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Provide tags and a correct Python 3 solution for this coding contest problem. For long time scientists study the behavior of sharks. Sharks, as many other species, alternate short movements in a certain location and long movements between locations. Max is a young biologist. For n days he watched a specific shark, and now he knows the distance the shark traveled in each of the days. All the distances are distinct. Max wants to know now how many locations the shark visited. He assumed there is such an integer k that if the shark in some day traveled the distance strictly less than k, then it didn't change the location; otherwise, if in one day the shark traveled the distance greater than or equal to k; then it was changing a location in that day. Note that it is possible that the shark changed a location for several consecutive days, in each of them the shark traveled the distance at least k. The shark never returned to the same location after it has moved from it. Thus, in the sequence of n days we can find consecutive nonempty segments when the shark traveled the distance less than k in each of the days: each such segment corresponds to one location. Max wants to choose such k that the lengths of all such segments are equal. Find such integer k, that the number of locations is as large as possible. If there are several such k, print the smallest one. Input The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of days. The second line contains n distinct positive integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the distance traveled in each of the day. Output Print a single integer k, such that 1. the shark was in each location the same number of days, 2. the number of locations is maximum possible satisfying the first condition, 3. k is smallest possible satisfying the first and second conditions. Examples Input 8 1 2 7 3 4 8 5 6 Output 7 Input 6 25 1 2 3 14 36 Output 2 Note In the first example the shark travels inside a location on days 1 and 2 (first location), then on 4-th and 5-th days (second location), then on 7-th and 8-th days (third location). There are three locations in total. In the second example the shark only moves inside a location on the 2-nd day, so there is only one location.
instruction
0
40,169
3
80,338
Tags: brute force, data structures, dsu, trees Correct Solution: ``` BigNum = 10 ** 10 n = int(input()) aa = [BigNum] + list(map(int, input().split(' '))) + [BigNum] appear = sorted([(v, i) for i, v in enumerate(aa)]) ans = -1 maxLocations = 0 intervals = [(i, i) for i in range(len(aa))] lengths = {} def incCount(val): global lengths lengths[val] = lengths.get(val, 0) + 1 def decCount(val): global lengths if lengths[val] == 1: del lengths[val] else: lengths[val] -= 1 def mergeIntervals(a, b): return (min(a[0], b[0]), max(a[1], b[1])) for v, i in appear: if v == BigNum: continue inter = intervals[i] if aa[i - 1] < aa[i]: li = intervals[i - 1] decCount(li[1] - li[0] + 1) inter = mergeIntervals(li, inter) if aa[i] > aa[i + 1]: ri = intervals[i + 1] decCount(ri[1] - ri[0] + 1) inter = mergeIntervals(ri, inter) intervals[inter[0]] = inter intervals[inter[1]] = inter incCount(inter[1] - inter[0] + 1) if len(lengths) == 1: count = list(lengths.values())[0] if count > maxLocations: maxLocations = count ans = v + 1 #print(v + 1, count) print(ans) ```
output
1
40,169
3
80,339
Provide tags and a correct Python 3 solution for this coding contest problem. For long time scientists study the behavior of sharks. Sharks, as many other species, alternate short movements in a certain location and long movements between locations. Max is a young biologist. For n days he watched a specific shark, and now he knows the distance the shark traveled in each of the days. All the distances are distinct. Max wants to know now how many locations the shark visited. He assumed there is such an integer k that if the shark in some day traveled the distance strictly less than k, then it didn't change the location; otherwise, if in one day the shark traveled the distance greater than or equal to k; then it was changing a location in that day. Note that it is possible that the shark changed a location for several consecutive days, in each of them the shark traveled the distance at least k. The shark never returned to the same location after it has moved from it. Thus, in the sequence of n days we can find consecutive nonempty segments when the shark traveled the distance less than k in each of the days: each such segment corresponds to one location. Max wants to choose such k that the lengths of all such segments are equal. Find such integer k, that the number of locations is as large as possible. If there are several such k, print the smallest one. Input The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of days. The second line contains n distinct positive integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the distance traveled in each of the day. Output Print a single integer k, such that 1. the shark was in each location the same number of days, 2. the number of locations is maximum possible satisfying the first condition, 3. k is smallest possible satisfying the first and second conditions. Examples Input 8 1 2 7 3 4 8 5 6 Output 7 Input 6 25 1 2 3 14 36 Output 2 Note In the first example the shark travels inside a location on days 1 and 2 (first location), then on 4-th and 5-th days (second location), then on 7-th and 8-th days (third location). There are three locations in total. In the second example the shark only moves inside a location on the 2-nd day, so there is only one location.
instruction
0
40,170
3
80,340
Tags: brute force, data structures, dsu, trees Correct Solution: ``` import bisect; def getIntList(): return list(map(int, input().split())); def getTransIntList(n): first=getIntList(); m=len(first); result=[[0]*n for _ in range(m)]; for i in range(m): result[i][0]=first[i]; for j in range(1, n): curr=getIntList(); for i in range(m): result[i][j]=curr[i]; return result; n=int(input()); a=getIntList(); anums=[(a[i], i) for i in range(n)]; anums.sort(); location=0; length=0; k=1; pieces=[]; def upgrade(x): curr=(x, x+1) i=bisect.bisect(pieces, curr); joinLeft=False; joinRight=False; if i>0 and pieces[i-1][1]==x: joinLeft=True; if i<len(pieces) and pieces[i][0]==x+1: joinRight=True; if joinLeft: if joinRight: pieces[i-1]=(pieces[i-1][0], pieces[i][1]) pieces.pop(i); else: pieces[i-1]=(pieces[i-1][0], x+1); return pieces[i-1][1]-pieces[i-1][0]; else: if joinRight: pieces[i]=(x, pieces[i][1]) else: pieces.insert(i, curr); return pieces[i][1]-pieces[i][0]; currLength=0; currSum=0; for x in anums: currSum+=1; val, num=x; l=upgrade(num); #print(pieces); currLength=max(currLength, l); #print(currLength,"*",len(pieces),"==",currSum) if currLength*len(pieces)==currSum: currK=val+1; currLocation=len(pieces); if currLocation>location: location=currLocation; k=currK; if (location+2)*currLength-1>n: break; print(k); ```
output
1
40,170
3
80,341
Provide tags and a correct Python 3 solution for this coding contest problem. For long time scientists study the behavior of sharks. Sharks, as many other species, alternate short movements in a certain location and long movements between locations. Max is a young biologist. For n days he watched a specific shark, and now he knows the distance the shark traveled in each of the days. All the distances are distinct. Max wants to know now how many locations the shark visited. He assumed there is such an integer k that if the shark in some day traveled the distance strictly less than k, then it didn't change the location; otherwise, if in one day the shark traveled the distance greater than or equal to k; then it was changing a location in that day. Note that it is possible that the shark changed a location for several consecutive days, in each of them the shark traveled the distance at least k. The shark never returned to the same location after it has moved from it. Thus, in the sequence of n days we can find consecutive nonempty segments when the shark traveled the distance less than k in each of the days: each such segment corresponds to one location. Max wants to choose such k that the lengths of all such segments are equal. Find such integer k, that the number of locations is as large as possible. If there are several such k, print the smallest one. Input The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of days. The second line contains n distinct positive integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the distance traveled in each of the day. Output Print a single integer k, such that 1. the shark was in each location the same number of days, 2. the number of locations is maximum possible satisfying the first condition, 3. k is smallest possible satisfying the first and second conditions. Examples Input 8 1 2 7 3 4 8 5 6 Output 7 Input 6 25 1 2 3 14 36 Output 2 Note In the first example the shark travels inside a location on days 1 and 2 (first location), then on 4-th and 5-th days (second location), then on 7-th and 8-th days (third location). There are three locations in total. In the second example the shark only moves inside a location on the 2-nd day, so there is only one location.
instruction
0
40,171
3
80,342
Tags: brute force, data structures, dsu, trees Correct Solution: ``` import os import sys from io import BytesIO, IOBase from types import GeneratorType from collections import defaultdict BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") def find(u): if parent[u]==-1: return -1 if parent[u] == u: return u parent[u] = find(parent[u]) return parent[u] def union(a, b): u = parent[a] v = parent[b] if size[u] > size[v]: parent[v] = u size[u] += size[v] else: parent[u] = v size[v] += size[u] n=int(input()) parent=[-1 for i in range(n+2)] size = [1 for i in range(n + 2)] b=list(map(int,input().split())) c=[] for i in range(n): c.append([b[i],i+1]) c.sort() ans=0 le=0 d=defaultdict(lambda:0) cnt=0 for j in range(n): val,ind=c[j] lpar=find(ind-1) rpar=find(ind+1) parent[ind]=ind if lpar!=-1: sz1=size[find(lpar)] d[sz1]+=-1 if d[sz1]==0: cnt+=-1 union(ind-1,ind) if rpar!=-1: sz2=size[find(rpar)] d[sz2]+=-1 if d[sz2]==0: cnt+=-1 union(ind,ind+1) sz=size[find(ind)] d[sz]+=1 if d[sz]==1: cnt+=1 if cnt == 1: if d[sz] > le: le = d[sz] ans = val+1 print(ans) ```
output
1
40,171
3
80,343
Provide tags and a correct Python 3 solution for this coding contest problem. For long time scientists study the behavior of sharks. Sharks, as many other species, alternate short movements in a certain location and long movements between locations. Max is a young biologist. For n days he watched a specific shark, and now he knows the distance the shark traveled in each of the days. All the distances are distinct. Max wants to know now how many locations the shark visited. He assumed there is such an integer k that if the shark in some day traveled the distance strictly less than k, then it didn't change the location; otherwise, if in one day the shark traveled the distance greater than or equal to k; then it was changing a location in that day. Note that it is possible that the shark changed a location for several consecutive days, in each of them the shark traveled the distance at least k. The shark never returned to the same location after it has moved from it. Thus, in the sequence of n days we can find consecutive nonempty segments when the shark traveled the distance less than k in each of the days: each such segment corresponds to one location. Max wants to choose such k that the lengths of all such segments are equal. Find such integer k, that the number of locations is as large as possible. If there are several such k, print the smallest one. Input The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of days. The second line contains n distinct positive integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the distance traveled in each of the day. Output Print a single integer k, such that 1. the shark was in each location the same number of days, 2. the number of locations is maximum possible satisfying the first condition, 3. k is smallest possible satisfying the first and second conditions. Examples Input 8 1 2 7 3 4 8 5 6 Output 7 Input 6 25 1 2 3 14 36 Output 2 Note In the first example the shark travels inside a location on days 1 and 2 (first location), then on 4-th and 5-th days (second location), then on 7-th and 8-th days (third location). There are three locations in total. In the second example the shark only moves inside a location on the 2-nd day, so there is only one location.
