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Provide tags and a correct Python 3 solution for this coding contest problem. You've got a rectangular parallelepiped with integer edge lengths. You know the areas of its three faces that have a common vertex. Your task is to find the sum of lengths of all 12 edges of this parallelepiped. Input The first and the single line contains three space-separated integers — the areas of the parallelepiped's faces. The area's values are positive ( > 0) and do not exceed 104. It is guaranteed that there exists at least one parallelepiped that satisfies the problem statement. Output Print a single number — the sum of all edges of the parallelepiped. Examples Input 1 1 1 Output 12 Input 4 6 6 Output 28 Note In the first sample the parallelepiped has sizes 1 × 1 × 1, in the second one — 2 × 2 × 3.
instruction
0
103,951
23
207,902
Tags: brute force, geometry, math Correct Solution: ``` import math arr = [int(x) for x in input().split()] print(int(4*(math.sqrt((arr[0]*arr[1])/arr[2])+math.sqrt((arr[0]*arr[2])/arr[1])+math.sqrt((arr[2]*arr[1])/arr[0])))) ```
output
1
103,951
23
207,903
Provide tags and a correct Python 3 solution for this coding contest problem. You've got a rectangular parallelepiped with integer edge lengths. You know the areas of its three faces that have a common vertex. Your task is to find the sum of lengths of all 12 edges of this parallelepiped. Input The first and the single line contains three space-separated integers — the areas of the parallelepiped's faces. The area's values are positive ( > 0) and do not exceed 104. It is guaranteed that there exists at least one parallelepiped that satisfies the problem statement. Output Print a single number — the sum of all edges of the parallelepiped. Examples Input 1 1 1 Output 12 Input 4 6 6 Output 28 Note In the first sample the parallelepiped has sizes 1 × 1 × 1, in the second one — 2 × 2 × 3.
instruction
0
103,952
23
207,904
Tags: brute force, geometry, math Correct Solution: ``` arr = input().split() ab , bc , ca = int(arr[0]), int(arr[1]), int(arr[2]) b = (ab*bc//ca)**(1/2) a = (ab*ca//bc)**(1/2) c = (bc*ca//ab)**(1/2) print(int((a+b+c)*4)) ```
output
1
103,952
23
207,905
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You've got a rectangular parallelepiped with integer edge lengths. You know the areas of its three faces that have a common vertex. Your task is to find the sum of lengths of all 12 edges of this parallelepiped. Input The first and the single line contains three space-separated integers — the areas of the parallelepiped's faces. The area's values are positive ( > 0) and do not exceed 104. It is guaranteed that there exists at least one parallelepiped that satisfies the problem statement. Output Print a single number — the sum of all edges of the parallelepiped. Examples Input 1 1 1 Output 12 Input 4 6 6 Output 28 Note In the first sample the parallelepiped has sizes 1 × 1 × 1, in the second one — 2 × 2 × 3. Submitted Solution: ``` import math def solve(areas): a = math.sqrt((areas[2] * areas[0]) / areas[1]) b = areas[0] / a c = areas[2] / a result = a * 4 + b * 4 + c * 4 return result areas = [int(num) for num in input().split()] result = solve(areas) print(int(result)) ```
instruction
0
103,953
23
207,906
Yes
output
1
103,953
23
207,907
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You've got a rectangular parallelepiped with integer edge lengths. You know the areas of its three faces that have a common vertex. Your task is to find the sum of lengths of all 12 edges of this parallelepiped. Input The first and the single line contains three space-separated integers — the areas of the parallelepiped's faces. The area's values are positive ( > 0) and do not exceed 104. It is guaranteed that there exists at least one parallelepiped that satisfies the problem statement. Output Print a single number — the sum of all edges of the parallelepiped. Examples Input 1 1 1 Output 12 Input 4 6 6 Output 28 Note In the first sample the parallelepiped has sizes 1 × 1 × 1, in the second one — 2 × 2 × 3. Submitted Solution: ``` x,y,z=map(int,input().split()) xx=(x*y/z)**0.5 yy=(y*z/x)**0.5 zz=(z*x/y)**0.5 print(int(xx+yy+zz)*4) ```
instruction
0
103,954
23
207,908
Yes
output
1
103,954
23
207,909
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You've got a rectangular parallelepiped with integer edge lengths. You know the areas of its three faces that have a common vertex. Your task is to find the sum of lengths of all 12 edges of this parallelepiped. Input The first and the single line contains three space-separated integers — the areas of the parallelepiped's faces. The area's values are positive ( > 0) and do not exceed 104. It is guaranteed that there exists at least one parallelepiped that satisfies the problem statement. Output Print a single number — the sum of all edges of the parallelepiped. Examples Input 1 1 1 Output 12 Input 4 6 6 Output 28 Note In the first sample the parallelepiped has sizes 1 × 1 × 1, in the second one — 2 × 2 × 3. Submitted Solution: ``` import math import sys import collections # imgur.com/Pkt7iIf.png def getdict(n): d = {} if type(n) is list: for i in n: if i in d: d[i] += 1 else: d[i] = 1 else: for i in range(n): t = ii() if t in d: d[t] += 1 else: d[t] = 1 return d def cdiv(n, k): return n // k + (n % k != 0) def ii(): return int(input()) def mi(): return map(int, input().split()) def li(): return list(map(int, input().split())) def lcm(a, b): return abs(a*b) // math.gcd(a, b) a, b, c = mi() q = math.sqrt(a*b/c) w = math.sqrt(b*c/a) e = math.sqrt(a*c/b) print(int(4*(q+w+e))) ```
instruction
0
103,955
23
207,910
Yes
output
1
103,955
23
207,911
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You've got a rectangular parallelepiped with integer edge lengths. You know the areas of its three faces that have a common vertex. Your task is to find the sum of lengths of all 12 edges of this parallelepiped. Input The first and the single line contains three space-separated integers — the areas of the parallelepiped's faces. The area's values are positive ( > 0) and do not exceed 104. It is guaranteed that there exists at least one parallelepiped that satisfies the problem statement. Output Print a single number — the sum of all edges of the parallelepiped. Examples Input 1 1 1 Output 12 Input 4 6 6 Output 28 Note In the first sample the parallelepiped has sizes 1 × 1 × 1, in the second one — 2 × 2 × 3. Submitted Solution: ``` import math a, b, c = input().split() a, b, c = int(a), int(b), int(c) a1 = math.sqrt(a * b / c) b1 = math.sqrt(c * a / b) c1 = math.sqrt(c * b / a) print(int(a1*4 + b1*4 + c1*4)) ```
instruction
0
103,956
23
207,912
Yes
output
1
103,956
23
207,913
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You've got a rectangular parallelepiped with integer edge lengths. You know the areas of its three faces that have a common vertex. Your task is to find the sum of lengths of all 12 edges of this parallelepiped. Input The first and the single line contains three space-separated integers — the areas of the parallelepiped's faces. The area's values are positive ( > 0) and do not exceed 104. It is guaranteed that there exists at least one parallelepiped that satisfies the problem statement. Output Print a single number — the sum of all edges of the parallelepiped. Examples Input 1 1 1 Output 12 Input 4 6 6 Output 28 Note In the first sample the parallelepiped has sizes 1 × 1 × 1, in the second one — 2 × 2 × 3. Submitted Solution: ``` import math a, b, c = map(int, input().split()) volume_sqr = math.sqrt(a * b * c) print(4 * (volume_sqr / a + volume_sqr / b + volume_sqr / c)) ```
instruction
0
103,957
23
207,914
No
output
1
103,957
23
207,915
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You've got a rectangular parallelepiped with integer edge lengths. You know the areas of its three faces that have a common vertex. Your task is to find the sum of lengths of all 12 edges of this parallelepiped. Input The first and the single line contains three space-separated integers — the areas of the parallelepiped's faces. The area's values are positive ( > 0) and do not exceed 104. It is guaranteed that there exists at least one parallelepiped that satisfies the problem statement. Output Print a single number — the sum of all edges of the parallelepiped. Examples Input 1 1 1 Output 12 Input 4 6 6 Output 28 Note In the first sample the parallelepiped has sizes 1 × 1 × 1, in the second one — 2 × 2 × 3. Submitted Solution: ``` '''input 152 108 4104 ''' def gcd(x, y): while y != 0: x, y = y, x % y return x a, b, c = map(int, input().split()) l = a * b // gcd(a, b) l = l * c // gcd(l, c) print((l // a + l // b + l // c) * 4 if l != max([a,b,c]) else (l // a + l // b + l // c) * 8) ```
instruction
0
103,958
23
207,916
No
output
1
103,958
23
207,917
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You've got a rectangular parallelepiped with integer edge lengths. You know the areas of its three faces that have a common vertex. Your task is to find the sum of lengths of all 12 edges of this parallelepiped. Input The first and the single line contains three space-separated integers — the areas of the parallelepiped's faces. The area's values are positive ( > 0) and do not exceed 104. It is guaranteed that there exists at least one parallelepiped that satisfies the problem statement. Output Print a single number — the sum of all edges of the parallelepiped. Examples Input 1 1 1 Output 12 Input 4 6 6 Output 28 Note In the first sample the parallelepiped has sizes 1 × 1 × 1, in the second one — 2 × 2 × 3. Submitted Solution: ``` a=[int(x) for x in input().split()] #d*b=a[0] #b*c=a[1] #d*c=a[2] #b=a[0]/d #c=a[2]/d #a[0]*a[2]/d**2=a[1] d=(a[0]*a[2]/a[1])**0.5 b=a[0]/d c=a[2]/d print(4*d + 4*b + 4*c) ```
instruction
0
103,959
23
207,918
No
output
1
103,959
23
207,919
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You've got a rectangular parallelepiped with integer edge lengths. You know the areas of its three faces that have a common vertex. Your task is to find the sum of lengths of all 12 edges of this parallelepiped. Input The first and the single line contains three space-separated integers — the areas of the parallelepiped's faces. The area's values are positive ( > 0) and do not exceed 104. It is guaranteed that there exists at least one parallelepiped that satisfies the problem statement. Output Print a single number — the sum of all edges of the parallelepiped. Examples Input 1 1 1 Output 12 Input 4 6 6 Output 28 Note In the first sample the parallelepiped has sizes 1 × 1 × 1, in the second one — 2 × 2 × 3. Submitted Solution: ``` def gcd(a, b): if b == 0: return a return gcd(b, a % b) x, y, z = map(int, input().split()) if x == y == z: print(int(x ** 0.5) * 12) else: if x == y: y, z = z, y a = gcd(x, y) if a == min(x, y): a = int(min(x, y) ** 0.5) b = x // a c = y // a if b * c != z: a = gcd(x, z) b = x // a c = z // a print(4 * (a + b + c)) ```
instruction
0
103,960
23
207,920
No
output
1
103,960
23
207,921
Provide a correct Python 3 solution for this coding contest problem. There are n points on a straight line, and the i-th point among them is located at xi. All these coordinates are distinct. Determine the number m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Input The first line contains a single integer n (3 ≤ n ≤ 100 000) — the number of points. The second line contains a sequence of integers x1, x2, ..., xn ( - 109 ≤ xi ≤ 109) — the coordinates of the points. All these coordinates are distinct. The points can be given in an arbitrary order. Output Print a single integer m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Examples Input 3 -5 10 5 Output 1 Input 6 100 200 400 300 600 500 Output 0 Input 4 10 9 0 -1 Output 8 Note In the first example you can add one point with coordinate 0. In the second example the distances between all neighboring points are already equal, so you shouldn't add anything.
