β€” contradiction with the third rule (there is a pair with costumes of the same color); * (1, 2), (2, 3), (1, 3), (2, 1) β€” contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same). Good color choosing: * (1, 2), (2, 1), (1, 3), (3, 1); * (1, 2), (3, 1), (2, 3), (3, 2); * (3, 1), (1, 2), (2, 3), (3, 2). You have to find any suitable color choosing or say that no suitable choosing exists. Input The only line of the input contains two integers n and k (2 ≀ n, k ≀ 2 β‹… 10^5) β€” the number of pairs and the number of colors. Output If it is impossible to find any suitable colors choosing, print "NO". Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β€” colors of costumes of man and woman in the i-th pair, respectively. You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable. Examples Input 4 3 Output YES 3 1 1 3 3 2 2 3 Input 10 4 Output YES 2 1 1 3 4 2 3 4 4 3 3 2 2 4 4 1 1 4 3 1 Input 13 4 Output NO
instruction
0
102,928
7
205,856
Tags: constructive algorithms, implementation Correct Solution: ``` n,k=map(int,input().rstrip().split(" ")) if((k*k-k)<n): print("NO") exit() print("YES") prev1=0;prev2=0 c=0; for i in range(1,k+1): for j in range(i+1,k+1): curr1=i;curr2=j if(prev1==curr1 or prev2==curr2): curr1,curr2=curr2,curr1 print(curr1,curr2) c+=1 if(c==n): exit() curr1,curr2=curr2,curr1 print(curr1,curr2) c+=1 if(c==n): exit() ```
output
1
102,928
7
205,857
Provide tags and a correct Python 3 solution for this coding contest problem. The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive. Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that: 1. for every i: b_i and g_i are integers between 1 and k, inclusive; 2. there are no two completely identical pairs, i.e. no two indices i, j (i β‰  j) such that b_i = b_j and g_i = g_j at the same time; 3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β‰  g_i for every i; 4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β‰  b_{i + 1} and g_i β‰  g_{i + 1} hold. Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second): Bad color choosing: * (1, 2), (2, 3), (3, 2), (1, 2) β€” contradiction with the second rule (there are equal pairs); * (2, 3), (1, 1), (3, 2), (1, 3) β€” contradiction with the third rule (there is a pair with costumes of the same color); * (1, 2), (2, 3), (1, 3), (2, 1) β€” contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same). Good color choosing: * (1, 2), (2, 1), (1, 3), (3, 1); * (1, 2), (3, 1), (2, 3), (3, 2); * (3, 1), (1, 2), (2, 3), (3, 2). You have to find any suitable color choosing or say that no suitable choosing exists. Input The only line of the input contains two integers n and k (2 ≀ n, k ≀ 2 β‹… 10^5) β€” the number of pairs and the number of colors. Output If it is impossible to find any suitable colors choosing, print "NO". Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β€” colors of costumes of man and woman in the i-th pair, respectively. You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable. Examples Input 4 3 Output YES 3 1 1 3 3 2 2 3 Input 10 4 Output YES 2 1 1 3 4 2 3 4 4 3 3 2 2 4 4 1 1 4 3 1 Input 13 4 Output NO
instruction
0
102,929
7
205,858
Tags: constructive algorithms, implementation Correct Solution: ``` def main(): n, k = map(int, input().split()) if n > k * (k - 1): print('NO') return print('YES') printed = 0 i = 0 while printed < n: first = i % k second = (i + i // k + 1) % k print(first + 1, second + 1) printed += 1 i += 1 main() ```
output
1
102,929
7
205,859
Provide tags and a correct Python 3 solution for this coding contest problem. The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive. Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that: 1. for every i: b_i and g_i are integers between 1 and k, inclusive; 2. there are no two completely identical pairs, i.e. no two indices i, j (i β‰  j) such that b_i = b_j and g_i = g_j at the same time; 3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β‰  g_i for every i; 4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β‰  b_{i + 1} and g_i β‰  g_{i + 1} hold. Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second): Bad color choosing: * (1, 2), (2, 3), (3, 2), (1, 2) β€” contradiction with the second rule (there are equal pairs); * (2, 3), (1, 1), (3, 2), (1, 3) β€” contradiction with the third rule (there is a pair with costumes of the same color); * (1, 2), (2, 3), (1, 3), (2, 1) β€” contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same). Good color choosing: * (1, 2), (2, 1), (1, 3), (3, 1); * (1, 2), (3, 1), (2, 3), (3, 2); * (3, 1), (1, 2), (2, 3), (3, 2). You have to find any suitable color choosing or say that no suitable choosing exists. Input The only line of the input contains two integers n and k (2 ≀ n, k ≀ 2 β‹… 10^5) β€” the number of pairs and the number of colors. Output If it is impossible to find any suitable colors choosing, print "NO". Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β€” colors of costumes of man and woman in the i-th pair, respectively. You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable. Examples Input 4 3 Output YES 3 1 1 3 3 2 2 3 Input 10 4 Output YES 2 1 1 3 4 2 3 4 4 3 3 2 2 4 4 1 1 4 3 1 Input 13 4 Output NO