instruction
0
40,172
3
80,344
Tags: brute force, data structures, dsu, trees Correct Solution: ``` class UnionFind(): def __init__(self, n): self.n = n self.parents = [-1] * (n) def find(self, x): if self.parents[x] < 0: return x else: self.parents[x] = self.find(self.parents[x]) return self.parents[x] def union(self, x, y): x = self.find(x) y = self.find(y) if x == y: return if self.parents[x] > self.parents[y]: x, y = y, x self.parents[x] += self.parents[y] self.parents[y] = x def size(self, x): return -self.parents[self.find(x)] def same(self, x, y): return self.find(x) == self.find(y) n = int(input()) a = list(map(int, input().split())) b = [(a[i], i) for i in range(n)] b.sort(key=lambda x: x[0]) group_cnt = [0]*(n + 1) ans = 0 uf = UnionFind(n) segment_count = 0 for add_count,(value, index) in enumerate(b): group_cnt[1] += 1 if index > 0: if a[index - 1] < value: if uf.same(index - 1, index) == False: size_l, size_r = uf.size(index - 1), uf.size(index) group_cnt[size_l] -= 1 group_cnt[size_r] -= 1 uf.union(index-1, index) size_new = uf.size(index) group_cnt[size_new] += 1 if index < n - 1: if a[index + 1] < value: if uf.same(index, index + 1) == False: size_l, size_r = uf.size(index), uf.size(index + 1) group_cnt[size_l] -= 1 group_cnt[size_r] -= 1 uf.union(index, index + 1) size_new = uf.size(index) group_cnt[size_new] += 1 size_new = uf.size(index) #print(group_cnt[size_new],size_new,add_count + 1,value) if group_cnt[size_new]*size_new == add_count + 1: if segment_count < group_cnt[size_new]: ans = value + 1 segment_count = group_cnt[size_new] print(ans) ```
output
1
40,172
3
80,345
Provide tags and a correct Python 3 solution for this coding contest problem. For long time scientists study the behavior of sharks. Sharks, as many other species, alternate short movements in a certain location and long movements between locations. Max is a young biologist. For n days he watched a specific shark, and now he knows the distance the shark traveled in each of the days. All the distances are distinct. Max wants to know now how many locations the shark visited. He assumed there is such an integer k that if the shark in some day traveled the distance strictly less than k, then it didn't change the location; otherwise, if in one day the shark traveled the distance greater than or equal to k; then it was changing a location in that day. Note that it is possible that the shark changed a location for several consecutive days, in each of them the shark traveled the distance at least k. The shark never returned to the same location after it has moved from it. Thus, in the sequence of n days we can find consecutive nonempty segments when the shark traveled the distance less than k in each of the days: each such segment corresponds to one location. Max wants to choose such k that the lengths of all such segments are equal. Find such integer k, that the number of locations is as large as possible. If there are several such k, print the smallest one. Input The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of days. The second line contains n distinct positive integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the distance traveled in each of the day. Output Print a single integer k, such that 1. the shark was in each location the same number of days, 2. the number of locations is maximum possible satisfying the first condition, 3. k is smallest possible satisfying the first and second conditions. Examples Input 8 1 2 7 3 4 8 5 6 Output 7 Input 6 25 1 2 3 14 36 Output 2 Note In the first example the shark travels inside a location on days 1 and 2 (first location), then on 4-th and 5-th days (second location), then on 7-th and 8-th days (third location). There are three locations in total. In the second example the shark only moves inside a location on the 2-nd day, so there is only one location.
instruction
0
40,173
3
80,346
Tags: brute force, data structures, dsu, trees Correct Solution: ``` def main(): n = int(input()) ori_a = [int(x) for x in input().split()] pos = {ori_a[i]: i for i in range(len(ori_a))} seg = [dict(left=None, right=None) for i in range(len(ori_a))] a = sorted(ori_a) seg_size = 0 seg_num = 0 fi_k = a[0] fi_seg_num = 0 for n_items, item in enumerate(a, 1): i = pos[item] seg[i]["left"], seg[i]["right"] = i, i seg_num += 1 size = seg[i]["right"] - seg[i]["left"] + 1 if size > seg_size: seg_size = size li = pos[item] - 1 if 0 <= li: if seg[li]["right"] == i - 1: seg[i]["left"] = seg[li]["left"] seg[li]["right"] = seg[i]["left"] seg_num -= 1 size = seg[i]["right"] - seg[i]["left"] + 1 if size > seg_size: seg_size = size ri = pos[item] + 1 if ri < n: if seg[ri]["left"] == i + 1: seg[i]["right"] = seg[ri]["right"] seg[ri]["left"] = seg[i]["left"] seg_num -= 1 size = seg[i]["right"] - seg[i]["left"] + 1 if size > seg_size: seg_size = size if seg_size * seg_num == n_items and seg_num > fi_seg_num: fi_seg_num = seg_num fi_k = item + 1 print(fi_k) if __name__ == '__main__': main() ```
output
1
40,173
3
80,347
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. For long time scientists study the behavior of sharks. Sharks, as many other species, alternate short movements in a certain location and long movements between locations. Max is a young biologist. For n days he watched a specific shark, and now he knows the distance the shark traveled in each of the days. All the distances are distinct. Max wants to know now how many locations the shark visited. He assumed there is such an integer k that if the shark in some day traveled the distance strictly less than k, then it didn't change the location; otherwise, if in one day the shark traveled the distance greater than or equal to k; then it was changing a location in that day. Note that it is possible that the shark changed a location for several consecutive days, in each of them the shark traveled the distance at least k. The shark never returned to the same location after it has moved from it. Thus, in the sequence of n days we can find consecutive nonempty segments when the shark traveled the distance less than k in each of the days: each such segment corresponds to one location. Max wants to choose such k that the lengths of all such segments are equal. Find such integer k, that the number of locations is as large as possible. If there are several such k, print the smallest one. Input The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of days. The second line contains n distinct positive integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the distance traveled in each of the day. Output Print a single integer k, such that 1. the shark was in each location the same number of days, 2. the number of locations is maximum possible satisfying the first condition, 3. k is smallest possible satisfying the first and second conditions. Examples Input 8 1 2 7 3 4 8 5 6 Output 7 Input 6 25 1 2 3 14 36 Output 2 Note In the first example the shark travels inside a location on days 1 and 2 (first location), then on 4-th and 5-th days (second location), then on 7-th and 8-th days (third location). There are three locations in total. In the second example the shark only moves inside a location on the 2-nd day, so there is only one location. Submitted Solution: ``` import os import sys from io import BytesIO, IOBase from types import GeneratorType from collections import defaultdict BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") def find(u): if parent[u]==-1: return -1 if parent[u] == u: return u parent[u] = find(parent[u]) return parent[u] def union(a, b): u = parent[a] v = parent[b] if size[u] > size[v]: parent[v] = u size[u] += size[v] else: parent[u] = v size[v] += size[u] n=int(input()) parent=[-1 for i in range(n+2)] size = [1 for i in range(n + 2)] b=list(map(int,input().split())) c=[] for i in range(n): c.append([b[i],i+1]) c.sort() ans=0 le=0 curr=0 d=defaultdict(lambda:0) cnt=0 for j in range(n): val,ind=c[j] if cnt==1: if d[curr]>le: le=d[curr] ans=val lpar=find(ind-1) rpar=find(ind+1) parent[ind]=ind if lpar!=-1: sz1=size[find(lpar)] d[sz1]+=-1 if d[sz1]==0: cnt+=-1 union(ind-1,ind) if rpar!=-1: sz2=size[find(rpar)] d[sz2]+=-1 if d[sz2]==0: cnt+=-1 union(ind,ind+1) sz=size[find(ind)] d[sz]+=1 if d[sz]==1: cnt+=1 if cnt==1: curr=sz print(ans) ```
instruction
0
40,174
3
80,348
No
output
1
40,174
3
80,349
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. For long time scientists study the behavior of sharks. Sharks, as many other species, alternate short movements in a certain location and long movements between locations. Max is a young biologist. For n days he watched a specific shark, and now he knows the distance the shark traveled in each of the days. All the distances are distinct. Max wants to know now how many locations the shark visited. He assumed there is such an integer k that if the shark in some day traveled the distance strictly less than k, then it didn't change the location; otherwise, if in one day the shark traveled the distance greater than or equal to k; then it was changing a location in that day. Note that it is possible that the shark changed a location for several consecutive days, in each of them the shark traveled the distance at least k. The shark never returned to the same location after it has moved from it. Thus, in the sequence of n days we can find consecutive nonempty segments when the shark traveled the distance less than k in each of the days: each such segment corresponds to one location. Max wants to choose such k that the lengths of all such segments are equal. Find such integer k, that the number of locations is as large as possible. If there are several such k, print the smallest one. Input The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of days. The second line contains n distinct positive integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the distance traveled in each of the day. Output Print a single integer k, such that 1. the shark was in each location the same number of days, 2. the number of locations is maximum possible satisfying the first condition, 3. k is smallest possible satisfying the first and second conditions. Examples Input 8 1 2 7 3 4 8 5 6 Output 7 Input 6 25 1 2 3 14 36 Output 2 Note In the first example the shark travels inside a location on days 1 and 2 (first location), then on 4-th and 5-th days (second location), then on 7-th and 8-th days (third location). There are three locations in total. In the second example the shark only moves inside a location on the 2-nd day, so there is only one location. Submitted Solution: ``` import os import sys from io import BytesIO, IOBase from types import GeneratorType from collections import defaultdict BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") def find(u): if parent[u] == u: return u parent[u] = find(parent[u]) return parent[u] def union(a, b): u = parent[a] v = parent[b] if size[u] > size[v]: parent[v] = u size[u] += size[v] else: parent[u] = v size[v] += size[u] n=int(input()) parent=[-1 for i in range(n+2)] size = [1 for i in range(n + 2)] b=list(map(int,input().split())) c=[] for i in range(n): c.append([b[i],i+1]) c.sort() ans=0 le=0 curr=0 d=defaultdict(lambda:0) cnt=0 for j in range(n): val,ind=c[j] if cnt==1: if d[curr]>le: le=d[curr] ans=val lpar=find(ind-1) rpar=find(ind+1) parent[ind]=ind if lpar!=-1: sz1=size[find(lpar)] d[sz1]+=-1 if d[sz1]==0: cnt+=-1 union(ind-1,ind) if rpar!=-1: sz2=size[find(rpar)] d[sz2]+=-1 if d[sz2]==0: cnt+=-1 union(ind,ind+1) sz=size[find(ind)] d[sz]+=1 if d[sz]==1: cnt+=1 if cnt==1: curr=sz print(ans) ```
instruction
0
40,175
3
80,350
No
output
1
40,175
3
80,351