instruction
0
104,152
23
208,304
"Correct Solution: ``` n = int(input()) a = [int(x) for x in input().strip().split()] a = sorted(a) d = [] for i in range(len(a) - 1): d.append(a[i + 1] - a[i]) def gcd(a, b): if(b == 0): return a else: return gcd(b, a % b) g = d[0] for e in d: g = gcd(g, e) cnt = len(a) print( int( ( a[len(a) - 1] - a[0]) / g + 1 - cnt)) ```
output
1
104,152
23
208,305
Provide a correct Python 3 solution for this coding contest problem. There are n points on a straight line, and the i-th point among them is located at xi. All these coordinates are distinct. Determine the number m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Input The first line contains a single integer n (3 ≤ n ≤ 100 000) — the number of points. The second line contains a sequence of integers x1, x2, ..., xn ( - 109 ≤ xi ≤ 109) — the coordinates of the points. All these coordinates are distinct. The points can be given in an arbitrary order. Output Print a single integer m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Examples Input 3 -5 10 5 Output 1 Input 6 100 200 400 300 600 500 Output 0 Input 4 10 9 0 -1 Output 8 Note In the first example you can add one point with coordinate 0. In the second example the distances between all neighboring points are already equal, so you shouldn't add anything.
instruction
0
104,153
23
208,306
"Correct Solution: ``` def nod(n, m): if(m==0): return n; if(n>m): return nod(m,n%m); else: return nod(n,m%n); n=input(); x = sorted(list(map(int, input().split()))) m = min(x) nnod=0 for i in range(len(x)): if(i>1): if(i==2): nnod=nod(x[i]-x[i-1], x[i-1]-x[i-2]) else: nnod=nod(nnod, x[i]-x[i-1]) res=0 for i in range(len(x)): if(i>0): res+=(x[i]-x[i-1])/nnod - 1; print(int(res)) ```
output
1
104,153
23
208,307
Provide a correct Python 3 solution for this coding contest problem. There are n points on a straight line, and the i-th point among them is located at xi. All these coordinates are distinct. Determine the number m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Input The first line contains a single integer n (3 ≤ n ≤ 100 000) — the number of points. The second line contains a sequence of integers x1, x2, ..., xn ( - 109 ≤ xi ≤ 109) — the coordinates of the points. All these coordinates are distinct. The points can be given in an arbitrary order. Output Print a single integer m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Examples Input 3 -5 10 5 Output 1 Input 6 100 200 400 300 600 500 Output 0 Input 4 10 9 0 -1 Output 8 Note In the first example you can add one point with coordinate 0. In the second example the distances between all neighboring points are already equal, so you shouldn't add anything.
instruction
0
104,154
23
208,308
"Correct Solution: ``` from fractions import gcd from functools import reduce n = int(input()) x = list(map(int, input().split())) x.sort() difs = [] for i in range(len(x)-1): difs.append(x[i+1]-x[i]) dif = reduce(gcd, difs) mmin = x[0] mmax = x[-1] x = set(x) cnt = (mmax-mmin+dif)//dif-n print(cnt) ```
output
1
104,154
23
208,309
Provide a correct Python 3 solution for this coding contest problem. There are n points on a straight line, and the i-th point among them is located at xi. All these coordinates are distinct. Determine the number m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Input The first line contains a single integer n (3 ≤ n ≤ 100 000) — the number of points. The second line contains a sequence of integers x1, x2, ..., xn ( - 109 ≤ xi ≤ 109) — the coordinates of the points. All these coordinates are distinct. The points can be given in an arbitrary order. Output Print a single integer m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Examples Input 3 -5 10 5 Output 1 Input 6 100 200 400 300 600 500 Output 0 Input 4 10 9 0 -1 Output 8 Note In the first example you can add one point with coordinate 0. In the second example the distances between all neighboring points are already equal, so you shouldn't add anything.
instruction
0
104,155
23
208,310
"Correct Solution: ``` from fractions import gcd n=int(input()) a=input().split() for i in range(0, n): a[i]=int(a[i]) a.sort() dists=[] for i in range(1, n): dists.append(a[i]-a[i-1]) s=dists[0] gdc=dists[0] for i in range(1,len(dists)): gdc=gcd(dists[i],gdc) s+=dists[i] print(s//gdc-n+1) ```
output
1
104,155
23
208,311
Provide a correct Python 3 solution for this coding contest problem. There are n points on a straight line, and the i-th point among them is located at xi. All these coordinates are distinct. Determine the number m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Input The first line contains a single integer n (3 ≤ n ≤ 100 000) — the number of points. The second line contains a sequence of integers x1, x2, ..., xn ( - 109 ≤ xi ≤ 109) — the coordinates of the points. All these coordinates are distinct. The points can be given in an arbitrary order. Output Print a single integer m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Examples Input 3 -5 10 5 Output 1 Input 6 100 200 400 300 600 500 Output 0 Input 4 10 9 0 -1 Output 8 Note In the first example you can add one point with coordinate 0. In the second example the distances between all neighboring points are already equal, so you shouldn't add anything.
instruction
0
104,156
23
208,312
"Correct Solution: ``` def nod(a, b): while a!=0 and b!=0: if a > b: a = a % b else: b = b % a return (a+b) n = int(input()) a = list(map(int, input().split())) a.sort() d = nod(a[1] - a[0], a[2] - a[1]) for i in range(2, n - 1): d = nod(a[i + 1] - a[i], d) count = 0 for i in range(n - 1): count += ((a[i + 1] - a[i]) // d - 1) print(count) ```
output
1
104,156
23
208,313
Provide a correct Python 3 solution for this coding contest problem. There are n points on a straight line, and the i-th point among them is located at xi. All these coordinates are distinct. Determine the number m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Input The first line contains a single integer n (3 ≤ n ≤ 100 000) — the number of points. The second line contains a sequence of integers x1, x2, ..., xn ( - 109 ≤ xi ≤ 109) — the coordinates of the points. All these coordinates are distinct. The points can be given in an arbitrary order. Output Print a single integer m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Examples Input 3 -5 10 5 Output 1 Input 6 100 200 400 300 600 500 Output 0 Input 4 10 9 0 -1 Output 8 Note In the first example you can add one point with coordinate 0. In the second example the distances between all neighboring points are already equal, so you shouldn't add anything.
instruction
0
104,157
23
208,314
"Correct Solution: ``` from fractions import gcd n = int(input()) a = list(map(int, input().split())) a.sort() for i in range(1, len(a)): a[i-1] = a[i] - a[i-1] a.pop() g = a[0] s = 0 for i in range(len(a)): s += a[i] g = gcd(g, a[i]) s = s // g - len(a) print(s) ```
output
1
104,157
23
208,315
Provide a correct Python 3 solution for this coding contest problem. There are n points on a straight line, and the i-th point among them is located at xi. All these coordinates are distinct. Determine the number m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Input The first line contains a single integer n (3 ≤ n ≤ 100 000) — the number of points. The second line contains a sequence of integers x1, x2, ..., xn ( - 109 ≤ xi ≤ 109) — the coordinates of the points. All these coordinates are distinct. The points can be given in an arbitrary order. Output Print a single integer m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Examples Input 3 -5 10 5 Output 1 Input 6 100 200 400 300 600 500 Output 0 Input 4 10 9 0 -1 Output 8 Note In the first example you can add one point with coordinate 0. In the second example the distances between all neighboring points are already equal, so you shouldn't add anything.
instruction
0
104,158
23
208,316
"Correct Solution: ``` import sys # For getting input from input.txt file #sys.stdin = open('input.txt', 'r') # Printing the Output to output.txt file #sys.stdout = open('output.txt', 'w') def gcd(a, b): while a != 0 and b != 0: if a > b: a = a % b else: b = b % a return max(a, b) n = int(input()) s = input() num = list(map(int, s.split(' '))) num.sort() slen = [] for i in range(1, n): slen.append(num[i] - num[i - 1]) slen.sort() minlen = slen[0] maxlen = slen[-1] for i in range(0, n - 1): if minlen == 1: break elif slen[i] % minlen != 0: minlen = gcd(minlen, slen[i]) print( int( (num[-1] - num[0]) / minlen - n + 1) ) ```
output
1
104,158
23
208,317
Provide a correct Python 3 solution for this coding contest problem. There are n points on a straight line, and the i-th point among them is located at xi. All these coordinates are distinct. Determine the number m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Input The first line contains a single integer n (3 ≤ n ≤ 100 000) — the number of points. The second line contains a sequence of integers x1, x2, ..., xn ( - 109 ≤ xi ≤ 109) — the coordinates of the points. All these coordinates are distinct. The points can be given in an arbitrary order. Output Print a single integer m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Examples Input 3 -5 10 5 Output 1 Input 6 100 200 400 300 600 500 Output 0 Input 4 10 9 0 -1 Output 8 Note In the first example you can add one point with coordinate 0. In the second example the distances between all neighboring points are already equal, so you shouldn't add anything.
