text stringlengths 198 433k | conversation_id int64 0 109k |
|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The flag of Berland is such rectangular field n × m that satisfies following conditions:
* Flag consists of three colors which correspond to letters 'R', 'G' and 'B'.
* Flag consists of three equal in width and height stripes, parralel to each other and to sides of the flag. Each stripe has exactly one color.
* Each color should be used in exactly one stripe.
You are given a field n × m, consisting of characters 'R', 'G' and 'B'. Output "YES" (without quotes) if this field corresponds to correct flag of Berland. Otherwise, print "NO" (without quotes).
Input
The first line contains two integer numbers n and m (1 ≤ n, m ≤ 100) — the sizes of the field.
Each of the following n lines consisting of m characters 'R', 'G' and 'B' — the description of the field.
Output
Print "YES" (without quotes) if the given field corresponds to correct flag of Berland . Otherwise, print "NO" (without quotes).
Examples
Input
6 5
RRRRR
RRRRR
BBBBB
BBBBB
GGGGG
GGGGG
Output
YES
Input
4 3
BRG
BRG
BRG
BRG
Output
YES
Input
6 7
RRRGGGG
RRRGGGG
RRRGGGG
RRRBBBB
RRRBBBB
RRRBBBB
Output
NO
Input
4 4
RRRR
RRRR
BBBB
GGGG
Output
NO
Note
The field in the third example doesn't have three parralel stripes.
Rows of the field in the fourth example are parralel to each other and to borders. But they have different heights — 2, 1 and 1.
Submitted Solution:
```
import sys, math
n, m = map(int, input().split())
a = ["" for i in range(n)]
for i in range(n):
a[i] = input()
if (a[0][0] == a[0][m-1]) and (n % 3 == 0):
for i in range(n // 3):
for j in range(m):
if (not a[i][j] == a[0][0]):
print("NO")
sys.exit()
for i in range(n // 3, 2 * n // 3):
for j in range(m):
if (not a[i][j] == a[n // 3][0]):
print("NO")
sys.exit()
for i in range(2 * n // 3, n):
for j in range(m):
if (not a[i][j] == a[2 * n // 3][0]):
print("NO")
sys.exit()
if (a[0][0] == a[n // 3][0]) or (a[0][0] == a[2 * n // 3][0]) or (a[2 * n // 3][0] == a[n // 3][0]):
print("NO")
sys.exit()
else:
print("YES")
sys.exit()
elif (a[0][0] == a[n - 1][0]) and (m % 3 == 0):
for i in range(n):
for j in range(m // 3):
if not ((a[i][j] == a[0][0]) and (a[i][j + m // 3] == a[0][m // 3]) and (
a[i][j + 2 * m // 3] == a[0][2 * m // 3])):
print("NO")
sys.exit()
if (a[0][0] == a[0][m // 3]) or (a[0][0] == a[0][2 * m // 3]) or (a[0][2 * m // 3] == a[0][m // 3]):
print("NO")
sys.exit()
else:
print("YES")
else:
print("NO")
```
Yes
| 1,400 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The flag of Berland is such rectangular field n × m that satisfies following conditions:
* Flag consists of three colors which correspond to letters 'R', 'G' and 'B'.
* Flag consists of three equal in width and height stripes, parralel to each other and to sides of the flag. Each stripe has exactly one color.
* Each color should be used in exactly one stripe.
You are given a field n × m, consisting of characters 'R', 'G' and 'B'. Output "YES" (without quotes) if this field corresponds to correct flag of Berland. Otherwise, print "NO" (without quotes).
Input
The first line contains two integer numbers n and m (1 ≤ n, m ≤ 100) — the sizes of the field.
Each of the following n lines consisting of m characters 'R', 'G' and 'B' — the description of the field.
Output
Print "YES" (without quotes) if the given field corresponds to correct flag of Berland . Otherwise, print "NO" (without quotes).
Examples
Input
6 5
RRRRR
RRRRR
BBBBB
BBBBB
GGGGG
GGGGG
Output
YES
Input
4 3
BRG
BRG
BRG
BRG
Output
YES
Input
6 7
RRRGGGG
RRRGGGG
RRRGGGG
RRRBBBB
RRRBBBB
RRRBBBB
Output
NO
Input
4 4
RRRR
RRRR
BBBB
GGGG
Output
NO
Note
The field in the third example doesn't have three parralel stripes.
Rows of the field in the fourth example are parralel to each other and to borders. But they have different heights — 2, 1 and 1.