Provide a correct Python 3 solution for this coding contest problem. On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size. There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other. A point on the plane is exposed to cosmic rays if the point is not within any of the barriers. Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel. Constraints * All input values are integers. * -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9 * (x_s, y_s) ≠ (x_t, y_t) * 1≤N≤1,000 * -10^9 ≤ x_i, y_i ≤ 10^9 * 1 ≤ r_i ≤ 10^9 Input The input is given from Standard Input in the following format: x_s y_s x_t y_t N x_1 y_1 r_1 x_2 y_2 r_2 : x_N y_N r_N Output Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}. Examples Input -2 -2 2 2 1 0 0 1 Output 3.6568542495 Input -2 0 2 0 2 -1 0 2 1 0 2 Output 0.0000000000 Input 4 -2 -2 4 3 0 0 2 4 0 1 0 4 1 Output 4.0000000000
instruction
0
40,310
3
80,620
"Correct Solution: ``` import math x1, y1, x2, y2 = [int(i) for i in input().split()] n = int(input()) xy = [[x1, y1, 0]] for _ in range(n): xy.append([int(i) for i in input().split()]) xy.append([x2, y2, 0]) def dif(x, y): return max(0, math.sqrt((x[0] - y[0]) ** 2 + (x[1] - y[1]) ** 2) - x[2] - y[2]) q = set([i for i in range(n + 2)]) mi = [10 ** 16] * (n + 2) mi[0] = 0 while q: u = -1 mm = 10**16 for i in q: if mm > mi[i]: mm = mi[i] u = i q.remove(u) for i in q: mi[i] = min(mi[i], mi[u] + dif(xy[i], xy[u])) print(mi[-1]) ```
output
1
40,310
3
80,621
Provide a correct Python 3 solution for this coding contest problem. On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size. There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other. A point on the plane is exposed to cosmic rays if the point is not within any of the barriers. Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel. Constraints * All input values are integers. * -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9 * (x_s, y_s) ≠ (x_t, y_t) * 1≤N≤1,000 * -10^9 ≤ x_i, y_i ≤ 10^9 * 1 ≤ r_i ≤ 10^9 Input The input is given from Standard Input in the following format: x_s y_s x_t y_t N x_1 y_1 r_1 x_2 y_2 r_2 : x_N y_N r_N Output Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}. Examples Input -2 -2 2 2 1 0 0 1 Output 3.6568542495 Input -2 0 2 0 2 -1 0 2 1 0 2 Output 0.0000000000 Input 4 -2 -2 4 3 0 0 2 4 0 1 0 4 1 Output 4.0000000000
instruction
0
40,311
3
80,622
"Correct Solution: ``` xs,ys,xt,yt = map(int,input().split()) n = int(input()) v = [(xs,ys,0),(xt,yt,0)] for i in range(n): x,y,r = map(int,input().split()) v.append((x,y,r)) path = [[] for i in range(n+2)] for i in range(n+1): for j in range(i+1,n+2): l = max(0, ((v[i][0] - v[j][0])**2 + (v[i][1] - v[j][1])**2)**0.5 - v[i][2] - v[j][2]) path[i].append((j,l)) path[j].append((i,l)) import heapq def Dijkstra(edge,start,v): d = [float('inf')]*v d[start] = 0 pq = [(0,start)] heapq.heapify(pq) while pq: dist,p = heapq.heappop(pq) if dist > d[p]:continue for to,cost in edge[p]: if d[to] <= dist + cost:continue d[to] = dist + cost heapq.heappush(pq, (d[to], to)) return d d = Dijkstra(path, 0, n+2) print(d[1]) ```
output
1
40,311
3
80,623
Provide a correct Python 3 solution for this coding contest problem. On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size. There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other. A point on the plane is exposed to cosmic rays if the point is not within any of the barriers. Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel. Constraints * All input values are integers. * -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9 * (x_s, y_s) ≠ (x_t, y_t) * 1≤N≤1,000 * -10^9 ≤ x_i, y_i ≤ 10^9 * 1 ≤ r_i ≤ 10^9 Input The input is given from Standard Input in the following format: x_s y_s x_t y_t N x_1 y_1 r_1 x_2 y_2 r_2 : x_N y_N r_N Output Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}. Examples Input -2 -2 2 2 1 0 0 1 Output 3.6568542495 Input -2 0 2 0 2 -1 0 2 1 0 2 Output 0.0000000000 Input 4 -2 -2 4 3 0 0 2 4 0 1 0 4 1 Output 4.0000000000
instruction
0
40,312
3
80,624
"Correct Solution: ``` from heapq import* def Dijkstra(G: list, source=0): INF = float("inf") V = len(G) D = [INF] * V D[source] = 0 vis = [False] * V H = [(0, source)] while H: dist, cur = heappop(H) if vis[cur]: continue vis[cur] = True for nxt, cost in G[cur]: t = dist + cost if D[nxt] > t: D[nxt] = t heappush(H, (t, nxt)) return D import sys input = sys.stdin.buffer.readline from math import hypot sx,sy,gx,gy=map(int,input().split()) n=int(input()) v=[(sx,sy,0),(gx,gy,0)] for _ in range(n): v.append(tuple(map(int,input().split()))) con=[[] for _ in range(n+2)] for i,p1 in enumerate(v): for j,p2 in enumerate(v[i+1:]): t=max(0,hypot(p1[0]-p2[0],p1[1]-p2[1])-p1[2]-p2[2]) con[i].append((i+j+1,t)) con[i+j+1].append((i,t)) print(Dijkstra(con)[1]) ```
output
1
40,312
3
80,625
Provide a correct Python 3 solution for this coding contest problem. On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size. There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other. A point on the plane is exposed to cosmic rays if the point is not within any of the barriers. Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel. Constraints * All input values are integers. * -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9 * (x_s, y_s) ≠ (x_t, y_t) * 1≤N≤1,000 * -10^9 ≤ x_i, y_i ≤ 10^9 * 1 ≤ r_i ≤ 10^9 Input The input is given from Standard Input in the following format: x_s y_s x_t y_t N x_1 y_1 r_1 x_2 y_2 r_2 : x_N y_N r_N Output Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}. Examples Input -2 -2 2 2 1 0 0 1 Output 3.6568542495 Input -2 0 2 0 2 -1 0 2 1 0 2 Output 0.0000000000 Input 4 -2 -2 4 3 0 0 2 4 0 1 0 4 1 Output 4.0000000000
instruction
0
40,313
3
80,626
"Correct Solution: ``` from heapq import heappush, heappop sx,sy,gx,gy=map(int,input().split()) n=int(input()) g = [[] for i in range(n+2)] data=[(sx+sy*1j,0)] for i in range(n): a,b,c=map(int,input().split()) data.append((a+b*1j,c)) data.append((gx+gy*1j,0)) for i in range(n+2): for j in range(i+1,n+2): tmp=abs(data[i][0]-data[j][0])-data[i][1]-data[j][1] g[i].append((tmp,j)) g[j].append((tmp,i)) dist=[2828427127 for i in range(n+2)] visited=[False for i in range(n+2)] dist[0]=0 que=[] heappush(que,(0,0)) while que: c,v=heappop(que) if visited[v]: continue visited[v]=True for x in g[v]: if visited[x[1]]: continue tmp=x[0]+c if not x[0]<0 else c if tmp<dist[x[1]]: dist[x[1]]=tmp heappush(que,(tmp,x[1])) print(dist[n+1]) ```
output
1
40,313
3
80,627
Provide a correct Python 3 solution for this coding contest problem. On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size. There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other. A point on the plane is exposed to cosmic rays if the point is not within any of the barriers. Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel. Constraints * All input values are integers. * -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9 * (x_s, y_s) ≠ (x_t, y_t) * 1≤N≤1,000 * -10^9 ≤ x_i, y_i ≤ 10^9 * 1 ≤ r_i ≤ 10^9 Input The input is given from Standard Input in the following format: x_s y_s x_t y_t N x_1 y_1 r_1 x_2 y_2 r_2 : x_N y_N r_N Output Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}. Examples Input -2 -2 2 2 1 0 0 1 Output 3.6568542495 Input -2 0 2 0 2 -1 0 2 1 0 2 Output 0.0000000000 Input 4 -2 -2 4 3 0 0 2 4 0 1 0 4 1 Output 4.0000000000
instruction
0
40,314
3
80,628
"Correct Solution: ``` import sys input = sys.stdin.readline from collections import defaultdict,deque from itertools import combinations from heapq import heappush, heappop xs,ys,xt,yt = map(int,input().split()) N = int(input()) xyr = [list(map(int,input().split())) for i in range(N)] #import random #N = 1000 #xs,ys = (-10**9,-10**9) #xt,yt = (10**9, 10**9) #xyr = [[random.randint(-10**9, 10**9),random.randint(-10**9, 10**9),random.randint(1,10)] for i in range(N)] #xyr = [[2*i,2*i,1] for i in range(N)] xyr = [[xs,ys,0]] + xyr + [[xt,yt,0]] cost = {} for s in range(0,N+1): for t in range(s+1,N+2): x1,y1,r1 = xyr[s] x2,y2,r2 = xyr[t] R = pow((x2-x1)**2+(y2-y1)**2,0.5) c = max(0, R-r1-r2) cost[(s,t)] = c cost[(t,s)] = c h = [(0,0)] dist = [10**15] * (N+2) dist[0] = 0 while h: d,v = heappop(h) if dist[v] < d: continue for nv in range(N+2): if v == nv: continue temp = d + cost[(v,nv)] if temp < dist[nv]: dist[nv] = temp heappush(h, (temp,nv)) print(dist[N+1]) ```
output
1
40,314
3
80,629
Provide a correct Python 3 solution for this coding contest problem. On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size. There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other. A point on the plane is exposed to cosmic rays if the point is not within any of the barriers. Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel. Constraints * All input values are integers. * -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9 * (x_s, y_s) ≠ (x_t, y_t) * 1≤N≤1,000 * -10^9 ≤ x_i, y_i ≤ 10^9 * 1 ≤ r_i ≤ 10^9 Input The input is given from Standard Input in the following format: x_s y_s x_t y_t N x_1 y_1 r_1 x_2 y_2 r_2 : x_N y_N r_N Output Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}. Examples Input -2 -2 2 2 1 0 0 1 Output 3.6568542495 Input -2 0 2 0 2 -1 0 2 1 0 2 Output 0.0000000000 Input 4 -2 -2 4 3 0 0 2 4 0 1 0 4 1 Output 4.0000000000
instruction
0
40,315
3
80,630
"Correct Solution: ``` import sys from collections import deque, defaultdict import copy import bisect sys.setrecursionlimit(10 ** 9) import math import heapq from itertools import product, permutations,combinations import fractions from operator import itemgetter import sys def input(): return sys.stdin.readline().strip() xs, ys, xt, yt = list(map(int, input().split())) N = int(input()) circle = [(xs, ys, 0)] for i in range(N): circle.append(tuple(map(int, input().split()))) circle.append((xt, yt, 0)) graph = [[0]*(N + 2) for _ in range(N + 2)] for i in range(N + 2): for j in range(i): dist = ((circle[i][0] - circle[j][0])**2 + (circle[i][1] - circle[j][1])**2)**0.5 - circle[i][2] - circle[j][2] dist = max(0, dist) graph[i][j] = dist graph[j][i] = dist dist = [10**13]*(N + 2) dist[0] = 0 node_list = [] heapq.heappush(node_list, (0, 0)) while len(node_list) > 0: node = heapq.heappop(node_list) if dist[node[1]] == node[0]: for i in range(N + 2): if i != node[1] and dist[i] > node[0] + graph[node[1]][i]: dist[i] = node[0] + graph[node[1]][i] heapq.heappush(node_list, (dist[i], i)) print(dist[-1]) ```
output
1
40,315
3
80,631
Provide a correct Python 3 solution for this coding contest problem. On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size. There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other. A point on the plane is exposed to cosmic rays if the point is not within any of the barriers. Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel. Constraints * All input values are integers. * -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9 * (x_s, y_s) ≠ (x_t, y_t) * 1≤N≤1,000 * -10^9 ≤ x_i, y_i ≤ 10^9 * 1 ≤ r_i ≤ 10^9 Input The input is given from Standard Input in the following format: x_s y_s x_t y_t N x_1 y_1 r_1 x_2 y_2 r_2 : x_N y_N r_N Output Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}. Examples Input -2 -2 2 2 1 0 0 1 Output 3.6568542495 Input -2 0 2 0 2 -1 0 2 1 0 2 Output 0.0000000000 Input 4 -2 -2 4 3 0 0 2 4 0 1 0 4 1 Output 4.0000000000
instruction
0
40,316
3
80,632
"Correct Solution: ``` #from collections import deque,defaultdict printn = lambda x: print(x,end='') inn = lambda : int(input()) inl = lambda: list(map(int, input().split())) inm = lambda: map(int, input().split()) ins = lambda : input().strip() DBG = True # and False BIG = 10**18 R = 10**9 + 7 #R = 998244353 def ddprint(x): if DBG: print(x) #import math,heapq from math import sqrt from heapq import heappush,heappop def pdist(x1,y1,x2,y2): return sqrt((x2-x1)**2+(y2-y1)**2) xs,ys,xt,yt = inm() n = inn() cir = [] for i in range(n): x,y,r = inm() cir.append((x,y,r)) dst = [[0]*(n+2) for i in range(n+2)] dst[n][n+1] = dst[n+1][n] = pdist(xs,ys,xt,yt) for i in range(n): x,y,r = cir[i] dst[n][i] = dst[i][n] = max(0.0,pdist(xs,ys,x,y)-r) dst[n+1][i] = dst[i][n+1] = max(0.0,pdist(xt,yt,x,y)-r) for j in range(i+1,n): xx,yy,rr = cir[j] dst[j][i] = dst[i][j] = \ max(0.0,pdist(xx,yy,x,y)-rr-r) if False and DBG: for i in range(n+2): ddprint(dst[i]) cost = [float(BIG)]*(n+2) q = [(0.0,n)] while len(q)>0: d,p = heappop(q) #ddprint(f"{d=} {p=}") if cost[p]<=d: continue cost[p] = d for v in range(n+2): newdist = d+dst[p][v] if v!=p and newdist<cost[v]: heappush(q,(newdist, v)) print(cost[n+1]) ```