instruction
0
104,159
23
208,318
"Correct Solution: ``` def gcd(a, b): while a != 0 and b != 0: if b > a: b = b % a else: a = a % b if a == 0: return b else: return a n = int(input()) a = input() a = a.split() for i in range(len(a)): a[i] = int(a[i]) a = sorted(a) b = a[1] - a[0] for i in range(0, len(a) - 1): b = gcd(b, a[i + 1] - a[i]) cnt = (a[len(a) - 1] - a[0]) // b + 1 print(cnt - n) ```
output
1
104,159
23
208,319
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n points on a straight line, and the i-th point among them is located at xi. All these coordinates are distinct. Determine the number m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Input The first line contains a single integer n (3 ≤ n ≤ 100 000) — the number of points. The second line contains a sequence of integers x1, x2, ..., xn ( - 109 ≤ xi ≤ 109) — the coordinates of the points. All these coordinates are distinct. The points can be given in an arbitrary order. Output Print a single integer m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Examples Input 3 -5 10 5 Output 1 Input 6 100 200 400 300 600 500 Output 0 Input 4 10 9 0 -1 Output 8 Note In the first example you can add one point with coordinate 0. In the second example the distances between all neighboring points are already equal, so you shouldn't add anything. Submitted Solution: ``` import sys import math from collections import defaultdict,deque n=int(sys.stdin.readline()) arr=list(map(int,sys.stdin.readline().split())) arr.sort() x=arr[1]-arr[0] for i in range(n-1): x=math.gcd(x,arr[i+1]-arr[i]) ans=0 for i in range(n-1): dis=arr[i+1]-arr[i] y=dis//x-1 ans+=y print(ans) ```
instruction
0
104,160
23
208,320
Yes
output
1
104,160
23
208,321
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n points on a straight line, and the i-th point among them is located at xi. All these coordinates are distinct. Determine the number m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Input The first line contains a single integer n (3 ≤ n ≤ 100 000) — the number of points. The second line contains a sequence of integers x1, x2, ..., xn ( - 109 ≤ xi ≤ 109) — the coordinates of the points. All these coordinates are distinct. The points can be given in an arbitrary order. Output Print a single integer m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Examples Input 3 -5 10 5 Output 1 Input 6 100 200 400 300 600 500 Output 0 Input 4 10 9 0 -1 Output 8 Note In the first example you can add one point with coordinate 0. In the second example the distances between all neighboring points are already equal, so you shouldn't add anything. Submitted Solution: ``` n = int(input()) m = list(map(int, input().split())) m.sort() min_dif = m[1] - m[0] def nod(a, b): if b == 0: return a else: return nod(b, a %b) for i in range(1, n): min_dif = nod(min_dif, m[i] - m[i-1]) ans = 0 for i in range(1, n): if m[i] - m[i-1] > min_dif: ans += (m[i] - m[i-1]) / min_dif - 1 print(int(ans)) ```
instruction
0
104,161
23
208,322
Yes
output
1
104,161
23
208,323
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n points on a straight line, and the i-th point among them is located at xi. All these coordinates are distinct. Determine the number m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Input The first line contains a single integer n (3 ≤ n ≤ 100 000) — the number of points. The second line contains a sequence of integers x1, x2, ..., xn ( - 109 ≤ xi ≤ 109) — the coordinates of the points. All these coordinates are distinct. The points can be given in an arbitrary order. Output Print a single integer m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Examples Input 3 -5 10 5 Output 1 Input 6 100 200 400 300 600 500 Output 0 Input 4 10 9 0 -1 Output 8 Note In the first example you can add one point with coordinate 0. In the second example the distances between all neighboring points are already equal, so you shouldn't add anything. Submitted Solution: ``` import math n,a,q,w=int(input()),sorted(map(int,input().split())),0,0 for i in range(1,n):q=math.gcd(q,a[i]-a[i-1]) for i in range(1,n):w+=(a[i]-a[i-1])//q-1 print(w) ```
instruction
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104,162
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Yes
output
1
104,162
23
208,325
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n points on a straight line, and the i-th point among them is located at xi. All these coordinates are distinct. Determine the number m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Input The first line contains a single integer n (3 ≤ n ≤ 100 000) — the number of points. The second line contains a sequence of integers x1, x2, ..., xn ( - 109 ≤ xi ≤ 109) — the coordinates of the points. All these coordinates are distinct. The points can be given in an arbitrary order. Output Print a single integer m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Examples Input 3 -5 10 5 Output 1 Input 6 100 200 400 300 600 500 Output 0 Input 4 10 9 0 -1 Output 8 Note In the first example you can add one point with coordinate 0. In the second example the distances between all neighboring points are already equal, so you shouldn't add anything. Submitted Solution: ``` def nod(a, b): if (b == 0): return a; else: return nod(b, a%b); def main(): n = int(input()); arr = [int(i) for i in input().split()] arr.sort() no = 0; for i in range(1, n): no = nod(arr[i] - arr[i-1], no) ans = 0; for i in range(1, n): ans += -1 + (arr[i] - arr[i-1]) // no print(ans) main() ```
instruction
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104,163
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Yes
output
1
104,163
23
208,327
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n points on a straight line, and the i-th point among them is located at xi. All these coordinates are distinct. Determine the number m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Input The first line contains a single integer n (3 ≤ n ≤ 100 000) — the number of points. The second line contains a sequence of integers x1, x2, ..., xn ( - 109 ≤ xi ≤ 109) — the coordinates of the points. All these coordinates are distinct. The points can be given in an arbitrary order. Output Print a single integer m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Examples Input 3 -5 10 5 Output 1 Input 6 100 200 400 300 600 500 Output 0 Input 4 10 9 0 -1 Output 8 Note In the first example you can add one point with coordinate 0. In the second example the distances between all neighboring points are already equal, so you shouldn't add anything. Submitted Solution: ``` n = int(input()) x = list(map(int, input().split())) x.sort() dif = 1e10 for i in range(len(x)-1): dif = min(dif, x[i+1]-x[i]) mmin = x[0] mmax = x[-1] x = set(x) cnt = 0 for i in range(mmin, mmax+100, dif): if i <= mmax and i not in x: cnt += 1 print(cnt) ```
instruction
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No
output
1
104,164
23
208,329
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n points on a straight line, and the i-th point among them is located at xi. All these coordinates are distinct. Determine the number m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Input The first line contains a single integer n (3 ≤ n ≤ 100 000) — the number of points. The second line contains a sequence of integers x1, x2, ..., xn ( - 109 ≤ xi ≤ 109) — the coordinates of the points. All these coordinates are distinct. The points can be given in an arbitrary order. Output Print a single integer m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Examples Input 3 -5 10 5 Output 1 Input 6 100 200 400 300 600 500 Output 0 Input 4 10 9 0 -1 Output 8 Note In the first example you can add one point with coordinate 0. In the second example the distances between all neighboring points are already equal, so you shouldn't add anything. Submitted Solution: ``` import sys # For getting input from input.txt file #sys.stdin = open('input.txt', 'r') # Printing the Output to output.txt file #sys.stdout = open('output.txt', 'w') def gcd(a, b): while a != 0 and b != 0: if a > b: a = a % b else: b = b % a return max(a, b) n = int(input()) s = input() num = list(map(int, s.split(' '))) num.sort() slen = [] for i in range(1, n): slen.append(num[i] - num[i - 1]) slen.sort() minlen = slen[0] maxlen = slen[-1] for i in range(0, n - 1): if minlen == 1: break elif slen[i] % minlen != 0: minlen = gcd(minlen, slen[i]) print((num[-1] - num[0]) / minlen - n + 1) ```
instruction
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No
output
1
104,165
23
208,331
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n points on a straight line, and the i-th point among them is located at xi. All these coordinates are distinct. Determine the number m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Input The first line contains a single integer n (3 ≤ n ≤ 100 000) — the number of points. The second line contains a sequence of integers x1, x2, ..., xn ( - 109 ≤ xi ≤ 109) — the coordinates of the points. All these coordinates are distinct. The points can be given in an arbitrary order. Output Print a single integer m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Examples Input 3 -5 10 5 Output 1 Input 6 100 200 400 300 600 500 Output 0 Input 4 10 9 0 -1 Output 8 Note In the first example you can add one point with coordinate 0. In the second example the distances between all neighboring points are already equal, so you shouldn't add anything. Submitted Solution: ``` def gcd(a, b): while b != 0: tmp = b b = a % b a = tmp return a n = int(input()) v = list(map(int, input().split())) minrast = abs(v[1] - v[0]) for i in range(1, n): minrast = min(minrast, abs(v[i] - v[i-1])) f = 1 tmp = 0 cur = v[0] for i in range(1, n): tmprast = abs(v[i] - cur) if (tmprast % minrast == 0): tmp += tmprast // minrast - 1 else: f = 0 break cur = v[i] if f == 1: ans = tmp print(ans) else: print(abs(v[n-1] - v[0]) - n + 1) ```
instruction
0
104,166
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208,332
No
output
1
104,166
23
208,333