instruction
0
102,930
7
205,860
Tags: constructive algorithms, implementation Correct Solution: ``` # Legends Always Come Up with Solution # Author: Manvir Singh import os import sys from io import BytesIO, IOBase def main(): n,k=map(int,input().split()) if (k-1)*k<n: print("NO") else: print("YES") z=0 for i in range(2,k+1): for j in range(1,i): print(j,i) z+=1 if z==n: return print(i,j) z+=1 if z==n: return # 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") if __name__ == "__main__": main() ```
output
1
102,930
7
205,861
Provide tags and a correct Python 3 solution for this coding contest problem. The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive. Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that: 1. for every i: b_i and g_i are integers between 1 and k, inclusive; 2. there are no two completely identical pairs, i.e. no two indices i, j (i β‰  j) such that b_i = b_j and g_i = g_j at the same time; 3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β‰  g_i for every i; 4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β‰  b_{i + 1} and g_i β‰  g_{i + 1} hold. Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second): Bad color choosing: * (1, 2), (2, 3), (3, 2), (1, 2) β€” contradiction with the second rule (there are equal pairs); * (2, 3), (1, 1), (3, 2), (1, 3) β€” contradiction with the third rule (there is a pair with costumes of the same color); * (1, 2), (2, 3), (1, 3), (2, 1) β€” contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same). Good color choosing: * (1, 2), (2, 1), (1, 3), (3, 1); * (1, 2), (3, 1), (2, 3), (3, 2); * (3, 1), (1, 2), (2, 3), (3, 2). You have to find any suitable color choosing or say that no suitable choosing exists. Input The only line of the input contains two integers n and k (2 ≀ n, k ≀ 2 β‹… 10^5) β€” the number of pairs and the number of colors. Output If it is impossible to find any suitable colors choosing, print "NO". Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β€” colors of costumes of man and woman in the i-th pair, respectively. You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable. Examples Input 4 3 Output YES 3 1 1 3 3 2 2 3 Input 10 4 Output YES 2 1 1 3 4 2 3 4 4 3 3 2 2 4 4 1 1 4 3 1 Input 13 4 Output NO
instruction
0
102,931
7
205,862
Tags: constructive algorithms, implementation Correct Solution: ``` ''' Auther: ghoshashis545 Ashis Ghosh College: jalpaiguri Govt Enggineering College ''' from os import path import sys from functools import cmp_to_key as ctk from collections import deque,defaultdict as dd from bisect import bisect,bisect_left,bisect_right,insort,insort_left,insort_right from itertools import permutations from datetime import datetime from math import ceil,sqrt,log,gcd def ii():return int(input()) def si():return input() def mi():return map(int,input().split()) def li():return list(mi()) abc='abcdefghijklmnopqrstuvwxyz' abd={'a': 0, 'b': 1, 'c': 2, 'd': 3, 'e': 4, 'f': 5, 'g': 6, 'h': 7, 'i': 8, 'j': 9, 'k': 10, 'l': 11, 'm': 12, 'n': 13, 'o': 14, 'p': 15, 'q': 16, 'r': 17, 's': 18, 't': 19, 'u': 20, 'v': 21, 'w': 22, 'x': 23, 'y': 24, 'z': 25} mod=1000000007 #mod=998244353 inf = float("inf") vow=['a','e','i','o','u'] dx,dy=[-1,1,0,0],[0,0,1,-1] def bo(i): return ord(i)-ord('a') def solve(): n,k=mi() a=[] for i in range(1,k+1): for j in range(i+1,k+1): a.append([i,j]) a.append([j,i]) if(len(a)>=n): print('YES') for i in range(n): print(*a[i]) exit(0) print("NO") if __name__ =="__main__": solve() ```
output
1
102,931
7
205,863