output
1
40,316
3
80,633
Provide a correct Python 3 solution for this coding contest problem. On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size. There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other. A point on the plane is exposed to cosmic rays if the point is not within any of the barriers. Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel. Constraints * All input values are integers. * -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9 * (x_s, y_s) ≠ (x_t, y_t) * 1≤N≤1,000 * -10^9 ≤ x_i, y_i ≤ 10^9 * 1 ≤ r_i ≤ 10^9 Input The input is given from Standard Input in the following format: x_s y_s x_t y_t N x_1 y_1 r_1 x_2 y_2 r_2 : x_N y_N r_N Output Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}. Examples Input -2 -2 2 2 1 0 0 1 Output 3.6568542495 Input -2 0 2 0 2 -1 0 2 1 0 2 Output 0.0000000000 Input 4 -2 -2 4 3 0 0 2 4 0 1 0 4 1 Output 4.0000000000
instruction
0
40,317
3
80,634
"Correct Solution: ``` import sys import heapq as h stdin = sys.stdin ni = lambda: int(ns()) nl = lambda: list(map(int, stdin.readline().split())) nm = lambda: map(int, stdin.readline().split()) ns = lambda: stdin.readline().rstrip() def dist(p,q): px,py,pr = p qx,qy,qr = q d = ((px-qx)**2 + (py-qy)**2)**.5 return max(d-(pr+qr),0) xs,ys,xt,yt = nm() n = ni() pl = [(xs,ys,0)] + [tuple(nm()) for _ in range(n)] + [(xt,yt,0)] gr = [dict() for _ in range(n+2)] for i in range(n+1): for j in range(i+1,n+2): gr[i][j] = dist(pl[i],pl[j]) gr[j][i] = gr[i][j] dis = [float("inf")]*(n+2) q = [(0,0)] while q: d,v = h.heappop(q) if dis[v] <= d: continue dis[v] = d for x in gr[v]: if dis[x] > dis[v]+gr[v][x]: h.heappush(q,(dis[v]+gr[v][x],x)) print(dis[-1]) ```
output
1
40,317
3
80,635
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size. There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other. A point on the plane is exposed to cosmic rays if the point is not within any of the barriers. Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel. Constraints * All input values are integers. * -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9 * (x_s, y_s) ≠ (x_t, y_t) * 1≤N≤1,000 * -10^9 ≤ x_i, y_i ≤ 10^9 * 1 ≤ r_i ≤ 10^9 Input The input is given from Standard Input in the following format: x_s y_s x_t y_t N x_1 y_1 r_1 x_2 y_2 r_2 : x_N y_N r_N Output Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}. Examples Input -2 -2 2 2 1 0 0 1 Output 3.6568542495 Input -2 0 2 0 2 -1 0 2 1 0 2 Output 0.0000000000 Input 4 -2 -2 4 3 0 0 2 4 0 1 0 4 1 Output 4.0000000000 Submitted Solution: ``` import sys input = sys.stdin.readline def dijkstra(edge_adj: list, node: int, start: int) -> list: # graph[node] = [(cost, to)] inf = 3 * 10 ** 9 dist = [inf] * node used = [False] * node dist[start] = 0 while True: v = -1 for i in range(node): if not used[i] and (v == -1 or dist[v] > dist[i]): v = i if v == -1: break used[v] = True for i in range(node): if dist[i] > dist[v] + edge_adj[v][i]: dist[i] = dist[v] + edge_adj[v][i] return dist # dist = [costs to nodes] xs, ys, xt, yt = map(int, input().split()) n = int(input()) circles = [(xs, ys, 0), (xt, yt, 0)] for i in range(n): circles.append(tuple(map(int, input().split()))) n += 2 edges = [[0] * n for i in range(n)] for i in range(n): for j in range(i+1, n): dist = ((circles[i][0] - circles[j][0]) ** 2 + (circles[i][1] - circles[j][1]) ** 2) ** 0.5 cost = max(0, dist - circles[i][2] - circles[j][2]) edges[i][j] = cost edges[j][i] = cost dist = dijkstra(edges, n, 0) print(dist[1]) ```
instruction
0
40,318
3
80,636
Yes
output
1
40,318
3
80,637
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size. There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other. A point on the plane is exposed to cosmic rays if the point is not within any of the barriers. Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel. Constraints * All input values are integers. * -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9 * (x_s, y_s) ≠ (x_t, y_t) * 1≤N≤1,000 * -10^9 ≤ x_i, y_i ≤ 10^9 * 1 ≤ r_i ≤ 10^9 Input The input is given from Standard Input in the following format: x_s y_s x_t y_t N x_1 y_1 r_1 x_2 y_2 r_2 : x_N y_N r_N Output Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}. Examples Input -2 -2 2 2 1 0 0 1 Output 3.6568542495 Input -2 0 2 0 2 -1 0 2 1 0 2 Output 0.0000000000 Input 4 -2 -2 4 3 0 0 2 4 0 1 0 4 1 Output 4.0000000000 Submitted Solution: ``` import sys import heapq my_input = sys.stdin.readline def main(): xs, ys, xt, yt = map(int, my_input().split()) N = int(my_input()) C = [(xs, ys, 0), (xt, yt, 0)] C += [tuple(map(int, my_input().split())) for i in range(N)] G = [[] for i in range(N+2)] for i in range(N + 2): for j in range(i + 1, N + 2): cost = max(0, ((C[i][0] - C[j][0]) ** 2 + (C[i][1] - C[j][1]) ** 2) ** 0.5 - (C[i][2] + C[j][2])) G[i].append((j, cost)) G[j].append((i, cost)) def dijkstra(graph, start, inf=float('inf')): import heapq n = len(graph) distances = [inf] * n distances[start] = 0 visited = [False] * n # 距離・頂点 hq = [(0, start)] while hq: dist, fr = heapq.heappop(hq) visited[fr] = True if distances[fr] < dist: continue if fr == 1: return distances for to, cost in graph[fr]: new_dist = distances[fr] + cost if (visited[to]) or (distances[to] <= new_dist): continue distances[to] = new_dist heapq.heappush(hq, (new_dist, to)) return distances dist = dijkstra(G, 0) print(dist[1]) if __name__ == '__main__': main() ```
instruction
0
40,319
3
80,638
Yes
output
1
40,319
3
80,639
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size. There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other. A point on the plane is exposed to cosmic rays if the point is not within any of the barriers. Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel. Constraints * All input values are integers. * -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9 * (x_s, y_s) ≠ (x_t, y_t) * 1≤N≤1,000 * -10^9 ≤ x_i, y_i ≤ 10^9 * 1 ≤ r_i ≤ 10^9 Input The input is given from Standard Input in the following format: x_s y_s x_t y_t N x_1 y_1 r_1 x_2 y_2 r_2 : x_N y_N r_N Output Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}. Examples Input -2 -2 2 2 1 0 0 1 Output 3.6568542495 Input -2 0 2 0 2 -1 0 2 1 0 2 Output 0.0000000000 Input 4 -2 -2 4 3 0 0 2 4 0 1 0 4 1 Output 4.0000000000 Submitted Solution: ``` import sys input = sys.stdin.readline from collections import defaultdict from heapq import heappop, heappush class Graph(object): def __init__(self): self.graph = defaultdict(list) def add_edge(self, a, b, w): self.graph[a].append((b, w)) class Dijkstra(object): def __init__(self, graph, s): self.g = graph.graph self.dist = defaultdict(lambda: float('inf')) self.dist[s] = 0 self.Q = [] heappush(self.Q, (self.dist[s], s)) while self.Q: dist_u, u = heappop(self.Q) if self.dist[u] < dist_u: continue for v, w in self.g[u]: alt = dist_u + w if self.dist[v] > alt: self.dist[v] = alt heappush(self.Q, (alt, v)) def s_d(self, goal): return self.dist[goal] xs, ys, xg, yg = list(map(int, input().split())) xyr = [] xyr.append([xs, ys, 0]) N = int(input()) for i in range(N): xyr.append(list(map(int, input().split()))) xyr.append([xg, yg, 0]) g_a = Graph() for i in range(N + 1): for j in range(i + 1, N + 2): R = ((xyr[i][0] - xyr[j][0]) * (xyr[i][0] - xyr[j][0]) + (xyr[i][1] - xyr[j][1]) * (xyr[i][1] - xyr[j][1])) R = R ** 0.5 if R > xyr[i][2] + xyr[j][2]: r = R - xyr[i][2] - xyr[j][2] else: r = 0 g_a.add_edge(i, j, r) g_a.add_edge(j, i, r) d_a = Dijkstra(g_a, 0) print(d_a.s_d(N + 1)) ```
instruction
0
40,320
3
80,640
Yes
output
1
40,320
3
80,641
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size. There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other. A point on the plane is exposed to cosmic rays if the point is not within any of the barriers. Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel. Constraints * All input values are integers. * -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9 * (x_s, y_s) ≠ (x_t, y_t) * 1≤N≤1,000 * -10^9 ≤ x_i, y_i ≤ 10^9 * 1 ≤ r_i ≤ 10^9 Input The input is given from Standard Input in the following format: x_s y_s x_t y_t N x_1 y_1 r_1 x_2 y_2 r_2 : x_N y_N r_N Output Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}. Examples Input -2 -2 2 2 1 0 0 1 Output 3.6568542495 Input -2 0 2 0 2 -1 0 2 1 0 2 Output 0.0000000000 Input 4 -2 -2 4 3 0 0 2 4 0 1 0 4 1 Output 4.0000000000 Submitted Solution: ``` # coding: utf-8 # Your code here! import sys read = sys.stdin.read readline = sys.stdin.readline xs,ys,xt,yt = map(int,readline().split()) n, = map(int,readline().split()) xyr = [tuple(map(int,readline().split())) for _ in range(n)] + [(xs,ys,0),(xt,yt,0)] """ d: 隣接行列に対する Dijkstra O(N^2) """ def Dijkstra_matrix(d,start): n = len(d) #INF = 1<<61 INF = float("inf") dist = d[start][:] #startからの最短距離 used = [0]*n # 最短距離が決まった頂点 used[start] = 1 for _ in range(n-1): d0 = INF idx = -1 for i in range(n): if not used[i] and dist[i] < d0: idx = i d0 = dist[i] if idx == -1: return dist else: used[idx] = 1 for j in range(n): if not used[j] and dist[j] > dist[idx]+d[idx][j]: dist[j] = dist[idx]+d[idx][j] return dist from math import hypot d = [[max(0.0,hypot((xi-xj),(yi-yj))-ri-rj) for xj,yj,rj in xyr] for xi,yi,ri in xyr] #print(d) dist = Dijkstra_matrix(d,n) print(dist[-1]) #print(dist) ```
instruction
0
40,321
3
80,642
Yes
output
1
40,321
3
80,643
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size. There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other. A point on the plane is exposed to cosmic rays if the point is not within any of the barriers. Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel. Constraints * All input values are integers. * -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9 * (x_s, y_s) ≠ (x_t, y_t) * 1≤N≤1,000 * -10^9 ≤ x_i, y_i ≤ 10^9 * 1 ≤ r_i ≤ 10^9 Input The input is given from Standard Input in the following format: x_s y_s x_t y_t N x_1 y_1 r_1 x_2 y_2 r_2 : x_N y_N r_N Output Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}. Examples Input -2 -2 2 2 1 0 0 1 Output 3.6568542495 Input -2 0 2 0 2 -1 0 2 1 0 2 Output 0.0000000000 Input 4 -2 -2 4 3 0 0 2 4 0 1 0 4 1 Output 4.0000000000 Submitted Solution: ``` from math import hypot def dijkstra(matrix): from heapq import heappush, heappop n = len(matrix) inf = 10**10 hq = [] ans = [inf]*n ans[0] = 0 heappush(hq, (0, 0)) while hq: d, p = heappop(hq) for i in range(n): if ans[p] == d and p != i and d + matrix[p][i] < ans[i]: ans[i] = d + matrix[p][i] heappush(hq, (ans[i], i)) return ans[n-1] x_s, y_s, x_t, y_t = map(int, input().split()) N = int(input()) xyr = [] xyr.append((x_s,y_s,0)) for i in range(N): x_i, y_i, r_i = map(int, input().split()) xyr.append((x_i, y_i, r_i)) xyr.append((x_t,y_t,0)) graph = [[0]*(N+2) for j in range(N+2)] for i in range(N+2): for j in range(i,N+2): graph[i][j] = max(hypot((xyr[i][1]-xyr[j][1]), (xyr[i][0]-xyr[j][0])) - xyr[i][2] - xyr[j][2], 0) graph[j][i] = graph[i][j] print(dijkstra(graph)) ```
instruction
0
40,322
3
80,644
No
output
1
40,322
3
80,645
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size. There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other. A point on the plane is exposed to cosmic rays if the point is not within any of the barriers. Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel. Constraints * All input values are integers. * -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9 * (x_s, y_s) ≠ (x_t, y_t) * 1≤N≤1,000 * -10^9 ≤ x_i, y_i ≤ 10^9 * 1 ≤ r_i ≤ 10^9 Input The input is given from Standard Input in the following format: x_s y_s x_t y_t N x_1 y_1 r_1 x_2 y_2 r_2 : x_N y_N r_N Output Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}. Examples Input -2 -2 2 2 1 0 0 1 Output 3.6568542495 Input -2 0 2 0 2 -1 0 2 1 0 2 Output 0.0000000000 Input 4 -2 -2 4 3 0 0 2 4 0 1 0 4 1 Output 4.0000000000 Submitted Solution: ``` import math from heapq import heapify, heappush as hpush, heappop as hpop xs, ys, xt, yt = map(int, input().split()) N = int(input()) X = [(xs, ys, 0), (xt, yt, 0)] for _ in range(N): x, y, r = map(int, input().split()) X.append((x, y, r)) N += 2 DD = [[0] * N for _ in range(N)] for i in range(N): xi, yi, ri = X[i] for j in range(N): xj, yj, rj = X[j] DD[i][j] = max(math.sqrt((xi-xj)**2 + (yi-yj)**2) - (ri+rj), 0) def dijkstra(n, E, i0=0): h = [[0, i0]] D = [1<<100] * n done = [0] * n D[i0] = 0 while h: d, i = hpop(h) done[i] = 1 for j in range(N): if j == i: continue w = DD[i][j] nd = d + w if D[j] > nd: if done[j] == 0: hpush(h, [nd, j]) D[j] = nd return D print(dijkstra(N, X)[1]) ```