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n points on a straight line, and the i-th point among them is located at xi. All these coordinates are distinct. Determine the number m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Input The first line contains a single integer n (3 ≤ n ≤ 100 000) — the number of points. The second line contains a sequence of integers x1, x2, ..., xn ( - 109 ≤ xi ≤ 109) — the coordinates of the points. All these coordinates are distinct. The points can be given in an arbitrary order. Output Print a single integer m — the smallest number of points you should add on the line to make the distances between all neighboring points equal. Examples Input 3 -5 10 5 Output 1 Input 6 100 200 400 300 600 500 Output 0 Input 4 10 9 0 -1 Output 8 Note In the first example you can add one point with coordinate 0. In the second example the distances between all neighboring points are already equal, so you shouldn't add anything. Submitted Solution: ``` a = input() a = int(a) x = sorted(list(map(int, input().split()))) mn = 100000000000 cnt = 0 i = 0 for i in range(a): if cnt > 0: if x[i] - x[i - 1] < mn: mn = x[i] - x[i - 1] cnt = cnt + 1 ans = 0 cnt = 0; i = 0 for i in range(a): if cnt > 0: ans = ans + ((x[i] - x[i - 1]) // mn - 1) cnt = cnt + 1 print(ans) ```
instruction
0
104,167
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208,334
No
output
1
104,167
23
208,335
Provide a correct Python 3 solution for this coding contest problem. There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left. Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it. Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it. Q queries are given. We ask you to process them in order. There are two kinds of queries. Their input format and description are as follows: * `1 x`: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone. * `2 x`: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone. How many black stones are there on the grid after processing all Q queries? Constraints * 3 \leq N \leq 2\times 10^5 * 0 \leq Q \leq \min(2N-4,2\times 10^5) * 2 \leq x \leq N-1 * Queries are pairwise distinct. Input Input is given from Standard Input in the following format: N Q Query_1 \vdots Query_Q Output Print how many black stones there are on the grid after processing all Q queries. Examples Input 5 5 1 3 2 3 1 4 2 2 1 2 Output 1 Input 200000 0 Output 39999200004 Input 176527 15 1 81279 2 22308 2 133061 1 80744 2 44603 1 170938 2 139754 2 15220 1 172794 1 159290 2 156968 1 56426 2 77429 1 97459 2 71282 Output 31159505795
instruction
0
104,187
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208,374
"Correct Solution: ``` N, Q, *Query = [int(_) for _ in open(0).read().split()] D = Query[::2] X = Query[1::2] class LazySegmentTree(): def __init__(self, array, f, g, h, ti, ei): """ Parameters ---------- array : list to construct segment tree from f : func binary operation of the monoid T x T -> T T is dat g : func binary operation of the monoid T x E -> T T is dat, E is laz h : func binary operation of the monoid E x E -> T E is laz ti : T identity element of T ei : E identity element of E """ self.f = f self.g = g self.h = h self.ti = ti self.ei = ei self.height = height = len(array).bit_length() self.n = n = 2**height self.dat = dat = [ti] * n + array + [ti] * (n - len(array)) self.laz = [ei] * (2 * n) for i in range(n - 1, 0, -1): # build dat[i] = f(dat[i << 1], dat[i << 1 | 1]) def reflect(self, k): dat = self.dat ei = self.ei laz = self.laz g = self.g return self.dat[k] if laz[k] is ei else g(dat[k], laz[k]) def evaluate(self, k): laz = self.laz ei = self.ei reflect = self.reflect dat = self.dat h = self.h if laz[k] is ei: return laz[(k << 1) | 0] = h(laz[(k << 1) | 0], laz[k]) laz[(k << 1) | 1] = h(laz[(k << 1) | 1], laz[k]) dat[k] = reflect(k) laz[k] = ei def thrust(self, k): height = self.height evaluate = self.evaluate for i in range(height, 0, -1): evaluate(k >> i) def recalc(self, k): dat = self.dat reflect = self.reflect f = self.f while k: k >>= 1 dat[k] = f(reflect((k << 1) | 0), reflect((k << 1) | 1)) def update(self, a, b, x): # set value at position [a, b) (0-indexed) thrust = self.thrust n = self.n h = self.h laz = self.laz recalc = self.recalc a += n b += n - 1 l = a r = b + 1 thrust(a) thrust(b) while l < r: if l & 1: laz[l] = h(laz[l], x) l += 1 if r & 1: r -= 1 laz[r] = h(laz[r], x) l >>= 1 r >>= 1 recalc(a) recalc(b) def set_val(self, a, x): n = self.n thrust = self.thrust dat = self.dat laz = self.laz recalc = self.recalc ei = self.ei a += n thrust(a) dat[a] = x laz[a] = ei recalc(a) def query(self, a, b): # result on interval [a, b) (0-indexed) f = self.f ti = self.ti n = self.n thrust = self.thrust reflect = self.reflect a += n b += n - 1 thrust(a) thrust(b) l = a r = b + 1 vl = vr = ti while l < r: if l & 1: vl = f(vl, reflect(l)) l += 1 if r & 1: r -= 1 vr = f(reflect(r), vr) l >>= 1 r >>= 1 return f(vl, vr) #RSQ and RUQ array = [N] * (N + 1) f = lambda a, b: a if b == 0 else b g = lambda a, b: min(a, b) h = lambda a, b: min(a, b) ti = 0 ei = float('inf') lst1 = LazySegmentTree(array=array, ti=ti, ei=ei, f=f, g=g, h=h) lst2 = LazySegmentTree(array=array, ti=ti, ei=ei, f=f, g=g, h=h) ans = 0 for d, x in zip(D, X): if d == 1: y = lst1.query(x, x + 1) ans += y - 2 lst2.update(1, y, x) else: y = lst2.query(x, x + 1) ans += y - 2 lst1.update(1, y, x) ans = (N - 2)**2 - ans print(ans) ```
output
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104,187
23
208,375
Provide a correct Python 3 solution for this coding contest problem. There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left. Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it. Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it. Q queries are given. We ask you to process them in order. There are two kinds of queries. Their input format and description are as follows: * `1 x`: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone. * `2 x`: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone. How many black stones are there on the grid after processing all Q queries? Constraints * 3 \leq N \leq 2\times 10^5 * 0 \leq Q \leq \min(2N-4,2\times 10^5) * 2 \leq x \leq N-1 * Queries are pairwise distinct. Input Input is given from Standard Input in the following format: N Q Query_1 \vdots Query_Q Output Print how many black stones there are on the grid after processing all Q queries. Examples Input 5 5 1 3 2 3 1 4 2 2 1 2 Output 1 Input 200000 0 Output 39999200004 Input 176527 15 1 81279 2 22308 2 133061 1 80744 2 44603 1 170938 2 139754 2 15220 1 172794 1 159290 2 156968 1 56426 2 77429 1 97459 2 71282 Output 31159505795
instruction
0
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208,376
"Correct Solution: ``` n,q = map(int,input().split()) yoko = [-n] yoko2 = [-n] yokol = 1 tate = [-n] tate2 = [-n] tatel = 1 last = [n,n] import bisect ans = (n-2)**2 #print(ans) for _ in range(q): a,c = map(int,input().split()) if a == 1: b = bisect.bisect_left(yoko,-c) if b == yokol: yoko.append(-c) yoko2.append(-last[0]) yokol += 1 last[1] = c ans -= last[0]-2 else: ans -= -yoko2[b] - 2 if a == 2: b = bisect.bisect_left(tate,-c) if b == tatel: tate.append(-c) tate2.append(-last[1]) tatel += 1 last[0] = c ans -= last[1]-2 else: ans -= -tate2[b] - 2 #print(yoko) #print(yoko2) #print(tate) #print(tate2) print(ans) ```
output
1
104,188
23
208,377
Provide a correct Python 3 solution for this coding contest problem. There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left. Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it. Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it. Q queries are given. We ask you to process them in order. There are two kinds of queries. Their input format and description are as follows: * `1 x`: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone. * `2 x`: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone. How many black stones are there on the grid after processing all Q queries? Constraints * 3 \leq N \leq 2\times 10^5 * 0 \leq Q \leq \min(2N-4,2\times 10^5) * 2 \leq x \leq N-1 * Queries are pairwise distinct. Input Input is given from Standard Input in the following format: N Q Query_1 \vdots Query_Q Output Print how many black stones there are on the grid after processing all Q queries. Examples Input 5 5 1 3 2 3 1 4 2 2 1 2 Output 1 Input 200000 0 Output 39999200004 Input 176527 15 1 81279 2 22308 2 133061 1 80744 2 44603 1 170938 2 139754 2 15220 1 172794 1 159290 2 156968 1 56426 2 77429 1 97459 2 71282 Output 31159505795
instruction
0
104,189
23
208,378
"Correct Solution: ``` import sys def input(): return sys.stdin.readline().strip() def mapint(): return map(int, input().split()) sys.setrecursionlimit(10**9) N, Q = mapint() verti = [N-2]*(N-1) horiz = [N-2]*(N-1) left, top = N-2, N-2 ans = (N-2)**2 last_top = (N-2, N-2) last_left = (N-2, N-2) for _ in range(Q): c, x = mapint() x -= 1 if c==1: if x<=left: ans -= top left = x-1 for i in range(left, last_left[0]+1): horiz[i] = last_top[1] last_left = (left, x-1) else: ans -= horiz[x-1] if c==2: if x<=top: ans -= left top = x-1 for i in range(top, last_top[0]+1): verti[i] = last_left[1] last_top = (top, x-1) else: ans -= verti[x-1] print(ans) ```
output
1
104,189
23
208,379
Provide a correct Python 3 solution for this coding contest problem. There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left. Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it. Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it. Q queries are given. We ask you to process them in order. There are two kinds of queries. Their input format and description are as follows: * `1 x`: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone. * `2 x`: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone. How many black stones are there on the grid after processing all Q queries? Constraints * 3 \leq N \leq 2\times 10^5 * 0 \leq Q \leq \min(2N-4,2\times 10^5) * 2 \leq x \leq N-1 * Queries are pairwise distinct. Input Input is given from Standard Input in the following format: N Q Query_1 \vdots Query_Q Output Print how many black stones there are on the grid after processing all Q queries. Examples Input 5 5 1 3 2 3 1 4 2 2 1 2 Output 1 Input 200000 0 Output 39999200004 Input 176527 15 1 81279 2 22308 2 133061 1 80744 2 44603 1 170938 2 139754 2 15220 1 172794 1 159290 2 156968 1 56426 2 77429 1 97459 2 71282 Output 31159505795
instruction
0
104,190
23
208,380