Submitted Solution:
```
height, width = map(int, input().split())
a = [input() for i in range(height)]
c = {'r': 0, 'g': 0, 'b': 0}
color = {'r': False, 'g': False, 'b': False}
all_lines = True
for i in range(height):
for j in range(width):
color[a[i][j].lower()] = True
for i in range(height):
for j in range(1, width):
if a[i][j] != a[i][j - 1]:
all_lines = False
break
c[a[i][j].lower()] += 1
if not all_lines:
all_lines = True
for key in c.keys():
c[key] = 0
for i in range(width):
for j in range(1, height):
if a[j][i] != a[j - 1][i]:
all_lines = False
break
c[a[j][i].lower()] += 1
if all_lines and c['r'] == c['b'] == c['g'] and color['r'] and color['b'] and color['g']:
print('YES')
else:
print('NO')
```
No
| 1,401 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The flag of Berland is such rectangular field n × m that satisfies following conditions:
* Flag consists of three colors which correspond to letters 'R', 'G' and 'B'.
* Flag consists of three equal in width and height stripes, parralel to each other and to sides of the flag. Each stripe has exactly one color.
* Each color should be used in exactly one stripe.
You are given a field n × m, consisting of characters 'R', 'G' and 'B'. Output "YES" (without quotes) if this field corresponds to correct flag of Berland. Otherwise, print "NO" (without quotes).
Input
The first line contains two integer numbers n and m (1 ≤ n, m ≤ 100) — the sizes of the field.
Each of the following n lines consisting of m characters 'R', 'G' and 'B' — the description of the field.
Output
Print "YES" (without quotes) if the given field corresponds to correct flag of Berland . Otherwise, print "NO" (without quotes).
Examples
Input
6 5
RRRRR
RRRRR
BBBBB
BBBBB
GGGGG
GGGGG
Output
YES
Input
4 3
BRG
BRG
BRG
BRG
Output
YES
Input
6 7
RRRGGGG
RRRGGGG
RRRGGGG
RRRBBBB
RRRBBBB
RRRBBBB
Output
NO
Input
4 4
RRRR
RRRR
BBBB
GGGG
Output
NO
Note
The field in the third example doesn't have three parralel stripes.
Rows of the field in the fourth example are parralel to each other and to borders. But they have different heights — 2, 1 and 1.
Submitted Solution:
```
#python 3.5.2
#Ввод n m и самих цветов
vv = input()
n = int(vv[0:vv.find(' ')])
m = int(vv[vv.find(' '):])
x = ''
for mm in range(n):
x += input()
col = 0
row = 0
res = True
types = 0
if x[0] == x[n*m - m]:
if m % 3 == 0:
col = m//3
row = n
types = 1
else:
res = False
else:
if x[0] == x[m - 1]:
if n%3 == 0:
col = m
row = n//3
types = 2
else:
res = False
else:
res = False
c1 = ''
c2 = ''
c3 = ''
if res:
if types == 1:
for i in range(row):
for j in range(col):
c1 += x[j + m*i]
for i in range(row):
for j in range(col, col*2):
c2 += x[j + m*i]
for i in range(row):
for j in range(col*2, col*3):
c3 += x[j + m*i]
if types == 2:
for i in range(m*n//3):
c1 += x[i]
for i in range(m*n//3, m*n//3*2):
c2 += x[i]
for i in range(m*n//3*2, m*n):
c3 += x[i]
if res:
let = c1[0]
for i in c1:
if i != let:
res = False
break
if res:
let = c2[0]
for i in c2:
if i != let:
res = False
break
if res:
let = c3[0]
for i in c3:
if i != let:
res = False
break
if res:
print('YES')
else:
print('NO')
```
No
| 1,402 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The flag of Berland is such rectangular field n × m that satisfies following conditions:
* Flag consists of three colors which correspond to letters 'R', 'G' and 'B'.
* Flag consists of three equal in width and height stripes, parralel to each other and to sides of the flag. Each stripe has exactly one color.
* Each color should be used in exactly one stripe.
You are given a field n × m, consisting of characters 'R', 'G' and 'B'. Output "YES" (without quotes) if this field corresponds to correct flag of Berland. Otherwise, print "NO" (without quotes).
Input
The first line contains two integer numbers n and m (1 ≤ n, m ≤ 100) — the sizes of the field.
Each of the following n lines consisting of m characters 'R', 'G' and 'B' — the description of the field.
Output
Print "YES" (without quotes) if the given field corresponds to correct flag of Berland . Otherwise, print "NO" (without quotes).