instruction
0
40,323
3
80,646
No
output
1
40,323
3
80,647
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size. There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other. A point on the plane is exposed to cosmic rays if the point is not within any of the barriers. Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel. Constraints * All input values are integers. * -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9 * (x_s, y_s) ≠ (x_t, y_t) * 1≤N≤1,000 * -10^9 ≤ x_i, y_i ≤ 10^9 * 1 ≤ r_i ≤ 10^9 Input The input is given from Standard Input in the following format: x_s y_s x_t y_t N x_1 y_1 r_1 x_2 y_2 r_2 : x_N y_N r_N Output Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}. Examples Input -2 -2 2 2 1 0 0 1 Output 3.6568542495 Input -2 0 2 0 2 -1 0 2 1 0 2 Output 0.0000000000 Input 4 -2 -2 4 3 0 0 2 4 0 1 0 4 1 Output 4.0000000000 Submitted Solution: ``` import heapq xs,ys,xt,yt=map(int,input().split()) n=int(input()) l=[list(map(int,input().split())) for _ in range(n)] f,g=float("inf"),float("inf") start,end=0,0 v=0 for i,(x,y,r) in enumerate(l): v1=(x-xs)**2+(y-ys)**2 v2=(x-xt)**2+(y-yt)**2 if v1<f: f=v1 start=i if v2<g: g=v2 end=i G=[[0]*n for _ in range(n)] for i in range(n): x1,y1,r1=l[i] for j in range(n): x2,y2,r2=l[j] G[i][j]=max(0,((x1-x2)**2+(y1-y2)**2)**0.5-r1-r2) x1,y1,r1=l[start] x2,y2,r2=l[end] v+=max(0,((xs-x1)**2+(ys-y1)**2)**0.5-r1) v+=max(0,((xt-x2)**2+(yt-y2)**2)**0.5-r2) d=[float("inf")]*(n+1) q=[] d[start]=0 heapq.heappush(q,(0,start)) while q: dist,pos=q.pop() if d[pos]<dist:continue for to,cost in enumerate(G[pos]): if d[to]>d[pos]+cost: d[to]=d[pos]+cost heapq.heappush(q,(d[to],to)) v+=d[end] print("{:.10f}".format(v)) ```
instruction
0
40,324
3
80,648
No
output
1
40,324
3
80,649
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size. There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other. A point on the plane is exposed to cosmic rays if the point is not within any of the barriers. Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel. Constraints * All input values are integers. * -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9 * (x_s, y_s) ≠ (x_t, y_t) * 1≤N≤1,000 * -10^9 ≤ x_i, y_i ≤ 10^9 * 1 ≤ r_i ≤ 10^9 Input The input is given from Standard Input in the following format: x_s y_s x_t y_t N x_1 y_1 r_1 x_2 y_2 r_2 : x_N y_N r_N Output Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}. Examples Input -2 -2 2 2 1 0 0 1 Output 3.6568542495 Input -2 0 2 0 2 -1 0 2 1 0 2 Output 0.0000000000 Input 4 -2 -2 4 3 0 0 2 4 0 1 0 4 1 Output 4.0000000000 Submitted Solution: ``` import heapq import sys input = sys.stdin.buffer.readline def dijkstra(adj, start): # adj: [[to, cost] * vertices], 0th index must be empty dist = [float('inf')] * len(adj) dist[start] = 0 q = [] heapq.heappush(q, [0, start]) while q: min_dist, v_from = heapq.heappop(q) if min_dist > dist[v_from]: continue v_tos = adj[v_from] for v_to_info in v_tos: v_to, cost = v_to_info if min_dist + cost < dist[v_to]: dist[v_to] = min_dist + cost heapq.heappush(q, [dist[v_to], v_to]) return dist def main(): xs, ys, xt, yt = map(int, input().split()) N = int(input()) br = [[xs, ys, 0], [xt, yt, 0]] for _ in range(N): br.append(list(map(int, input().split()))) adj = [[] for _ in range(N+3)] for i in range(N+2): for j in range(i+1, N+2): dij = max(((br[i][0] - br[j][0])**2 + (br[i][1] - br[j][1])**2) ** (1/2) - (br[i][2] + br[j][2]), 0) adj[i+1].append([j+1, dij]) adj[j+1].append([i+1, dij]) print(dijkstra(adj, 1)[2]) if __name__ == '__main__': main() ```
instruction
0
40,325
3
80,650
No
output
1
40,325
3
80,651
Provide a correct Python 3 solution for this coding contest problem. A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out. <image> However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B. Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1). Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215. (1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively. Input Given multiple datasets. Each dataset is given in the following format: a1 m1 a2 m2 a3 m3 The input ends with a line containing 6 0s. The number of datasets does not exceed 50. Output For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line. Example Input 2 5 3 7 6 13 517 1024 746 6561 4303 3125 0 0 0 0 0 0 Output 12 116640000
instruction
0
40,342
3
80,684
"Correct Solution: ``` import math def loop(a, x, m): count = 0 while 1: count += 1 x = (a * x) % m if x == 1: break return count while 1: a1, m1, a2, m2, a3, m3 = map(int, input().split()) if a1 == 0: break x = y = z = 1 x = loop(a1, x, m1) y = loop(a2, y, m2) z = loop(a3, z, m3) xy = int(x * y / math.gcd(x, y)) xyz = int(xy * z / math.gcd(xy, z)) print(xyz) ```
output
1
40,342
3
80,685
Provide a correct Python 3 solution for this coding contest problem. A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out. <image> However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B. Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1). Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215. (1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively. Input Given multiple datasets. Each dataset is given in the following format: a1 m1 a2 m2 a3 m3 The input ends with a line containing 6 0s. The number of datasets does not exceed 50. Output For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line. Example Input 2 5 3 7 6 13 517 1024 746 6561 4303 3125 0 0 0 0 0 0 Output 12 116640000
instruction
0
40,343
3
80,686
"Correct Solution: ``` from fractions import gcd while True: a = list(map(int, input().split())) if a.count(0) == 6: break x = a[0] % a[1] ix = 1 while x != 1: x = a[0] * x % a[1] ix += 1 y = a[2] % a[3] iy = 1 while y != 1: y = a[2] * y % a[3] iy += 1 z = a[4] % a[5] iz = 1 while z != 1: z = a[4] * z % a[5] iz += 1 ixy = ix * iy // gcd(ix, iy) print(ixy * iz // gcd(ixy, iz)) ```
output
1
40,343
3
80,687
Provide a correct Python 3 solution for this coding contest problem. A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out. <image> However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B. Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1). Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215. (1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively. Input Given multiple datasets. Each dataset is given in the following format: a1 m1 a2 m2 a3 m3 The input ends with a line containing 6 0s. The number of datasets does not exceed 50. Output For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line. Example Input 2 5 3 7 6 13 517 1024 746 6561 4303 3125 0 0 0 0 0 0 Output 12 116640000
instruction
0
40,344
3
80,688
"Correct Solution: ``` import math def get_input(): while True: try: yield ''.join(input()) except EOFError: break def lcm(a,b): d = math.gcd(a,b) aa = int(a/d) bb = int(b/d) return aa*bb*d while True: a1,m1,a2,m2,a3,m3 = [int(i) for i in input().split()] if a1 == 0 and m1 == 0 and a2 == 0 and m2 == 0 and a3 == 0 and m3 == 0: break x = 1 y = 1 z = 1 cnt1 = 0 cnt2 = 0 cnt3 = 0 while True: x = a1*x % m1 cnt1 += 1 if x == 1: break while True: y = a2*y % m2 cnt2 += 1 if y == 1: break while True: z = a3*z % m3 cnt3 += 1 if z == 1: break print(lcm(lcm(cnt1,cnt2),cnt3)) ```
output
1
40,344
3
80,689
Provide a correct Python 3 solution for this coding contest problem. A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out. <image> However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B. Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1). Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215. (1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively. Input Given multiple datasets. Each dataset is given in the following format: a1 m1 a2 m2 a3 m3 The input ends with a line containing 6 0s. The number of datasets does not exceed 50. Output For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line. Example Input 2 5 3 7 6 13 517 1024 746 6561 4303 3125 0 0 0 0 0 0 Output 12 116640000
instruction
0
40,345
3
80,690
"Correct Solution: ``` # 0114 def gcd(a, b): if b == 0: return a return gcd(b, a % b) def lcm(a, b): return a * b / gcd(a, b) def times(a, m): c = 1 x = a * 1 % m while x != 1: x = a * x % m c += 1 return c while True: x, y, z = 1, 1, 1 c1, c2 ,c3 = 0, 0, 0 a1, m1, a2, m2, a3, m3 = map(int, input().split()) if sum([a1, m1, a2, m2, a3, m3]) == 0: break c1 = times(a1, m1) c2 = times(a2, m2) c3 = times(a3, m3) print(int(lcm(c1, lcm(c2, c3)))) ```
output
1
40,345
3
80,691
Provide a correct Python 3 solution for this coding contest problem. A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out. <image> However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B. Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1). Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215. (1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively. Input Given multiple datasets. Each dataset is given in the following format: a1 m1 a2 m2 a3 m3 The input ends with a line containing 6 0s. The number of datasets does not exceed 50. Output For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line. Example Input 2 5 3 7 6 13 517 1024 746 6561 4303 3125 0 0 0 0 0 0 Output 12 116640000
instruction
0
40,346
3
80,692
"Correct Solution: ``` def gcd(a, b): if a < b: a, b = b, a while b > 0: r = a % b a, b = b, r return a def lcm(a,b): return ((a*b) // gcd(a,b)) def getCnt(a,m): cnt = 0 n = 1 while(1): n = (a * n) % m cnt += 1 if n == 1: return cnt while(1): a1,m1,a2,m2,a3,m3 = (int(x) for x in input().split()) if a1 == 0: break x = y = z = 1 cnt1 = getCnt(a1,m1) cnt2 = getCnt(a2,m2) cnt3 = getCnt(a3,m3) ans = lcm(cnt1,cnt2) ans = lcm(ans,cnt3) print(ans) ```
output
1
40,346
3
80,693
Provide a correct Python 3 solution for this coding contest problem. A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out. <image> However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B. Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1). Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215. (1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively. Input Given multiple datasets. Each dataset is given in the following format: a1 m1 a2 m2 a3 m3 The input ends with a line containing 6 0s. The number of datasets does not exceed 50. Output For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line. Example Input 2 5 3 7 6 13 517 1024 746 6561 4303 3125 0 0 0 0 0 0 Output 12 116640000
instruction
0
40,347
3
80,694
"Correct Solution: ``` from math import gcd def get_loop(a, m): count = 1 acc = a while acc != 1: count += 1 acc *= a acc %= m return count while True: a1, m1, a2, m2, a3, m3 = map(int, input().split()) if not a1: break loop_a = get_loop(a1, m1) loop_b = get_loop(a2, m2) loop_c = get_loop(a3, m3) loop_ab = loop_a * loop_b // gcd(loop_a, loop_b) loop_abc = loop_ab * loop_c // gcd(loop_ab, loop_c) print(loop_abc) ```
output
1
40,347
3
80,695
Provide a correct Python 3 solution for this coding contest problem. A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out. <image> However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B. Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1). Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215. (1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively. Input Given multiple datasets. Each dataset is given in the following format: a1 m1 a2 m2 a3 m3 The input ends with a line containing 6 0s. The number of datasets does not exceed 50. Output For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line. Example Input 2 5 3 7 6 13 517 1024 746 6561 4303 3125 0 0 0 0 0 0 Output 12 116640000