"Correct Solution: ``` class SegTree: X_unit = 1 << 30 X_f = min def __init__(self, N): self.N = N self.X = [self.X_unit] * (N + N) def build(self, seq): for i, x in enumerate(seq, self.N): self.X[i] = x for i in range(self.N - 1, 0, -1): self.X[i] = self.X_f(self.X[i << 1], self.X[i << 1 | 1]) def set_val(self, i, x): i += self.N self.X[i] = x while i > 1: i >>= 1 self.X[i] = self.X_f(self.X[i << 1], self.X[i << 1 | 1]) def fold(self, L, R): L += self.N R += self.N vL = self.X_unit vR = self.X_unit while L < R: if L & 1: vL = self.X_f(vL, self.X[L]) L += 1 if R & 1: R -= 1 vR = self.X_f(self.X[R], vR) L >>= 1 R >>= 1 return self.X_f(vL, vR) N, Q=map(int,input().split()) S1=SegTree(N) S2=SegTree(N) S1.build([N]*N) S2.build([N]*N) ans=(N-2)**2 for i in range(Q): j, x=map(int,input().split()) if j==1: l=S2.fold(x-1,N) ans-=l-2 S1.set_val(l-1,min(x,S1.X[l-1+N])) if j==2: l=S1.fold(x-1,N) ans-=l-2 S2.set_val(l-1,min(x,S2.X[l-1+N])) print(ans) ```
output
1
104,190
23
208,381
Provide a correct Python 3 solution for this coding contest problem. There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left. Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it. Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it. Q queries are given. We ask you to process them in order. There are two kinds of queries. Their input format and description are as follows: * `1 x`: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone. * `2 x`: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone. How many black stones are there on the grid after processing all Q queries? Constraints * 3 \leq N \leq 2\times 10^5 * 0 \leq Q \leq \min(2N-4,2\times 10^5) * 2 \leq x \leq N-1 * Queries are pairwise distinct. Input Input is given from Standard Input in the following format: N Q Query_1 \vdots Query_Q Output Print how many black stones there are on the grid after processing all Q queries. Examples Input 5 5 1 3 2 3 1 4 2 2 1 2 Output 1 Input 200000 0 Output 39999200004 Input 176527 15 1 81279 2 22308 2 133061 1 80744 2 44603 1 170938 2 139754 2 15220 1 172794 1 159290 2 156968 1 56426 2 77429 1 97459 2 71282 Output 31159505795
instruction
0
104,191
23
208,382
"Correct Solution: ``` import sys def solve(): input = sys.stdin.readline N, Q = map(int, input().split()) total = (N - 2) ** 2 rb = N db = N D = [N] * (N + 1) R = [N] * (N + 1) for _ in range(Q): a, b = map(int, input().split()) if a == 1: #横向き if b < db: total -= (rb - 2) for i in range(b, db): R[i] = rb db = b else: total -= (R[b] - 2) else: #縦向き if b < rb: total -= (db - 2) for i in range(b, rb): D[i] = db rb = b else: total -= (D[b] - 2) print(total) return 0 if __name__ == "__main__": solve() ```
output
1
104,191
23
208,383
Provide a correct Python 3 solution for this coding contest problem. There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left. Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it. Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it. Q queries are given. We ask you to process them in order. There are two kinds of queries. Their input format and description are as follows: * `1 x`: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone. * `2 x`: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone. How many black stones are there on the grid after processing all Q queries? Constraints * 3 \leq N \leq 2\times 10^5 * 0 \leq Q \leq \min(2N-4,2\times 10^5) * 2 \leq x \leq N-1 * Queries are pairwise distinct. Input Input is given from Standard Input in the following format: N Q Query_1 \vdots Query_Q Output Print how many black stones there are on the grid after processing all Q queries. Examples Input 5 5 1 3 2 3 1 4 2 2 1 2 Output 1 Input 200000 0 Output 39999200004 Input 176527 15 1 81279 2 22308 2 133061 1 80744 2 44603 1 170938 2 139754 2 15220 1 172794 1 159290 2 156968 1 56426 2 77429 1 97459 2 71282 Output 31159505795
instruction
0
104,192
23
208,384
"Correct Solution: ``` # coding: utf-8 import sys # from operator import itemgetter sysread = sys.stdin.buffer.readline read = sys.stdin.buffer.read printout = sys.stdout.write sprint = sys.stdout.flush # from heapq import heappop, heappush # from collections import defaultdict sys.setrecursionlimit(10 ** 7) import math # from itertools import product, accumulate, combinations, product # import bisect # import numpy as np # from copy import deepcopy #from collections import deque # from decimal import Decimal # from numba import jit INF = 1 << 50 EPS = 1e-8 mod = 998244353 def intread(): return int(sysread()) def mapline(t=int): return map(t, sysread().split()) def mapread(t=int): return map(t, read().split()) class segtree: '''init_val : 1-indexed (init_val[0] = self.bin[1])''' def __init__(self, n, init = 0, init_val=None): self.n = n self.init = init self.k = math.ceil(math.log2(n)) self.add_val = 1 << self.k self.bins = [self.init] * (1 << (self.k + 1)) if init_val != None: self.update_set(init_val) self.caliculate() def __getitem__(self, idx): # return idx-value return self.bins[idx + self.add_val] def update_set(self, vals): for idx, i in enumerate(range(self.add_val, self.add_val * 2)): if len(vals) > idx: self.bins[i] = vals[idx] else:continue def compare(self, l, r): return min(l ,r) def caliculate(self): k = self.k while k: for i in range(1<<k, 1<<(k+1)): if not i%2: self.bins[i//2] = self.compare(self.bins[i], self.bins[i+1]) else:continue k -= 1 def update(self, idx, val, by=True): '''idx : 0-started index''' k = (1<<self.k) + idx if by: self.bins[k] += val else: self.bins[k] = val while k>1: self.bins[k // 2] = self.compare(self.bins[k // 2 * 2], self.bins[k // 2 * 2 + 1]) k = k//2 def eval(self, l, r): if l == r: return self.bins[l + self.add_val] ret = self.init l = (1 << self.k) + l r = (1 << self.k) + r #print(l, r) while True: #print(l, r) if r - l == 1: ret = self.compare(ret, self.bins[l]) ret = self.compare(ret, self.bins[r]) break elif l == r: ret = self.compare(ret, self.bins[l]) break else: done = False if l % 2: ret = self.compare(ret, self.bins[l]) l += 1 done = True if not r % 2: ret = self.compare(ret, self.bins[r]) r -= 1 done = True if not done: l = l // 2 r = r // 2 #print(ret) return ret def run(): N, Q = mapline() X = segtree(N+1, init = INF) Y = segtree(N+1, init = INF) sub = 0 for _ in range(Q): q, x = mapline() x -= 1 if q == 1: v = X.eval(x, N-2) if v == INF: sub += N-2 if Y[N-2] > x: Y.update(N-2, x,by = False) else: sub += v-1 if Y[v] > x: Y.update(v, x, by = False) else: v = Y.eval(x, N - 2) if v == INF: sub += N - 2 if X[N - 2] > x: X.update(N - 2, x, by=False) else: sub += v - 1 if X[v] > x: X.update(v, x, by=False) print((N-2) ** 2 - sub) if __name__ == "__main__": run() ```
output
1
104,192
23
208,385
Provide a correct Python 3 solution for this coding contest problem. There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left. Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it. Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it. Q queries are given. We ask you to process them in order. There are two kinds of queries. Their input format and description are as follows: * `1 x`: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone. * `2 x`: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone. How many black stones are there on the grid after processing all Q queries? Constraints * 3 \leq N \leq 2\times 10^5 * 0 \leq Q \leq \min(2N-4,2\times 10^5) * 2 \leq x \leq N-1 * Queries are pairwise distinct. Input Input is given from Standard Input in the following format: N Q Query_1 \vdots Query_Q Output Print how many black stones there are on the grid after processing all Q queries. Examples Input 5 5 1 3 2 3 1 4 2 2 1 2 Output 1 Input 200000 0 Output 39999200004 Input 176527 15 1 81279 2 22308 2 133061 1 80744 2 44603 1 170938 2 139754 2 15220 1 172794 1 159290 2 156968 1 56426 2 77429 1 97459 2 71282 Output 31159505795
instruction
0
104,193
23
208,386
"Correct Solution: ``` def f_simplified_reversi(): N, Q = [int(i) for i in input().split()] Queries = [[int(i) for i in input().split()] for j in range(Q)] a, b = [N] * N, [N] * N # editorial に準じる black_stone = (N - 2)**2 row, col = N, N for type, x in Queries: if type == 1: if x < col: for i in range(x, col): b[i] = row col = x black_stone -= b[x] - 2 else: if x < row: for i in range(x, row): a[i] = col row = x black_stone -= a[x] - 2 return black_stone print(f_simplified_reversi()) ```
output
1
104,193
23
208,387
Provide a correct Python 3 solution for this coding contest problem. There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left. Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it. Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it. Q queries are given. We ask you to process them in order. There are two kinds of queries. Their input format and description are as follows: * `1 x`: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone. * `2 x`: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone. How many black stones are there on the grid after processing all Q queries? Constraints * 3 \leq N \leq 2\times 10^5 * 0 \leq Q \leq \min(2N-4,2\times 10^5) * 2 \leq x \leq N-1 * Queries are pairwise distinct. Input Input is given from Standard Input in the following format: N Q Query_1 \vdots Query_Q Output Print how many black stones there are on the grid after processing all Q queries. Examples Input 5 5 1 3 2 3 1 4 2 2 1 2 Output 1 Input 200000 0 Output 39999200004 Input 176527 15 1 81279 2 22308 2 133061 1 80744 2 44603 1 170938 2 139754 2 15220 1 172794 1 159290 2 156968 1 56426 2 77429 1 97459 2 71282 Output 31159505795
instruction
0
104,194
23
208,388
"Correct Solution: ``` #!python3 import sys iim = lambda: map(int, sys.stdin.readline().rstrip().split()) def resolve(): N, Q = iim() it = map(int, sys.stdin.read().split()) M = N + 1if N & 1 else N NM = 1<<M.bit_length() ans = (N-2)**2 A = [[N-2]*(NM+M) for i in range(2)] def set(a, i, j, x): i += NM; j += NM while i < j: a[i] = min(a[i], x) if i&1: i += 1 a[j] = min(a[j], x) if j&1 == 0: j -= 1 i >>= 1; j >>= 1 a[i] = min(a[i], x) def get(a, i): i += NM ans = a[i] while i > 0: i >>= 1 ans = min(ans, a[i]) return ans for q, i in zip(it, it): q -= 1; i -= 2 val = get(A[q], i) ans -= val set(A[q^1], 0, val, i) print(ans) if __name__ == "__main__": resolve() ```
output
1
104,194
23
208,389