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive. Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that: 1. for every i: b_i and g_i are integers between 1 and k, inclusive; 2. there are no two completely identical pairs, i.e. no two indices i, j (i β‰  j) such that b_i = b_j and g_i = g_j at the same time; 3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β‰  g_i for every i; 4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β‰  b_{i + 1} and g_i β‰  g_{i + 1} hold. Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second): Bad color choosing: * (1, 2), (2, 3), (3, 2), (1, 2) β€” contradiction with the second rule (there are equal pairs); * (2, 3), (1, 1), (3, 2), (1, 3) β€” contradiction with the third rule (there is a pair with costumes of the same color); * (1, 2), (2, 3), (1, 3), (2, 1) β€” contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same). Good color choosing: * (1, 2), (2, 1), (1, 3), (3, 1); * (1, 2), (3, 1), (2, 3), (3, 2); * (3, 1), (1, 2), (2, 3), (3, 2). You have to find any suitable color choosing or say that no suitable choosing exists. Input The only line of the input contains two integers n and k (2 ≀ n, k ≀ 2 β‹… 10^5) β€” the number of pairs and the number of colors. Output If it is impossible to find any suitable colors choosing, print "NO". Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β€” colors of costumes of man and woman in the i-th pair, respectively. You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable. Examples Input 4 3 Output YES 3 1 1 3 3 2 2 3 Input 10 4 Output YES 2 1 1 3 4 2 3 4 4 3 3 2 2 4 4 1 1 4 3 1 Input 13 4 Output NO Submitted Solution: ``` n,k=map(int,input().split()) if(n>(k*(k-1))): print('NO') else: ans=[0 for i in range(n)] for i in range(len(ans)): ans[i]=(i+1)%k if(ans[i]==0): ans[i]=k count=1 temp=[0 for i in range(len(ans))] for i in range(len(ans)): if(i%k==0): temp[i]=count+1 count+=1 else: temp[i]=temp[i-1]+1 if(temp[i]>k): temp[i]%=k print('YES') for i in range(n): print(ans[i],temp[i]) ```
instruction
0
102,932
7
205,864
Yes
output
1
102,932
7
205,865
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive. Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that: 1. for every i: b_i and g_i are integers between 1 and k, inclusive; 2. there are no two completely identical pairs, i.e. no two indices i, j (i β‰  j) such that b_i = b_j and g_i = g_j at the same time; 3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β‰  g_i for every i; 4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β‰  b_{i + 1} and g_i β‰  g_{i + 1} hold. Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second): Bad color choosing: * (1, 2), (2, 3), (3, 2), (1, 2) β€” contradiction with the second rule (there are equal pairs); * (2, 3), (1, 1), (3, 2), (1, 3) β€” contradiction with the third rule (there is a pair with costumes of the same color); * (1, 2), (2, 3), (1, 3), (2, 1) β€” contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same). Good color choosing: * (1, 2), (2, 1), (1, 3), (3, 1); * (1, 2), (3, 1), (2, 3), (3, 2); * (3, 1), (1, 2), (2, 3), (3, 2). You have to find any suitable color choosing or say that no suitable choosing exists. Input The only line of the input contains two integers n and k (2 ≀ n, k ≀ 2 β‹… 10^5) β€” the number of pairs and the number of colors. Output If it is impossible to find any suitable colors choosing, print "NO". Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β€” colors of costumes of man and woman in the i-th pair, respectively. You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable. Examples Input 4 3 Output YES 3 1 1 3 3 2 2 3 Input 10 4 Output YES 2 1 1 3 4 2 3 4 4 3 3 2 2 4 4 1 1 4 3 1 Input 13 4 Output NO Submitted Solution: ``` import math n,k=map(int,input().split()) if n>k*(k-1): print("NO") else: print("YES") count,ok=0,False for i in range(math.ceil(n/k)): for j in range(k): count+=1 if (j+i+2)%k==0: print(j+1,k) else: print(j+1,(j+1+i+1)%k) if count==n: ok=True break if ok==True: break ```
instruction
0
102,933
7
205,866
Yes
output
1
102,933
7
205,867
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive. Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that: 1. for every i: b_i and g_i are integers between 1 and k, inclusive; 2. there are no two completely identical pairs, i.e. no two indices i, j (i β‰  j) such that b_i = b_j and g_i = g_j at the same time; 3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β‰  g_i for every i; 4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β‰  b_{i + 1} and g_i β‰  g_{i + 1} hold. Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second): Bad color choosing: * (1, 2), (2, 3), (3, 2), (1, 2) β€” contradiction with the second rule (there are equal pairs); * (2, 3), (1, 1), (3, 2), (1, 3) β€” contradiction with the third rule (there is a pair with costumes of the same color); * (1, 2), (2, 3), (1, 3), (2, 1) β€” contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same). Good color choosing: * (1, 2), (2, 1), (1, 3), (3, 1); * (1, 2), (3, 1), (2, 3), (3, 2); * (3, 1), (1, 2), (2, 3), (3, 2). You have to find any suitable color choosing or say that no suitable choosing exists. Input The only line of the input contains two integers n and k (2 ≀ n, k ≀ 2 β‹… 10^5) β€” the number of pairs and the number of colors. Output If it is impossible to find any suitable colors choosing, print "NO". Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β€” colors of costumes of man and woman in the i-th pair, respectively. You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable. Examples Input 4 3 Output YES 3 1 1 3 3 2 2 3 Input 10 4 Output YES 2 1 1 3 4 2 3 4 4 3 3 2 2 4 4 1 1 4 3 1 Input 13 4 Output NO Submitted Solution: ``` from sys import stdin n,k=map(int,stdin.readline().strip().split()) mx=(k*(k-1)) if mx<n: print("NO") exit(0) x=0 print("YES") for i in range(1,k): for j in range(i+1,k+1): print(i,j) x+=1 if x==n: exit(0) print(j,i) x+=1 if x==n: exit(0) ```