instruction
0
40,348
3
80,696
"Correct Solution: ``` # 0114 def gcd(a, b): if b == 0: return a return gcd(b, a % b) def lcm(a, b): return a * b / gcd(a, b) def times(a, m): c = 1 x = a * 1 % m while x != 1: x = a * x % m c += 1 return c while True: try: x, y, z = 1, 1, 1 c1, c2 ,c3 = 0, 0, 0 a1, m1, a2, m2, a3, m3 = map(int, input().split()) if sum([a1, m1, a2, m2, a3, m3]) == 0: break c1 = times(a1, m1) c2 = times(a2, m2) c3 = times(a3, m3) print(int(lcm(c1, lcm(c2, c3)))) except EOFError: break ```
output
1
40,348
3
80,697
Provide a correct Python 3 solution for this coding contest problem. A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out. <image> However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B. Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1). Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215. (1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively. Input Given multiple datasets. Each dataset is given in the following format: a1 m1 a2 m2 a3 m3 The input ends with a line containing 6 0s. The number of datasets does not exceed 50. Output For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line. Example Input 2 5 3 7 6 13 517 1024 746 6561 4303 3125 0 0 0 0 0 0 Output 12 116640000
instruction
0
40,349
3
80,698
"Correct Solution: ``` def gcd(a, b): if b == 0: return a return gcd(b, a % b) while True: a = list(map(int, input().split())) if a.count(0) == 6: break x = a[0] % a[1] ix = 1 while x != 1: x = a[0] * x % a[1] ix += 1 y = a[2] % a[3] iy = 1 while y != 1: y = a[2] * y % a[3] iy += 1 z = a[4] % a[5] iz = 1 while z != 1: z = a[4] * z % a[5] iz += 1 ixy = ix * iy // gcd(ix, iy) print(ixy * iz // gcd(ixy, iz)) ```
output
1
40,349
3
80,699
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out. <image> However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B. Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1). Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215. (1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively. Input Given multiple datasets. Each dataset is given in the following format: a1 m1 a2 m2 a3 m3 The input ends with a line containing 6 0s. The number of datasets does not exceed 50. Output For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line. Example Input 2 5 3 7 6 13 517 1024 746 6561 4303 3125 0 0 0 0 0 0 Output 12 116640000 Submitted Solution: ``` # 0114 def gcd(a, b): if b == 0: return a return gcd(b, a % b) def lcm(a, b): return a * b / gcd(a, b) while True: try: x, y, z = 1, 1, 1 c1, c2 ,c3 = 0, 0, 0 a1, m1, a2, m2, a3, m3 = map(int, input().split()) if sum([a1, m1, a2, m2, a3, m3]) == 0: break while True: x = a1 * x % m1 c1 += 1 if x == 1: break while True: y = a2 * y % m2 c2 += 1 if y == 1: break while True: z = a3 * z % m3 c3 += 1 if z == 1: break print(int(lcm(c1, lcm(c2, c3)))) except EOFError: break ```
instruction
0
40,350
3
80,700
Yes
output
1
40,350
3
80,701
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out. <image> However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B. Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1). Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215. (1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively. Input Given multiple datasets. Each dataset is given in the following format: a1 m1 a2 m2 a3 m3 The input ends with a line containing 6 0s. The number of datasets does not exceed 50. Output For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line. Example Input 2 5 3 7 6 13 517 1024 746 6561 4303 3125 0 0 0 0 0 0 Output 12 116640000 Submitted Solution: ``` import itertools as I,math; def lcm(x,y):return x*y//math.gcd(x,y); while 1: a,b,c,d,e,f=map(int,input().split()); if a==0:break; A=I.dropwhile(lambda x:1<pow(a,x,b),range(1,b)); B=I.dropwhile(lambda x:1<pow(c,x,d),range(1,d)); C=I.dropwhile(lambda x:1<pow(e,x,f),range(1,f)); x,y,z=map(lambda u:list(u)[0],[A,B,C]); print(lcm(x,lcm(y,z))) ```
instruction
0
40,351
3
80,702
Yes
output
1
40,351
3
80,703
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out. <image> However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B. Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1). Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215. (1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively. Input Given multiple datasets. Each dataset is given in the following format: a1 m1 a2 m2 a3 m3 The input ends with a line containing 6 0s. The number of datasets does not exceed 50. Output For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line. Example Input 2 5 3 7 6 13 517 1024 746 6561 4303 3125 0 0 0 0 0 0 Output 12 116640000 Submitted Solution: ``` from decimal import * class Fry: def __init__(self,a1,m1,a2,m2,a3,m3): self.a1 = a1 self.m1 = m1 self.a2 = a2 self.m2 = m2 self.a3 = a3 self.m3 = m3 def euc(self,m,n): if n==0: return(m) else: r = m % n return(self.euc(n,r)) def test(self,a,m): n = 0 x = 1 while True: x1 = (a * x) % m n += 1 if x1 == 1: break else: x = x1 return(n) def mv(self): n1 = Decimal(self.test(self.a1,self.m1)) n2 = Decimal(self.test(self.a2,self.m2)) n3 = Decimal(self.test(self.a3,self.m3)) m1 = n1*n2/self.euc(n1,n2) m2 = m1*n3/self.euc(m1,n3) return(m2) while True: a1,m1,a2,m2,a3,m3 = list(map(int, input().strip().split())) if a1==m1==a2==m2==a3==m3==0: break fry = Fry(a1,m1,a2,m2,a3,m3) print(fry.mv()) ```
instruction
0
40,352
3
80,704
Yes
output
1
40,352
3
80,705
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out. <image> However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B. Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1). Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215. (1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively. Input Given multiple datasets. Each dataset is given in the following format: a1 m1 a2 m2 a3 m3 The input ends with a line containing 6 0s. The number of datasets does not exceed 50. Output For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line. Example Input 2 5 3 7 6 13 517 1024 746 6561 4303 3125 0 0 0 0 0 0 Output 12 116640000 Submitted Solution: ``` # -*- coding: utf-8 -*- """ http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0114 """ import sys def lcm(x, y): return x*y//gcd(x, y) def gcd(x, y): if x < y: temp = x x = y y = temp while y > 0: r = x % y x = y y = r return x def calc_cycle(a, m): x = 1 cycle = 0 while True: x = (a * x) % m cycle += 1 if x == 1: break return cycle def solve(data): a1, m1, a2, m2, a3, m3 = data x_cycle = calc_cycle(a1, m1) y_cycle = calc_cycle(a2, m2) z_cycle = calc_cycle(a3, m3) return lcm(lcm(x_cycle, y_cycle), z_cycle) def main(args): # data = [2, 5, 3, 7, 6, 13] #data = [517, 1024, 746, 6561, 4303, 3125] while True: data = [int(x) for x in input().split(' ')] if data.count(0) == 6: break result = solve(data) print(result) if __name__ == '__main__': main(sys.argv[1:]) ```
instruction
0
40,353
3
80,706
Yes
output
1
40,353
3
80,707
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out. <image> However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B. Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1). Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215. (1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively. Input Given multiple datasets. Each dataset is given in the following format: a1 m1 a2 m2 a3 m3 The input ends with a line containing 6 0s. The number of datasets does not exceed 50. Output For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line. Example Input 2 5 3 7 6 13 517 1024 746 6561 4303 3125 0 0 0 0 0 0 Output 12 116640000 Submitted Solution: ``` # -*- coding: utf-8 -*- import sys import os import math def lcm(a, b): return (a * b) // math.gcd(a, b) def interval(a, m): cnt = 0 x = 1 while True: x = (a * x) % m cnt += 1 if x == 1: return cnt for s in sys.stdin: a1, m1, a2, m2, a3, m3 = map(int, s.split()) if sum([a1, m1, a2, m2, a3, m3]) == 0: break x_num = interval(a1, m1) y_num = interval(a2, m2) z_num = interval(a3, m3) a = lcm(x_num, y_num) b = lcm(a, z_num) print(b) ```
instruction
0
40,354
3
80,708
No
output
1
40,354
3
80,709
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out. <image> However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B. Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1). Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215. (1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively. Input Given multiple datasets. Each dataset is given in the following format: a1 m1 a2 m2 a3 m3 The input ends with a line containing 6 0s. The number of datasets does not exceed 50. Output For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line. Example Input 2 5 3 7 6 13 517 1024 746 6561 4303 3125 0 0 0 0 0 0 Output 12 116640000 Submitted Solution: ``` # -*- coding: utf-8 -*- import sys import os import math def lcm(a, b): return (a * b) // math.gcd(a, b) for s in sys.stdin: a1, m1, a2, m2, a3, m3 = map(int, s.split()) if a1 == m1 == a2 == m2 == a3 == m3 == 0: break x = 1 y = 1 z = 1 x_num = 0 while True: x = (a1 * x) % m1 x_num += 1 if x == 1: break y_num = 0 while True: y = (a2 * y) % m2 y_num += 1 if y == 1: break z_num = 0 while True: z = (a3 * z) % m3 z_num += 1 if z == 1: break a = lcm(x_num, y_num) b = lcm(a, z_num) print(b) ```
instruction
0
40,355
3
80,710
No
output
1
40,355
3
80,711
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out. <image> However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B. Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1). Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215. (1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively. Input Given multiple datasets. Each dataset is given in the following format: a1 m1 a2 m2 a3 m3 The input ends with a line containing 6 0s. The number of datasets does not exceed 50. Output For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line. Example Input 2 5 3 7 6 13 517 1024 746 6561 4303 3125 0 0 0 0 0 0 Output 12 116640000 Submitted Solution: ``` from math import gcd while True: a = list(map(int, input().split())) if a.count(0) == 6: break x = a[0] % a[1] ix = 1 while x != 1: x = a[0] * x % a[1] ix += 1 y = a[2] % a[3] iy = 1 while y != 1: y = a[2] * y % a[3] iy += 1 z = a[4] % a[5] iz = 1 while z != 1: z = a[4] * z % a[5] iz += 1 ixy = ix * iy // gcd(ix, iy) print(ixy * iz // gcd(ixy, iz)) ```
instruction
0
40,356
3
80,712
No
output
1
40,356
3
80,713
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out. <image> However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B. Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1). Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215. (1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively. Input Given multiple datasets. Each dataset is given in the following format: a1 m1 a2 m2 a3 m3 The input ends with a line containing 6 0s. The number of datasets does not exceed 50. Output For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line. Example Input 2 5 3 7 6 13 517 1024 746 6561 4303 3125 0 0 0 0 0 0 Output 12 116640000 Submitted Solution: ``` from math import gcd def get_loop(a, m): count = 1 acc = a while acc % m != 1: count += 1 acc *= a return count while True: a1, m1, a2, m2, a3, m3 = map(int, input().split()) if not a1: break loop_a = get_loop(a1, m1) loop_b = get_loop(a2, m2) loop_c = get_loop(a3, m3) loop_ab = loop_a * loop_b // gcd(loop_a, loop_b) loop_abc = loop_ab * loop_c // gcd(loop_ab, loop_c) print(loop_abc) ```
instruction
0
40,357
3
80,714
No
output
1
40,357
3
80,715