Examples
Input
6 5
RRRRR
RRRRR
BBBBB
BBBBB
GGGGG
GGGGG
Output
YES
Input
4 3
BRG
BRG
BRG
BRG
Output
YES
Input
6 7
RRRGGGG
RRRGGGG
RRRGGGG
RRRBBBB
RRRBBBB
RRRBBBB
Output
NO
Input
4 4
RRRR
RRRR
BBBB
GGGG
Output
NO
Note
The field in the third example doesn't have three parralel stripes.
Rows of the field in the fourth example are parralel to each other and to borders. But they have different heights — 2, 1 and 1.
Submitted Solution:
```
lines = []
m,n = input().split()
for i in range(int(m)):
lines.append(input())
noError = 'YES'
lineInx = 0
direction = 'vert'
for l in lines:
if l[0] != lines[0][0]:
direction = 'gorz'
if direction == 'gorz':
while noError == 'YES' and lineInx < int(m):
if direction == 'gorz':
if lines[lineInx][0] == 'R':
if 'G' in lines[lineInx] or 'B' in lines[lineInx]:
noError = 'NO'
elif lines[lineInx][0] == 'G':
if 'R' in lines[lineInx] or 'B' in lines[lineInx]:
noError = 'NO'
elif lines[lineInx][0] == 'B':
if 'G' in lines[lineInx] or 'R' in lines[lineInx]:
noError = 'NO'
else:
noError = 'NO'
lineInx += 1
else:
for i in range(int(n)):
for j in range(int(m)-1):
if lines[j][i] != lines[j+1][i]:
noError = 'NO'
print(noError)
```
No
| 1,403 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The flag of Berland is such rectangular field n × m that satisfies following conditions:
* Flag consists of three colors which correspond to letters 'R', 'G' and 'B'.
* Flag consists of three equal in width and height stripes, parralel to each other and to sides of the flag. Each stripe has exactly one color.
* Each color should be used in exactly one stripe.
You are given a field n × m, consisting of characters 'R', 'G' and 'B'. Output "YES" (without quotes) if this field corresponds to correct flag of Berland. Otherwise, print "NO" (without quotes).
Input
The first line contains two integer numbers n and m (1 ≤ n, m ≤ 100) — the sizes of the field.
Each of the following n lines consisting of m characters 'R', 'G' and 'B' — the description of the field.
Output
Print "YES" (without quotes) if the given field corresponds to correct flag of Berland . Otherwise, print "NO" (without quotes).
Examples
Input
6 5
RRRRR
RRRRR
BBBBB
BBBBB
GGGGG
GGGGG
Output
YES
Input
4 3
BRG
BRG
BRG
BRG
Output
YES
Input
6 7
RRRGGGG
RRRGGGG
RRRGGGG
RRRBBBB
RRRBBBB
RRRBBBB
Output
NO
Input
4 4
RRRR
RRRR
BBBB
GGGG
Output
NO
Note
The field in the third example doesn't have three parralel stripes.
Rows of the field in the fourth example are parralel to each other and to borders. But they have different heights — 2, 1 and 1.
Submitted Solution:
```
n, m = map(int, input().split())
a = []
for i in range(n):
a.append(input())
f1 = 0
f2 = 0
if n % 3 == 0:
f1 = 1
o1 = a[0][0]
o2 = a[n // 3][0]
o3 = a[2 * n // 3][0]
for i in range(n):
if i < n // 3:
if a[i] != o1 * m:
f1 = 0
break
elif i < 2 * n // 3:
if a[i] != o2 * m:
f1 = 0
break
else:
if a[i] != o3 * m:
f1 = 0
break
if m % 3 == 0:
f2 = 1
o1 = a[0][0]
o2 = a[0][m // 3]
o3 = a[0][2 * m // 3]
for i in range(n):
for j in range(m):
if j < m // 3:
if a[i][j] != o1:
f2 = 0
break
elif i < 2 * m // 3:
if a[i][j] != o2:
f2 = 0
break
else:
if a[i][j] != o3:
f2 = 0
break
if not f2:
break
if f1 or f2:
print("YES")
else:
print("NO")
```
No
| 1,404 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Game field is represented by a line of n square cells. In some cells there are packmen, in some cells there are asterisks and the rest of the cells are empty. Packmen eat asterisks.
Before the game starts you can choose a movement direction, left or right, for each packman. Once the game begins all the packmen simultaneously start moving according their directions. A packman can't change the given direction.
Once a packman enters a cell containing an asterisk, packman immediately eats the asterisk. Once the packman leaves the cell it becomes empty. Each packman moves at speed 1 cell per second. If a packman enters a border cell, the packman stops. Packmen do not interfere with the movement of other packmen; in one cell there can be any number of packmen moving in any directions.