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left. Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it. Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it. Q queries are given. We ask you to process them in order. There are two kinds of queries. Their input format and description are as follows: * `1 x`: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone. * `2 x`: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone. How many black stones are there on the grid after processing all Q queries? Constraints * 3 \leq N \leq 2\times 10^5 * 0 \leq Q \leq \min(2N-4,2\times 10^5) * 2 \leq x \leq N-1 * Queries are pairwise distinct. Input Input is given from Standard Input in the following format: N Q Query_1 \vdots Query_Q Output Print how many black stones there are on the grid after processing all Q queries. Examples Input 5 5 1 3 2 3 1 4 2 2 1 2 Output 1 Input 200000 0 Output 39999200004 Input 176527 15 1 81279 2 22308 2 133061 1 80744 2 44603 1 170938 2 139754 2 15220 1 172794 1 159290 2 156968 1 56426 2 77429 1 97459 2 71282 Output 31159505795 Submitted Solution: ``` class LazyPropSegmentTree: def __init__(self, N): self.N = N self.LV = (N - 1).bit_length() self.N0 = 2 ** self.LV self.data = [N - 1] * (2 * self.N0) self.lazy = [float('inf')] * (2 * self.N0) # 遅延伝播を行うindexを生成 def gindex(self, l, r): L = (l + self.N0) >> 1; R = (r + self.N0) >> 1 lc = 0 if l & 1 else (L & -L).bit_length() rc = 0 if r & 1 else (R & -R).bit_length() for i in range(self.LV): if rc <= i: yield R if L < R and lc <= i: yield L L >>= 1; R >>= 1 # 遅延伝搬処理 def propagates(self, *ids): for i in reversed(ids): v = self.lazy[i - 1] if v == float('inf'): continue self.lazy[2 * i - 1] = min(self.lazy[2 * i - 1], v) self.lazy[2 * i] = min(self.lazy[2 * i], v) self.data[2 * i - 1] = min(self.data[2 * i - 1], v) self.data[2 * i] = min(self.data[2 * i], v) self.lazy[i - 1] = float('inf') def update(self, l, r, x): *ids, = self.gindex(l, r + 1) self.propagates(*ids) L = self.N0 + l; R = self.N0 + r + 1 while L < R: if R & 1: R -= 1 self.lazy[R - 1] = min(self.lazy[R - 1], x) self.data[R - 1] = min(self.data[R - 1], x) if L & 1: self.lazy[L - 1] = min(self.lazy[L - 1], x) self.data[L - 1] = min(self.data[L - 1], x) L += 1 L >>= 1; R >>= 1 for i in ids: self.data[i - 1] = min(self.data[2 * i - 1], self.data[2 * i]) def point_query(self, k): *ids, = self.gindex(k, k + 1) self.propagates(*ids) return self.data[k + self.N0 - 1] N, Q = map(int, input().split()) query = [tuple(map(int, input().split())) for i in range(Q)] row = LazyPropSegmentTree(N+1) column = LazyPropSegmentTree(N+1) ans = (N-2) ** 2 for t, x in query: if t == 1: n = row.point_query(x) # print(n) ans -= n - 2 column.update(2, n, x) else: n = column.point_query(x) # print(n) ans -= n - 2 row.update(2, n, x) print(ans) ```
instruction
0
104,195
23
208,390
Yes
output
1
104,195
23
208,391
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left. Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it. Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it. Q queries are given. We ask you to process them in order. There are two kinds of queries. Their input format and description are as follows: * `1 x`: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone. * `2 x`: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone. How many black stones are there on the grid after processing all Q queries? Constraints * 3 \leq N \leq 2\times 10^5 * 0 \leq Q \leq \min(2N-4,2\times 10^5) * 2 \leq x \leq N-1 * Queries are pairwise distinct. Input Input is given from Standard Input in the following format: N Q Query_1 \vdots Query_Q Output Print how many black stones there are on the grid after processing all Q queries. Examples Input 5 5 1 3 2 3 1 4 2 2 1 2 Output 1 Input 200000 0 Output 39999200004 Input 176527 15 1 81279 2 22308 2 133061 1 80744 2 44603 1 170938 2 139754 2 15220 1 172794 1 159290 2 156968 1 56426 2 77429 1 97459 2 71282 Output 31159505795 Submitted Solution: ``` from bisect import bisect_left, bisect_right n,q = map(int, input().split()) hori_cnt = [n-2]*(n+2) # 2から ql = [] for _ in range(q): c,x = map(int, input().split()) ql.append((c,x)) tate_min = n yoko_min = n yoko_kyokai = [] ans1 = 0 for c,x in ql: if c == 1: if x < tate_min: hori_cnt[yoko_min] = x-2 yoko_kyokai.append(yoko_min*(-1)) tate_min = x else: # print(c,x,'---------') if x < yoko_min: yoko_min = x # print(yoko_kyokai) ind = bisect_left(yoko_kyokai, x*(-1))-1 # print(x,ind) if ind == -1: if x < yoko_min: ans1 += (tate_min-2) else: ans1 += (n-2) # print(tate_min-2,'++') else: val = yoko_kyokai[ind] ans1 += hori_cnt[val*(-1)] # print(hori_cnt[val*(-1)],'++s') tate_cnt = [n-2]*(n+2) # 2から yoko_min = n tate_min = n tate_kyokai = [] ans2 = 0 for c,x in ql: if c == 2: if x < yoko_min: tate_cnt[tate_min] = x-2 tate_kyokai.append(tate_min*(-1)) yoko_min =x else: # print(c,x,'---------') if x < tate_min: tate_min = x ind = bisect_left(tate_kyokai, x*(-1))-1 # print(tate_kyokai,'aaa') if ind == -1: if x < tate_min: ans2 += (yoko_min-2) else: ans2 += (n-2) # print(yoko_min-2,'+++') else: val = tate_kyokai[ind] ans2 += tate_cnt[val*(-1)] # print(tate_cnt[val*(-1)],'+++s') print((n-2)*(n-2)-ans1-ans2) ```
instruction
0
104,196
23
208,392
Yes
output
1
104,196
23
208,393
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left. Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it. Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it. Q queries are given. We ask you to process them in order. There are two kinds of queries. Their input format and description are as follows: * `1 x`: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone. * `2 x`: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone. How many black stones are there on the grid after processing all Q queries? Constraints * 3 \leq N \leq 2\times 10^5 * 0 \leq Q \leq \min(2N-4,2\times 10^5) * 2 \leq x \leq N-1 * Queries are pairwise distinct. Input Input is given from Standard Input in the following format: N Q Query_1 \vdots Query_Q Output Print how many black stones there are on the grid after processing all Q queries. Examples Input 5 5 1 3 2 3 1 4 2 2 1 2 Output 1 Input 200000 0 Output 39999200004 Input 176527 15 1 81279 2 22308 2 133061 1 80744 2 44603 1 170938 2 139754 2 15220 1 172794 1 159290 2 156968 1 56426 2 77429 1 97459 2 71282 Output 31159505795 Submitted Solution: ``` #!usr/bin/env python3 from collections import defaultdict, deque from heapq import heappush, heappop from itertools import permutations, accumulate import sys import math import bisect def LI(): return [int(x) for x in sys.stdin.readline().split()] def I(): return int(sys.stdin.readline()) def LS():return [list(x) for x in sys.stdin.readline().split()] def S(): res = list(sys.stdin.readline()) if res[-1] == "\n": return res[:-1] return res def IR(n): return [I() for _ in range(n)] def LIR(n): return [LI() for _ in range(n)] def SR(n): return [S() for _ in range(n)] def LSR(n): return [LS() for _ in range(n)] sys.setrecursionlimit(1000000) mod = 1000000007 from math import log2, ceil class SegmentTree: def __init__(self, n, default): self.n = n tn = 2 ** ceil(log2(n)) self.a = [default] * (tn * 2) self.tn = tn def find(self, s, t): return self.__find(1, 0, self.tn - 1, s, t) def __find(self, c, l, r, s, t): if self.a[c] == -1: return self.a[c // 2] if s <= l and r <= t: return self.a[c] mid = (l + r) // 2 if t <= mid: return self.__find(c * 2, l, mid, s, t) elif s > mid: return self.__find(c * 2 + 1, mid + 1, r, s, t) else: return min( self.__find(c * 2, l, mid, s, mid), self.__find(c * 2 + 1, mid + 1, r, mid + 1, t)) def update(self, s, t, x): self.__update(1, 0, self.tn - 1, s, t, x) def __update(self, c, l, r, s, t, x, f=None): if f is None and self.a[c] == -1: f = self.a[c // 2] if l == s and r == t: return self.__set(c, x) mid = (l + r) // 2 if t <= mid: rv, f = self.__get_child(c, c * 2 + 1, f) u = min(self.__update(c * 2, l, mid, s, t, x, f), rv) elif s > mid: lv, f = self.__get_child(c, c * 2, f) u = min(lv, self.__update(c * 2 + 1, mid + 1, r, s, t, x, f)) else: u = min( self.__update(c * 2, l, mid, s, mid, x, f), self.__update(c * 2 + 1, mid + 1, r, mid + 1, t, x, f)) if f is not None: u = min(f, u) self.a[c] = u return u def __set(self, c, x): self.a[c] = x if c < self.tn: self.a[c * 2] = self.a[c * 2 + 1] = -1 return x def __get_child(self, c, child, f): if f is not None: return self.__set(child, f), f v = self.a[child] if v == -1: f = self.a[c] v = self.__set(child, f) return v, f def solve(): n,q = LI() ans = (n-2)*(n-2) right = SegmentTree(n+1,n) down = SegmentTree(n+1,n) for _ in range(q): t,x = LI() if t == 1: d = down.find(x,x) ans -= d-2 k = right.find(0,0) if k > x: right.update(0,d,x) else: r = right.find(x,x) ans -= r-2 k = down.find(0,0) if k > x: down.update(0,r,x) print(ans) return #Solve if __name__ == "__main__": solve() ```
instruction
0
104,197
23
208,394
Yes
output
1
104,197
23
208,395
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left. Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it. Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it. Q queries are given. We ask you to process them in order. There are two kinds of queries. Their input format and description are as follows: * `1 x`: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone. * `2 x`: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone. How many black stones are there on the grid after processing all Q queries? Constraints * 3 \leq N \leq 2\times 10^5 * 0 \leq Q \leq \min(2N-4,2\times 10^5) * 2 \leq x \leq N-1 * Queries are pairwise distinct. Input Input is given from Standard Input in the following format: N Q Query_1 \vdots Query_Q Output Print how many black stones there are on the grid after processing all Q queries. Examples Input 5 5 1 3 2 3 1 4 2 2 1 2 Output 1 Input 200000 0 Output 39999200004 Input 176527 15 1 81279 2 22308 2 133061 1 80744 2 44603 1 170938 2 139754 2 15220 1 172794 1 159290 2 156968 1 56426 2 77429 1 97459 2 71282 Output 31159505795 Submitted Solution: ``` from functools import reduce from fractions import gcd import math import bisect import itertools import sys input = sys.stdin.readline INF = float("inf") # 処理内容 def main(): N, Q = map(int, input().split()) h = N w = N a = [N]*N b = [N]*N ans = (N-2)**2 for _ in range(Q): q, x = map(int, input().split()) if q == 1: if x < w: for i in range(x, w): b[i] = h w = x ans -= b[x] - 2 elif q == 2: if x < h: for i in range(x, h): a[i] = w h = x ans -= a[x] - 2 print(ans) if __name__ == '__main__': main() ```
instruction
0
104,198
23
208,396
Yes
output
1
104,198
23
208,397