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. People like to be fit. That's why many of them are ready to wake up at dawn, go to the stadium and run. In this problem your task is to help a company design a new stadium. The city of N has a shabby old stadium. Many people like it and every morning thousands of people come out to this stadium to run. The stadium can be represented as a circle, its length is exactly l meters with a marked start line. However, there can't be simultaneous start in the morning, so exactly at 7, each runner goes to his favorite spot on the stadium and starts running from there. Note that not everybody runs in the same manner as everybody else. Some people run in the clockwise direction, some of them run in the counter-clockwise direction. It mostly depends on the runner's mood in the morning, so you can assume that each running direction is equiprobable for each runner in any fixed morning. The stadium is tiny and is in need of major repair, for right now there only is one running track! You can't get too playful on a single track, that's why all runners keep the same running speed — exactly 1 meter per a time unit. Nevertheless, the runners that choose different directions bump into each other as they meet. The company wants to design a new stadium, but they first need to know how bad the old one is. For that they need the expectation of the number of bumpings by t time units after the running has begun. Help the company count the required expectation. Note that each runner chooses a direction equiprobably, independently from the others and then all runners start running simultaneously at 7 a.m. Assume that each runner runs for t time units without stopping. Consider the runners to bump at a certain moment if at that moment they found themselves at the same point in the stadium. A pair of runners can bump more than once. Input The first line of the input contains three integers n, l, t (1 ≤ n ≤ 106, 1 ≤ l ≤ 109, 1 ≤ t ≤ 109). The next line contains n distinct integers a1, a2, ..., an (0 ≤ a1 < a2 < ... < an < l), here ai is the clockwise distance from the start line to the i-th runner's starting position. Output Print a single real number — the answer to the problem with absolute or relative error of at most 10 - 6. Examples Input 2 5 1 0 2 Output 0.2500000000 Input 3 7 3 0 1 6 Output 1.5000000000 Note There are two runners in the first example. If the first runner run clockwise direction, then in 1 time unit he will be 1m away from the start line. If the second runner run counter-clockwise direction then in 1 time unit he will be also 1m away from the start line. And it is the only possible way to meet. We assume that each running direction is equiprobable, so the answer for the example is equal to 0.5·0.5 = 0.25. Submitted Solution: ``` def sol(): n, l, t = list(map(int, input().split(" "))) b = list(map(int, input().split(" "))) ans_a = (t // l) * (n * (n - 1) // 2) c = t - ((2*t) // l) * l*2 e = 0 for i in range(0, n - 1): for j in range(i + 1, n): if b[j] - b[i] <= 2 * c: e += 1 if b[j] - b[i] > 2 * c: break for i in range(0, n - 1): for j in range(i + 1, n): if b[j] - b[i] >= l - 2 * c: e += n - j break ans_b = e * 0.25 ans = ans_a + ans_b print(ans) sol() ```
instruction
0
40,740
3
81,480
No
output
1
40,740
3
81,481
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. People like to be fit. That's why many of them are ready to wake up at dawn, go to the stadium and run. In this problem your task is to help a company design a new stadium. The city of N has a shabby old stadium. Many people like it and every morning thousands of people come out to this stadium to run. The stadium can be represented as a circle, its length is exactly l meters with a marked start line. However, there can't be simultaneous start in the morning, so exactly at 7, each runner goes to his favorite spot on the stadium and starts running from there. Note that not everybody runs in the same manner as everybody else. Some people run in the clockwise direction, some of them run in the counter-clockwise direction. It mostly depends on the runner's mood in the morning, so you can assume that each running direction is equiprobable for each runner in any fixed morning. The stadium is tiny and is in need of major repair, for right now there only is one running track! You can't get too playful on a single track, that's why all runners keep the same running speed — exactly 1 meter per a time unit. Nevertheless, the runners that choose different directions bump into each other as they meet. The company wants to design a new stadium, but they first need to know how bad the old one is. For that they need the expectation of the number of bumpings by t time units after the running has begun. Help the company count the required expectation. Note that each runner chooses a direction equiprobably, independently from the others and then all runners start running simultaneously at 7 a.m. Assume that each runner runs for t time units without stopping. Consider the runners to bump at a certain moment if at that moment they found themselves at the same point in the stadium. A pair of runners can bump more than once. Input The first line of the input contains three integers n, l, t (1 ≤ n ≤ 106, 1 ≤ l ≤ 109, 1 ≤ t ≤ 109). The next line contains n distinct integers a1, a2, ..., an (0 ≤ a1 < a2 < ... < an < l), here ai is the clockwise distance from the start line to the i-th runner's starting position. Output Print a single real number — the answer to the problem with absolute or relative error of at most 10 - 6. Examples Input 2 5 1 0 2 Output 0.2500000000 Input 3 7 3 0 1 6 Output 1.5000000000 Note There are two runners in the first example. If the first runner run clockwise direction, then in 1 time unit he will be 1m away from the start line. If the second runner run counter-clockwise direction then in 1 time unit he will be also 1m away from the start line. And it is the only possible way to meet. We assume that each running direction is equiprobable, so the answer for the example is equal to 0.5·0.5 = 0.25. Submitted Solution: ``` def sol(): n, l, t = list(map(int, input().split(" "))) b = list(map(int, input().split(" "))) ans_a = (t//l)*(n*(n-1)//2)*0.5 c = t-(t//l)*l e = 0 for i in range(0, n-1): for j in range(i+1, n): if b[j]-b[i] <= 2*c: e += 1 if b[j]-b[i] > 2*c: break for i in range(0, n - 1): for j in range(i+1, n): if b[j] - b[i] >= l - 2 * c: e += n-j break ans_b = e*0.25 ans = ans_a+ans_b print (ans) sol() ```
instruction
0
40,741
3
81,482
No
output
1
40,741
3
81,483
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. People like to be fit. That's why many of them are ready to wake up at dawn, go to the stadium and run. In this problem your task is to help a company design a new stadium. The city of N has a shabby old stadium. Many people like it and every morning thousands of people come out to this stadium to run. The stadium can be represented as a circle, its length is exactly l meters with a marked start line. However, there can't be simultaneous start in the morning, so exactly at 7, each runner goes to his favorite spot on the stadium and starts running from there. Note that not everybody runs in the same manner as everybody else. Some people run in the clockwise direction, some of them run in the counter-clockwise direction. It mostly depends on the runner's mood in the morning, so you can assume that each running direction is equiprobable for each runner in any fixed morning. The stadium is tiny and is in need of major repair, for right now there only is one running track! You can't get too playful on a single track, that's why all runners keep the same running speed — exactly 1 meter per a time unit. Nevertheless, the runners that choose different directions bump into each other as they meet. The company wants to design a new stadium, but they first need to know how bad the old one is. For that they need the expectation of the number of bumpings by t time units after the running has begun. Help the company count the required expectation. Note that each runner chooses a direction equiprobably, independently from the others and then all runners start running simultaneously at 7 a.m. Assume that each runner runs for t time units without stopping. Consider the runners to bump at a certain moment if at that moment they found themselves at the same point in the stadium. A pair of runners can bump more than once. Input The first line of the input contains three integers n, l, t (1 ≤ n ≤ 106, 1 ≤ l ≤ 109, 1 ≤ t ≤ 109). The next line contains n distinct integers a1, a2, ..., an (0 ≤ a1 < a2 < ... < an < l), here ai is the clockwise distance from the start line to the i-th runner's starting position. Output Print a single real number — the answer to the problem with absolute or relative error of at most 10 - 6. Examples Input 2 5 1 0 2 Output 0.2500000000 Input 3 7 3 0 1 6 Output 1.5000000000 Note There are two runners in the first example. If the first runner run clockwise direction, then in 1 time unit he will be 1m away from the start line. If the second runner run counter-clockwise direction then in 1 time unit he will be also 1m away from the start line. And it is the only possible way to meet. We assume that each running direction is equiprobable, so the answer for the example is equal to 0.5·0.5 = 0.25. Submitted Solution: ``` def sol(): n, l, t = list(map(int, input().split(" "))) b = list(map(int, input().split(" "))) ans_a = (t//l)*(n*(n-1)//2) c = t-(t//l)*l e = 0 f = 0 for i in range(0, n-1): for j in range(i+1, n): if b[j]-b[i] <= 2*c: e += 1 if b[j]-b[i] > 2*c: break for i in range(0, n - 1): for j in range(i+1, n): if b[j] - b[i] >= l - 2 * c: f += 1 ans_b = (e+f)*0.5 ans = ans_a+ans_b print (ans) sol() ```
instruction
0
40,742
3
81,484
No
output
1
40,742
3
81,485
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. People like to be fit. That's why many of them are ready to wake up at dawn, go to the stadium and run. In this problem your task is to help a company design a new stadium. The city of N has a shabby old stadium. Many people like it and every morning thousands of people come out to this stadium to run. The stadium can be represented as a circle, its length is exactly l meters with a marked start line. However, there can't be simultaneous start in the morning, so exactly at 7, each runner goes to his favorite spot on the stadium and starts running from there. Note that not everybody runs in the same manner as everybody else. Some people run in the clockwise direction, some of them run in the counter-clockwise direction. It mostly depends on the runner's mood in the morning, so you can assume that each running direction is equiprobable for each runner in any fixed morning. The stadium is tiny and is in need of major repair, for right now there only is one running track! You can't get too playful on a single track, that's why all runners keep the same running speed — exactly 1 meter per a time unit. Nevertheless, the runners that choose different directions bump into each other as they meet. The company wants to design a new stadium, but they first need to know how bad the old one is. For that they need the expectation of the number of bumpings by t time units after the running has begun. Help the company count the required expectation. Note that each runner chooses a direction equiprobably, independently from the others and then all runners start running simultaneously at 7 a.m. Assume that each runner runs for t time units without stopping. Consider the runners to bump at a certain moment if at that moment they found themselves at the same point in the stadium. A pair of runners can bump more than once. Input The first line of the input contains three integers n, l, t (1 ≤ n ≤ 106, 1 ≤ l ≤ 109, 1 ≤ t ≤ 109). The next line contains n distinct integers a1, a2, ..., an (0 ≤ a1 < a2 < ... < an < l), here ai is the clockwise distance from the start line to the i-th runner's starting position. Output Print a single real number — the answer to the problem with absolute or relative error of at most 10 - 6. Examples Input 2 5 1 0 2 Output 0.2500000000 Input 3 7 3 0 1 6 Output 1.5000000000 Note There are two runners in the first example. If the first runner run clockwise direction, then in 1 time unit he will be 1m away from the start line. If the second runner run counter-clockwise direction then in 1 time unit he will be also 1m away from the start line. And it is the only possible way to meet. We assume that each running direction is equiprobable, so the answer for the example is equal to 0.5·0.5 = 0.25. Submitted Solution: ``` def sol(): n, l, t = list(map(int, input().split(" "))) b = list(map(int, input().split(" "))) ans_a = (t//l)*(n*(n-1)//2)*0.5*2 c = t-(t//l)*l e = 0 for i in range(0, n-1): for j in range(i+1, n): if b[j]-b[i] <= 2*c: e += 1 if b[j]-b[i] > 2*c: break for i in range(0, n - 1): for j in range(i+1, n): if b[j] - b[i] >= l - 2 * c: e += n-j break ans_b = e*0.25 ans = ans_a+ans_b print (ans) sol() ```