instruction
0
102,934
7
205,868
Yes
output
1
102,934
7
205,869
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive. Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that: 1. for every i: b_i and g_i are integers between 1 and k, inclusive; 2. there are no two completely identical pairs, i.e. no two indices i, j (i β‰  j) such that b_i = b_j and g_i = g_j at the same time; 3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β‰  g_i for every i; 4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β‰  b_{i + 1} and g_i β‰  g_{i + 1} hold. Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second): Bad color choosing: * (1, 2), (2, 3), (3, 2), (1, 2) β€” contradiction with the second rule (there are equal pairs); * (2, 3), (1, 1), (3, 2), (1, 3) β€” contradiction with the third rule (there is a pair with costumes of the same color); * (1, 2), (2, 3), (1, 3), (2, 1) β€” contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same). Good color choosing: * (1, 2), (2, 1), (1, 3), (3, 1); * (1, 2), (3, 1), (2, 3), (3, 2); * (3, 1), (1, 2), (2, 3), (3, 2). You have to find any suitable color choosing or say that no suitable choosing exists. Input The only line of the input contains two integers n and k (2 ≀ n, k ≀ 2 β‹… 10^5) β€” the number of pairs and the number of colors. Output If it is impossible to find any suitable colors choosing, print "NO". Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β€” colors of costumes of man and woman in the i-th pair, respectively. You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable. Examples Input 4 3 Output YES 3 1 1 3 3 2 2 3 Input 10 4 Output YES 2 1 1 3 4 2 3 4 4 3 3 2 2 4 4 1 1 4 3 1 Input 13 4 Output NO Submitted Solution: ``` n, k = map(int, input().split()) if n > k*(k-1): print("NO") else: print("YES") cnt = 0 for delta in range(k): for c in range(1, k+1): if cnt < n: cnt +=1 print(c, 1+(c+delta)%k) else: break ```
instruction
0
102,935
7
205,870
Yes
output
1
102,935
7
205,871
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive. Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that: 1. for every i: b_i and g_i are integers between 1 and k, inclusive; 2. there are no two completely identical pairs, i.e. no two indices i, j (i β‰  j) such that b_i = b_j and g_i = g_j at the same time; 3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β‰  g_i for every i; 4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β‰  b_{i + 1} and g_i β‰  g_{i + 1} hold. Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second): Bad color choosing: * (1, 2), (2, 3), (3, 2), (1, 2) β€” contradiction with the second rule (there are equal pairs); * (2, 3), (1, 1), (3, 2), (1, 3) β€” contradiction with the third rule (there is a pair with costumes of the same color); * (1, 2), (2, 3), (1, 3), (2, 1) β€” contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same). Good color choosing: * (1, 2), (2, 1), (1, 3), (3, 1); * (1, 2), (3, 1), (2, 3), (3, 2); * (3, 1), (1, 2), (2, 3), (3, 2). You have to find any suitable color choosing or say that no suitable choosing exists. Input The only line of the input contains two integers n and k (2 ≀ n, k ≀ 2 β‹… 10^5) β€” the number of pairs and the number of colors. Output If it is impossible to find any suitable colors choosing, print "NO". Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β€” colors of costumes of man and woman in the i-th pair, respectively. You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable. Examples Input 4 3 Output YES 3 1 1 3 3 2 2 3 Input 10 4 Output YES 2 1 1 3 4 2 3 4 4 3 3 2 2 4 4 1 1 4 3 1 Input 13 4 Output NO Submitted Solution: ``` n, k = map(int, input().split()) flg = [[True for _ in range(k + 1)] for _ in range(k + 1)] ans = [[1, 2]] flg[1][2] = False for pair in range(1, n): ok = False for b in range(1, k + 1): for g in range(1, k + 1): if flg[b][g] and b != g and b != ans[pair - 1][0] and g != ans[pair - 1][1]: ans.append([b, g]) flg[b][g] = False ok = True break if ok: break if not ok: print("NO") exit(0) print("YES") for a in ans: print(a[0], a[1]) ```
instruction
0
102,936
7
205,872
No
output
1
102,936
7
205,873