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left. Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it. Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it. Q queries are given. We ask you to process them in order. There are two kinds of queries. Their input format and description are as follows: * `1 x`: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone. * `2 x`: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone. How many black stones are there on the grid after processing all Q queries? Constraints * 3 \leq N \leq 2\times 10^5 * 0 \leq Q \leq \min(2N-4,2\times 10^5) * 2 \leq x \leq N-1 * Queries are pairwise distinct. Input Input is given from Standard Input in the following format: N Q Query_1 \vdots Query_Q Output Print how many black stones there are on the grid after processing all Q queries. Examples Input 5 5 1 3 2 3 1 4 2 2 1 2 Output 1 Input 200000 0 Output 39999200004 Input 176527 15 1 81279 2 22308 2 133061 1 80744 2 44603 1 170938 2 139754 2 15220 1 172794 1 159290 2 156968 1 56426 2 77429 1 97459 2 71282 Output 31159505795 Submitted Solution: ``` N, Q = map(int, input().split()) ans = (N-2)*(N-2) R = [N]*(N+1) W = [N]*(N+1) for i in range(Q): a, b = map(int, input().split()) if a == 1: ans -= max(0, R[b] - 2) if b <= W[1]: for j in range(1, R[b]+1): W[j] = b R[b] = 0 else: ans -= max(0, W[b] - 2) if b <= R[1]: for j in range(1, W[b] + 1): R[j] = b W[b] = 0 print(ans) ```
instruction
0
104,199
23
208,398
No
output
1
104,199
23
208,399
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left. Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it. Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it. Q queries are given. We ask you to process them in order. There are two kinds of queries. Their input format and description are as follows: * `1 x`: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone. * `2 x`: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone. How many black stones are there on the grid after processing all Q queries? Constraints * 3 \leq N \leq 2\times 10^5 * 0 \leq Q \leq \min(2N-4,2\times 10^5) * 2 \leq x \leq N-1 * Queries are pairwise distinct. Input Input is given from Standard Input in the following format: N Q Query_1 \vdots Query_Q Output Print how many black stones there are on the grid after processing all Q queries. Examples Input 5 5 1 3 2 3 1 4 2 2 1 2 Output 1 Input 200000 0 Output 39999200004 Input 176527 15 1 81279 2 22308 2 133061 1 80744 2 44603 1 170938 2 139754 2 15220 1 172794 1 159290 2 156968 1 56426 2 77429 1 97459 2 71282 Output 31159505795 Submitted Solution: ``` import bisect, collections, copy, heapq, itertools, math, string import sys def I(): return int(sys.stdin.readline().rstrip()) def MI(): return map(int, sys.stdin.readline().rstrip().split()) def LI(): return list(map(int, sys.stdin.readline().rstrip().split())) def S(): return sys.stdin.readline().rstrip() def LS(): return list(sys.stdin.readline().rstrip().split()) from collections import deque from collections import Counter import bisect from collections import defaultdict import itertools def main(): N, Q = MI() #i行の一番右をline_right[i], j列目の一番下をcolumn_under[j]とする。 line_right = [N] * N column_under = [N] * N bla = pow(N - 2, 2) x_min = N y_min = N for i in range(Q): query = LI() if query[0] == 1: w = query[1] x = column_under[w] bla -= x - 2 if w < x_min: for j in range(x): line_right[j] = w x_min = w else: y = query[1] z = line_right[y] bla -= z - 2 if y < y_min: for j in range(z): column_under[j] = y y_min = y print(bla) if __name__ == "__main__": main() ```
instruction
0
104,200
23
208,400
No
output
1
104,200
23
208,401
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left. Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it. Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it. Q queries are given. We ask you to process them in order. There are two kinds of queries. Their input format and description are as follows: * `1 x`: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone. * `2 x`: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone. How many black stones are there on the grid after processing all Q queries? Constraints * 3 \leq N \leq 2\times 10^5 * 0 \leq Q \leq \min(2N-4,2\times 10^5) * 2 \leq x \leq N-1 * Queries are pairwise distinct. Input Input is given from Standard Input in the following format: N Q Query_1 \vdots Query_Q Output Print how many black stones there are on the grid after processing all Q queries. Examples Input 5 5 1 3 2 3 1 4 2 2 1 2 Output 1 Input 200000 0 Output 39999200004 Input 176527 15 1 81279 2 22308 2 133061 1 80744 2 44603 1 170938 2 139754 2 15220 1 172794 1 159290 2 156968 1 56426 2 77429 1 97459 2 71282 Output 31159505795 Submitted Solution: ``` n, q = map(int, input().split()) q = [list(map(int, input().split())) for _i in range(q)] x_list = [n for _i in range(n+1)] y_list = [n for _i in range(n+1)] res = (n-2)**2 from bisect import bisect_right for i, j in q: if i==1: position = x_list[j] res -= position-2 for s in range(1, position): y_list[s] = min(y_list[s], j) else: position = y_list[j] res -= position-2 for s in range(1, position): x_list[s] = min(x_list[s], j) print(res) ```
instruction
0
104,201
23
208,402
No
output
1
104,201
23
208,403
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left. Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it. Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it. Q queries are given. We ask you to process them in order. There are two kinds of queries. Their input format and description are as follows: * `1 x`: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone. * `2 x`: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone. How many black stones are there on the grid after processing all Q queries? Constraints * 3 \leq N \leq 2\times 10^5 * 0 \leq Q \leq \min(2N-4,2\times 10^5) * 2 \leq x \leq N-1 * Queries are pairwise distinct. Input Input is given from Standard Input in the following format: N Q Query_1 \vdots Query_Q Output Print how many black stones there are on the grid after processing all Q queries. Examples Input 5 5 1 3 2 3 1 4 2 2 1 2 Output 1 Input 200000 0 Output 39999200004 Input 176527 15 1 81279 2 22308 2 133061 1 80744 2 44603 1 170938 2 139754 2 15220 1 172794 1 159290 2 156968 1 56426 2 77429 1 97459 2 71282 Output 31159505795 Submitted Solution: ``` class segtree(): def segfunc(x,y): return min(x,y) #####単位元###### ide_ele = -1 n=1 init_val=[0]*n #num:n以上の最小の2のべき乗 num =2**(n-1).bit_length() seg=[ide_ele]*2*num def __init__(self,INIT_VAL,SEGFUNC,IDE_ELE): self.ide_ele=IDE_ELE self.init_val=[i for i in INIT_VAL] self.segfunc=SEGFUNC self.n=len(self.init_val) self.num =2**(self.n-1).bit_length() self.seg=[self.ide_ele]*2*self.num #set_val for i in range(self.n): self.seg[i+self.num-1]=self.init_val[i] #built for i in range(self.num-2,-1,-1) : self.seg[i]=self.segfunc(self.seg[2*i+1],self.seg[2*i+2]) def update(self,k,x): k += self.num-1 self.seg[k] = x while k+1: k = (k-1)//2 self.seg[k] = self.segfunc(self.seg[k*2+1],self.seg[k*2+2]) def query(self,p,q): if q<=p: return self.ide_ele p += self.num-1 q += self.num-2 res=self.ide_ele while q-p>1: if p&1 == 0: res = self.segfunc(res,self.seg[p]) if q&1 == 1: res = self.segfunc(res,self.seg[q]) q -= 1 p = p//2 q = (q-1)//2 if p == q: res = self.segfunc(res,self.seg[p]) else: res = self.segfunc(self.segfunc(res,self.seg[p]),self.seg[q]) return res N,Q=map(int,input().split()) X=segtree([0 for i in range(N)],(lambda x,y:x+y),0) Y=segtree([0 for i in range(N)],(lambda x,y:x+y),0) ans=(N-2)*(N-2) for i in range(Q): k,x=map(int,input().split()) #print(i,ans) #print([X.query(0,i) for i in range(1,N)],[Y.query(0,i) for i in range(1,N)]) dp=[[-1 for i in range(N)] for i in range(N)] for i in range(1,N): dp[-i-1][-1]=Y.query(0,i) dp[-1][-1-i]=X.query(0,i) x=N-x+1 #for line in dp: # print(line) if k==1: a=X.query(0,x) ans-=N-2-a if Y.query(a,a+1)<x-1: Y.update(a,x-1) else: b=Y.query(0,x) ans-=N-2-b if X.query(b,b+1)<x-1: X.update(b,x-1) print(ans) ```
instruction
0
104,202
23
208,404
No
output
1
104,202
23
208,405
Provide a correct Python 3 solution for this coding contest problem. Niwango bought a piece of land that can be represented as a half-open interval [0, X). Niwango will lay out N vinyl sheets on this land. The sheets are numbered 1,2, \ldots, N, and they are distinguishable. For Sheet i, he can choose an integer j such that 0 \leq j \leq X - L_i and cover [j, j + L_i) with this sheet. Find the number of ways to cover the land with the sheets such that no point in [0, X) remains uncovered, modulo (10^9+7). We consider two ways to cover the land different if and only if there is an integer i (1 \leq i \leq N) such that the region covered by Sheet i is different. Constraints * 1 \leq N \leq 100 * 1 \leq L_i \leq X \leq 500 * All values in input are integers. Input Input is given from Standard Input in the following format: N X L_1 L_2 \ldots L_N Output Print the answer. Examples Input 3 3 1 1 2 Output 10 Input 18 477 324 31 27 227 9 21 41 29 50 34 2 362 92 11 13 17 183 119 Output 134796357
instruction
0
104,219
23
208,438
"Correct Solution: ``` N,X=map(int,input().split()) L=sorted(map(int,input().split()),reverse=True) mod=10**9+7 D=[[0]*(X+1) for i in range(N//2+2)] D[1][L[0]]=1 for l in L[1:]: ND=[[0]*(X+1) for i in range(N//2+1)] for c in range(1,N//2+1): for s in range(X+1): if D[c][s]==0: continue k=D[c][s] if s+l+c<=X and c+1<=N//2: ND[c+1][s+l]=(ND[c+1][s+l]+k*(c+1))%mod ND[c][s]=(ND[c][s]+k*(s-c*(l-1)))%mod for i in range(1,min(X-s-c+2,l+1)): ND[c][s+i]=(ND[c][s+i]+k*2*c)%mod if c==1: continue for i in range(1,min(X-s-c+3,l+1)): ND[c-1][s+i]=(ND[c-1][s+i]+k*(c-1)*(l-i+1))%mod D=ND print(D[1][X]) ```
output
1
104,219
23
208,439
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Niwango bought a piece of land that can be represented as a half-open interval [0, X). Niwango will lay out N vinyl sheets on this land. The sheets are numbered 1,2, \ldots, N, and they are distinguishable. For Sheet i, he can choose an integer j such that 0 \leq j \leq X - L_i and cover [j, j + L_i) with this sheet. Find the number of ways to cover the land with the sheets such that no point in [0, X) remains uncovered, modulo (10^9+7). We consider two ways to cover the land different if and only if there is an integer i (1 \leq i \leq N) such that the region covered by Sheet i is different. Constraints * 1 \leq N \leq 100 * 1 \leq L_i \leq X \leq 500 * All values in input are integers. Input Input is given from Standard Input in the following format: N X L_1 L_2 \ldots L_N Output Print the answer. Examples Input 3 3 1 1 2 Output 10 Input 18 477 324 31 27 227 9 21 41 29 50 34 2 362 92 11 13 17 183 119 Output 134796357 Submitted Solution: ``` N,X=map(int,input().split()) L=sorted(map(int,input().split()),reverse=True) mod=10**9+7 D=[[0]*(X+1) for i in range(N//2+1)] D[1][L[0]]=1 for l in L[1:]: ND=[[0]*(X+1) for i in range(N//2+1)] for c in range(1,N//2+1): for s in range(X+1): if D[c][s]==0: continue k=D[c][s] if s+l+c<=X and c+1<=N//2: ND[c+1][s+l]=(ND[c+1][s+l]+k*(c+1))%mod ND[c][s]=(ND[c][s]+k*(s-c*(l-1)))%mod for i in range(1,min(X-s-c+2,l+1)): ND[c][s+i]=(ND[c][s+i]+k*2*c)%mod if c==1: continue for i in range(1,min(X-s-c+3,l+1)): ND[c-1][s+i]=(ND[c-1][s+i]+k*(c-1)*(l-i+1))%mod D=ND print(D[1][X]) ```