instruction
0
40,743
3
81,486
No
output
1
40,743
3
81,487
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Recently Luba bought a monitor. Monitor is a rectangular matrix of size n × m. But then she started to notice that some pixels cease to work properly. Luba thinks that the monitor will become broken the first moment when it contains a square k × k consisting entirely of broken pixels. She knows that q pixels are already broken, and for each of them she knows the moment when it stopped working. Help Luba to determine when the monitor became broken (or tell that it's still not broken even after all q pixels stopped working). Input The first line contains four integer numbers n, m, k, q (1 ≤ n, m ≤ 500, 1 ≤ k ≤ min(n, m), 0 ≤ q ≤ n·m) — the length and width of the monitor, the size of a rectangle such that the monitor is broken if there is a broken rectangle with this size, and the number of broken pixels. Each of next q lines contain three integer numbers xi, yi, ti (1 ≤ xi ≤ n, 1 ≤ yi ≤ m, 0 ≤ t ≤ 109) — coordinates of i-th broken pixel (its row and column in matrix) and the moment it stopped working. Each pixel is listed at most once. We consider that pixel is already broken at moment ti. Output Print one number — the minimum moment the monitor became broken, or "-1" if it's still not broken after these q pixels stopped working. Examples Input 2 3 2 5 2 1 8 2 2 8 1 2 1 1 3 4 2 3 2 Output 8 Input 3 3 2 5 1 2 2 2 2 1 2 3 5 3 2 10 2 1 100 Output -1 Submitted Solution: ``` n, m, k, q = map(int, input().split()) def sort(x): return x[2] def check(matrix): sas = matrix.copy() for i in range(n + 1): for j in range(m + 1): sas[i][j] = matrix[i][j] if i: sas[i][j] += sas[i - 1][j] if j: sas[i][j] += sas[i][j - 1] if i and j: sas[i][j] -= sas[i - 1][j - 1] for i in range(k, n + 1): for j in range(k, m + 1): if (sas[i][j] - sas[i - k][j] - sas[i][j - k] + sas[i - k][j - k]) == (k * k): return True return False h = sorted([list(map(int, input().split())) for _ in range(q)], key=sort) matrix = [[0 for _ in range(m + 1)] for __ in range(n + 1)] for i in h: matrix[i[0]][i[1]] = 1 if not check(matrix): print(-1) exit() l, r = -1, len(h) while l < r: mid = (l + r) // 2 matrix = [[0 for _ in range(m + 1)] for __ in range(n + 1)] for i in h[:mid]: matrix[i[0]][i[1]] = 1 parasha = check(matrix) if parasha: r = mid - 1 else: l = mid + 1 mid = (l + r) // 2 if mid < 0: mid = 0 if mid >= len(h): mid = len(h) - 1 print(h[mid][2]) ```
instruction
0
40,908
3
81,816
No
output
1
40,908
3
81,817
Provide tags and a correct Python 3 solution for this coding contest problem. In one one-dimensional world there are n platforms. Platform with index k (platforms are numbered from 1) is a segment with coordinates [(k - 1)m, (k - 1)m + l], and l < m. Grasshopper Bob starts to jump along the platforms from point 0, with each jump he moves exactly d units right. Find out the coordinate of the point, where Bob will fall down. The grasshopper falls down, if he finds himself not on the platform, but if he finds himself on the edge of the platform, he doesn't fall down. Input The first input line contains 4 integer numbers n, d, m, l (1 ≤ n, d, m, l ≤ 106, l < m) — respectively: amount of platforms, length of the grasshopper Bob's jump, and numbers m and l needed to find coordinates of the k-th platform: [(k - 1)m, (k - 1)m + l]. Output Output the coordinates of the point, where the grosshopper will fall down. Don't forget that if Bob finds himself on the platform edge, he doesn't fall down. Examples Input 2 2 5 3 Output 4 Input 5 4 11 8 Output 20
instruction
0
41,498
3
82,996
Tags: brute force, math Correct Solution: ``` n, d, m, l = [int(i) for i in input().split()] x = 0 if m % d == 0: x = ((n-1)*m+l) // d * d + d elif (m - l) > d: x = l // d * d + d else: for k in range(1, n+1): r = k*m % d if r < (m-l) and r != 0: x = k*m - r x = ((k-1)*m+l) // d * d + d break if x==0: x = ((n-1)*m+l) // d * d + d print(x) ```
output
1
41,498
3
82,997
Provide tags and a correct Python 3 solution for this coding contest problem. In one one-dimensional world there are n platforms. Platform with index k (platforms are numbered from 1) is a segment with coordinates [(k - 1)m, (k - 1)m + l], and l < m. Grasshopper Bob starts to jump along the platforms from point 0, with each jump he moves exactly d units right. Find out the coordinate of the point, where Bob will fall down. The grasshopper falls down, if he finds himself not on the platform, but if he finds himself on the edge of the platform, he doesn't fall down. Input The first input line contains 4 integer numbers n, d, m, l (1 ≤ n, d, m, l ≤ 106, l < m) — respectively: amount of platforms, length of the grasshopper Bob's jump, and numbers m and l needed to find coordinates of the k-th platform: [(k - 1)m, (k - 1)m + l]. Output Output the coordinates of the point, where the grosshopper will fall down. Don't forget that if Bob finds himself on the platform edge, he doesn't fall down. Examples Input 2 2 5 3 Output 4 Input 5 4 11 8 Output 20
instruction
0
41,499
3
82,998
Tags: brute force, math Correct Solution: ``` import sys input = sys.stdin.readline n, d, m, l = map(int, input().split()) res = 0 for i in range(n): z = m * i + l + d; res = z - z % d if m * (i+1) > z - z % d: break print(res) ```
output
1
41,499
3
82,999
Provide tags and a correct Python 3 solution for this coding contest problem. In one one-dimensional world there are n platforms. Platform with index k (platforms are numbered from 1) is a segment with coordinates [(k - 1)m, (k - 1)m + l], and l < m. Grasshopper Bob starts to jump along the platforms from point 0, with each jump he moves exactly d units right. Find out the coordinate of the point, where Bob will fall down. The grasshopper falls down, if he finds himself not on the platform, but if he finds himself on the edge of the platform, he doesn't fall down. Input The first input line contains 4 integer numbers n, d, m, l (1 ≤ n, d, m, l ≤ 106, l < m) — respectively: amount of platforms, length of the grasshopper Bob's jump, and numbers m and l needed to find coordinates of the k-th platform: [(k - 1)m, (k - 1)m + l]. Output Output the coordinates of the point, where the grosshopper will fall down. Don't forget that if Bob finds himself on the platform edge, he doesn't fall down. Examples Input 2 2 5 3 Output 4 Input 5 4 11 8 Output 20
instruction
0
41,500
3
83,000
Tags: brute force, math Correct Solution: ``` #coding gbk while True: try: n,d,m,l=map(int,input().strip().split()) mi = 0 mx = 0 step = 0 for i in range(n): mi = i*m+l mx = (i+1)*m step = (mi+d)//d if step*d<mx: break print(step*d) except EOFError: break ```
output
1
41,500
3
83,001
Provide tags and a correct Python 3 solution for this coding contest problem. In one one-dimensional world there are n platforms. Platform with index k (platforms are numbered from 1) is a segment with coordinates [(k - 1)m, (k - 1)m + l], and l < m. Grasshopper Bob starts to jump along the platforms from point 0, with each jump he moves exactly d units right. Find out the coordinate of the point, where Bob will fall down. The grasshopper falls down, if he finds himself not on the platform, but if he finds himself on the edge of the platform, he doesn't fall down. Input The first input line contains 4 integer numbers n, d, m, l (1 ≤ n, d, m, l ≤ 106, l < m) — respectively: amount of platforms, length of the grasshopper Bob's jump, and numbers m and l needed to find coordinates of the k-th platform: [(k - 1)m, (k - 1)m + l]. Output Output the coordinates of the point, where the grosshopper will fall down. Don't forget that if Bob finds himself on the platform edge, he doesn't fall down. Examples Input 2 2 5 3 Output 4 Input 5 4 11 8 Output 20
instruction
0
41,501
3
83,002
Tags: brute force, math Correct Solution: ``` n, d, m, l = [int(i) for i in input().split()] x = 0 for k in range(1, n+1): r = k*m % d if r < (m-l) and r != 0: x = k*m - r x = ((k-1)*m+l) // d * d + d break if x==0: x = ((n-1)*m+l) // d * d + d print(x) ```
output
1
41,501
3
83,003
Provide tags and a correct Python 3 solution for this coding contest problem. In one one-dimensional world there are n platforms. Platform with index k (platforms are numbered from 1) is a segment with coordinates [(k - 1)m, (k - 1)m + l], and l < m. Grasshopper Bob starts to jump along the platforms from point 0, with each jump he moves exactly d units right. Find out the coordinate of the point, where Bob will fall down. The grasshopper falls down, if he finds himself not on the platform, but if he finds himself on the edge of the platform, he doesn't fall down. Input The first input line contains 4 integer numbers n, d, m, l (1 ≤ n, d, m, l ≤ 106, l < m) — respectively: amount of platforms, length of the grasshopper Bob's jump, and numbers m and l needed to find coordinates of the k-th platform: [(k - 1)m, (k - 1)m + l]. Output Output the coordinates of the point, where the grosshopper will fall down. Don't forget that if Bob finds himself on the platform edge, he doesn't fall down. Examples Input 2 2 5 3 Output 4 Input 5 4 11 8 Output 20
instruction
0
41,502
3
83,004
Tags: brute force, math Correct Solution: ``` n,d,m,l = [int(x) for x in input().split()] c = 0 counter = 0 fall = False while counter <= m: c += d counter += 1 if c%m > l: print(c) fall = True break if not fall: print(((m*(n-1)+l)//d)*d +d) ```
output
1
41,502
3
83,005
Provide tags and a correct Python 3 solution for this coding contest problem. In one one-dimensional world there are n platforms. Platform with index k (platforms are numbered from 1) is a segment with coordinates [(k - 1)m, (k - 1)m + l], and l < m. Grasshopper Bob starts to jump along the platforms from point 0, with each jump he moves exactly d units right. Find out the coordinate of the point, where Bob will fall down. The grasshopper falls down, if he finds himself not on the platform, but if he finds himself on the edge of the platform, he doesn't fall down. Input The first input line contains 4 integer numbers n, d, m, l (1 ≤ n, d, m, l ≤ 106, l < m) — respectively: amount of platforms, length of the grasshopper Bob's jump, and numbers m and l needed to find coordinates of the k-th platform: [(k - 1)m, (k - 1)m + l]. Output Output the coordinates of the point, where the grosshopper will fall down. Don't forget that if Bob finds himself on the platform edge, he doesn't fall down. Examples Input 2 2 5 3 Output 4 Input 5 4 11 8 Output 20
instruction
0
41,503
3
83,006
Tags: brute force, math Correct Solution: ``` import os import sys from io import BytesIO, IOBase from typing import Text from collections import* ''' 2 2 5 3 1 : 0,3 2 : 5, ''' def main(): n,d,m,l = map(int,input().split()) Coordinate = 0 for i in range(n): left = i*m right = i*m + l if(Coordinate < left): print(Coordinate) exit(0) NumberOfMoves = ((right - Coordinate) // d) + 1 Coordinate += NumberOfMoves * d # print(i , Coordinate) pass print(Coordinate) # region fastio BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # endregion if __name__ == "__main__": main() ```
output
1
41,503
3
83,007