instruction
0
104,220
23
208,440
No
output
1
104,220
23
208,441
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Niwango bought a piece of land that can be represented as a half-open interval [0, X). Niwango will lay out N vinyl sheets on this land. The sheets are numbered 1,2, \ldots, N, and they are distinguishable. For Sheet i, he can choose an integer j such that 0 \leq j \leq X - L_i and cover [j, j + L_i) with this sheet. Find the number of ways to cover the land with the sheets such that no point in [0, X) remains uncovered, modulo (10^9+7). We consider two ways to cover the land different if and only if there is an integer i (1 \leq i \leq N) such that the region covered by Sheet i is different. Constraints * 1 \leq N \leq 100 * 1 \leq L_i \leq X \leq 500 * All values in input are integers. Input Input is given from Standard Input in the following format: N X L_1 L_2 \ldots L_N Output Print the answer. Examples Input 3 3 1 1 2 Output 10 Input 18 477 324 31 27 227 9 21 41 29 50 34 2 362 92 11 13 17 183 119 Output 134796357 Submitted Solution: ``` N,X=map(int,input().split()) L=sorted(map(int,input().split()),reverse=True) mod=10**9+7 from collections import defaultdict D=defaultdict(int) D[1,L[0]]=1 for l in L[1:]: ND=defaultdict(int) for c,s in D: k=D[c,s] if s+l+c-1<=X: ND[c+1,s+l]=(ND[c+1,s+l]+k*(c+1))%mod ND[c,s]=(ND[c,s]+k*(s-c*(l-1)))%mod for i in range(1,min(X-s-c+2,l+1)): ND[c,s+i]=(ND[c,s+i]+k*2*c)%mod for i in range(1,min(X-s-c+3,l+1)): ND[c-1,s+i]=(ND[c-1,s+i]+k*(c-1)*(l-i+1))%mod D=ND print(D[1,X]) ```
instruction
0
104,221
23
208,442
No
output
1
104,221
23
208,443
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Niwango bought a piece of land that can be represented as a half-open interval [0, X). Niwango will lay out N vinyl sheets on this land. The sheets are numbered 1,2, \ldots, N, and they are distinguishable. For Sheet i, he can choose an integer j such that 0 \leq j \leq X - L_i and cover [j, j + L_i) with this sheet. Find the number of ways to cover the land with the sheets such that no point in [0, X) remains uncovered, modulo (10^9+7). We consider two ways to cover the land different if and only if there is an integer i (1 \leq i \leq N) such that the region covered by Sheet i is different. Constraints * 1 \leq N \leq 100 * 1 \leq L_i \leq X \leq 500 * All values in input are integers. Input Input is given from Standard Input in the following format: N X L_1 L_2 \ldots L_N Output Print the answer. Examples Input 3 3 1 1 2 Output 10 Input 18 477 324 31 27 227 9 21 41 29 50 34 2 362 92 11 13 17 183 119 Output 134796357 Submitted Solution: ``` N,X=map(int,input().split()) L=sorted(map(int,input().split()),reverse=True) mod=10**9+7 from collections import defaultdict D=dict() D[1,L[0]]=1 for l in L[1:]: ND=defaultdict(int) for c,s in D: k=D[c,s] if s+l<=X: ND[c+1,s+l]=(ND[c+1,s+l]+k*(c+1))%mod ND[c,s]=(ND[c,s]+k*(s-c*(l-1)))%mod for i in range(1,min(X-s+1,l+1)): ND[c,s+i]=(ND[c,s+i]+k*2*c)%mod for i in range(1,min(X-s+1,l+1)): ND[c-1,s+i]=(ND[c-1,s+i]+k*(c-1)*(l-i+1))%mod D=ND print(D[1,X]) ```
instruction
0
104,222
23
208,444
No
output
1
104,222
23
208,445
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Niwango bought a piece of land that can be represented as a half-open interval [0, X). Niwango will lay out N vinyl sheets on this land. The sheets are numbered 1,2, \ldots, N, and they are distinguishable. For Sheet i, he can choose an integer j such that 0 \leq j \leq X - L_i and cover [j, j + L_i) with this sheet. Find the number of ways to cover the land with the sheets such that no point in [0, X) remains uncovered, modulo (10^9+7). We consider two ways to cover the land different if and only if there is an integer i (1 \leq i \leq N) such that the region covered by Sheet i is different. Constraints * 1 \leq N \leq 100 * 1 \leq L_i \leq X \leq 500 * All values in input are integers. Input Input is given from Standard Input in the following format: N X L_1 L_2 \ldots L_N Output Print the answer. Examples Input 3 3 1 1 2 Output 10 Input 18 477 324 31 27 227 9 21 41 29 50 34 2 362 92 11 13 17 183 119 Output 134796357 Submitted Solution: ``` N,X=map(int,input().split()) L=sorted(map(int,input().split()),reverse=True) mod=10**9+7 D=[[0]*(X+1) for i in range(N//2+2)] D[1][L[0]]=1 for l in L[1:]: ND=[[0]*(X+1) for i in range(N//2+1)] for c in range(1,N//2+1): for s in range(X+1): if D[c][s]==0: continue k=D[c][s] if s+l+c<=X and c+1<=N//2: ND[c+1][s+l]=(ND[c+1][s+l]+k*(c+1))%mod ND[c][s]=(ND[c][s]+k*(s-c*(l-1)))%mod for i in range(1,min(X-s-c+2,l+1)): ND[c][s+i]=(ND[c][s+i]+k*2*c)%mod if c==1: continue for i in range(1,min(X-s-c+3,l+1)): ND[c-1][s+i]=(ND[c-1][s+i]+k*(c-1)*(l-i+1))%mod D=ND print(D[1][X]) ```
instruction
0
104,223
23
208,446
No
output
1
104,223
23
208,447
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Lengths are measures in Baden in inches and feet. To a length from centimeters it is enough to know that an inch equals three centimeters in Baden and one foot contains 12 inches. You are given a length equal to n centimeters. Your task is to convert it to feet and inches so that the number of feet was maximum. The result should be an integer rounded to the closest value containing an integral number of inches. Note that when you round up, 1 cm rounds up to 0 inches and 2 cm round up to 1 inch. Input The only line contains an integer n (1 ≤ n ≤ 10000). Output Print two non-negative space-separated integers a and b, where a is the numbers of feet and b is the number of inches. Examples Input 42 Output 1 2 Input 5 Output 0 2 Submitted Solution: ``` n = int(input())/3 ft = int(n//12) inch = round(n%12) if inch == 12: inch = 0 ft += 1 print(ft, inch) ```
instruction
0
104,534
23
209,068
Yes
output
1
104,534
23
209,069
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Lengths are measures in Baden in inches and feet. To a length from centimeters it is enough to know that an inch equals three centimeters in Baden and one foot contains 12 inches. You are given a length equal to n centimeters. Your task is to convert it to feet and inches so that the number of feet was maximum. The result should be an integer rounded to the closest value containing an integral number of inches. Note that when you round up, 1 cm rounds up to 0 inches and 2 cm round up to 1 inch. Input The only line contains an integer n (1 ≤ n ≤ 10000). Output Print two non-negative space-separated integers a and b, where a is the numbers of feet and b is the number of inches. Examples Input 42 Output 1 2 Input 5 Output 0 2 Submitted Solution: ``` cm = int(input()) cm += 1 dm = divmod(cm, 36) print(dm[0], end=' ') cm = dm[1] print(round(cm / 3)) ```
instruction
0
104,535
23
209,070
No
output
1
104,535
23
209,071
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. One day, as Sherlock Holmes was tracking down one very important criminal, he found a wonderful painting on the wall. This wall could be represented as a plane. The painting had several concentric circles that divided the wall into several parts. Some parts were painted red and all the other were painted blue. Besides, any two neighboring parts were painted different colors, that is, the red and the blue color were alternating, i. e. followed one after the other. The outer area of the wall (the area that lied outside all circles) was painted blue. Help Sherlock Holmes determine the total area of red parts of the wall. Let us remind you that two circles are called concentric if their centers coincide. Several circles are called concentric if any two of them are concentric. Input The first line contains the single integer n (1 ≤ n ≤ 100). The second line contains n space-separated integers ri (1 ≤ ri ≤ 1000) — the circles' radii. It is guaranteed that all circles are different. Output Print the single real number — total area of the part of the wall that is painted red. The answer is accepted if absolute or relative error doesn't exceed 10 - 4. Examples Input 1 1 Output 3.1415926536 Input 3 1 4 2 Output 40.8407044967 Note In the first sample the picture is just one circle of radius 1. Inner part of the circle is painted red. The area of the red part equals π × 12 = π. In the second sample there are three circles of radii 1, 4 and 2. Outside part of the second circle is painted blue. Part between the second and the third circles is painted red. Part between the first and the third is painted blue. And, finally, the inner part of the first circle is painted red. Overall there are two red parts: the ring between the second and the third circles and the inner part of the first circle. Total area of the red parts is equal (π × 42 - π × 22) + π × 12 = π × 12 + π = 13π Submitted Solution: ``` import sys from functools import lru_cache, cmp_to_key from heapq import merge, heapify, heappop, heappush from math import * from collections import defaultdict as dd, deque, Counter as C from itertools import combinations as comb, permutations as perm from bisect import bisect_left as bl, bisect_right as br, bisect from time import perf_counter from fractions import Fraction import copy import time # import numpy as np starttime = time.time() # import numpy as np mod = int(pow(10, 9) + 7) mod2 = 998244353 def data(): return sys.stdin.readline().strip() def out(*var, end="\n"): sys.stdout.write(' '.join(map(str, var))+end) def L(): return list(sp()) def sl(): return list(ssp()) def sp(): return map(int, data().split()) def ssp(): return map(str, data().split()) def l1d(n, val=0): return [val for i in range(n)] def l2d(n, m, val=0): return [l1d(n, val) for j in range(m)] try: # sys.setrecursionlimit(int(pow(10,6))) sys.stdin = open("input.txt", "r") # sys.stdout = open("../output.txt", "w") except: pass n=L()[0]+1 A=[0]+sorted(L()) # for i in range(1,n): # A[i]+=A[i-1] ans=0 for i in range(n-1,0,-2): ans+=(pi*(A[i]**2-A[i-1]**2)) print(ans) endtime = time.time() # print(f"Runtime of the program is {endtime - starttime}") ```
instruction
0
104,709
23
209,418
Yes
output
1
104,709
23
209,419