Your task is to assign a direction to each packman so that they eat the maximal number of asterisks. If there are multiple ways to assign directions to eat the maximal number of asterisks, you should choose the way which minimizes the time to do that.
Input
The first line contains integer number n (2 ≤ n ≤ 1 000 000) — the number of cells in the game field.
The second line contains n characters. If the i-th character is '.', the i-th cell is empty. If the i-th character is '*', the i-th cell contains an asterisk. If the i-th character is 'P', the i-th cell contains a packman.
The field contains at least one asterisk and at least one packman.
Output
Print two integer numbers — the maximal number of asterisks packmen can eat and the minimal time to do it.
Examples
Input
6
*.P*P*
Output
3 4
Input
8
*...P..*
Output
1 3
Note
In the first example the leftmost packman should move to the right, the rightmost packman should move to the left. All the asterisks will be eaten, the last asterisk will be eaten after 4 seconds.
Submitted Solution:
```
size = int(input())
board = input()
pos = []
init = ""
i = 0
for char in board:
if char == "P":
pos.append(i)
init += " "
else:
init += char
i += 1
count = len(pos)
##init : "*. * *"
##pos : [2,4]
##count: 2
#size, count
def charchng(text, pos, new):
return text[:pos] + new + text[pos+1:]
def step(dirs, pos, board, ate, time):
for i in range(count):
p = pos[i] + dirs[i]
if p < 0 or p >= size:
continue
pos[i] = p
if board[p] == "*":
board = charchng(board, p, ".")
ate += 1
time += 1
return (board, ate, time)
def evaluate(dirs, pos_, board):
ate = 0
time = 0
maxate = 0
mintime = 0
pos = pos_.copy()
while (time < len(board)) and ("*" in board):
board, ate, time = step(dirs, pos, board, ate, time)
if ate > maxate:
maxate = ate
mintime = time
return maxate, mintime
#sDirs = []
#sPos = []
#sAte = []
#sBoard = []
#sTime = []
dirs = [-1 for i in range(count)]
maxate = 0
mintime = 0
while count > 0:
p = 0
while dirs[p] > 0:
dirs[p] = -1
p += 1
if p == count:
break
if p == count:
break
dirs[p] = 1
ate, time = evaluate(dirs, pos, init)
if ate > maxate:
maxate = ate
mintime = time
elif (ate == maxate) and (time < mintime):
mintime = time
print(str(maxate) + " " + str(mintime))
```
No
| 1,405 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Game field is represented by a line of n square cells. In some cells there are packmen, in some cells there are asterisks and the rest of the cells are empty. Packmen eat asterisks.
Before the game starts you can choose a movement direction, left or right, for each packman. Once the game begins all the packmen simultaneously start moving according their directions. A packman can't change the given direction.
Once a packman enters a cell containing an asterisk, packman immediately eats the asterisk. Once the packman leaves the cell it becomes empty. Each packman moves at speed 1 cell per second. If a packman enters a border cell, the packman stops. Packmen do not interfere with the movement of other packmen; in one cell there can be any number of packmen moving in any directions.
Your task is to assign a direction to each packman so that they eat the maximal number of asterisks. If there are multiple ways to assign directions to eat the maximal number of asterisks, you should choose the way which minimizes the time to do that.
Input
The first line contains integer number n (2 ≤ n ≤ 1 000 000) — the number of cells in the game field.
The second line contains n characters. If the i-th character is '.', the i-th cell is empty. If the i-th character is '*', the i-th cell contains an asterisk. If the i-th character is 'P', the i-th cell contains a packman.
The field contains at least one asterisk and at least one packman.
Output
Print two integer numbers — the maximal number of asterisks packmen can eat and the minimal time to do it.
Examples
Input
6
*.P*P*
Output
3 4
Input
8
*...P..*
Output
1 3
Note
In the first example the leftmost packman should move to the right, the rightmost packman should move to the left. All the asterisks will be eaten, the last asterisk will be eaten after 4 seconds.
Submitted Solution:
```
size = int(input())
board = input()
pos = []
init = ""
i = 0
for char in board:
if char == "P":
pos.append(i)
init += " "
else:
init += char
i += 1
count = len(pos)
##init : "*. * *"
##pos : [2,4]
##count: 2
#size, count
def charchng(text, pos, new):
return text[:pos] + new + text[pos+1:]
def step(dirs, pos, board, ate, time):
for i in range(count):
p = pos[i] + dirs[i]
if p < 0 or p >= size:
continue
pos[i] = p
if board[p] == "*":
board = charchng(board, p, ".")
ate += 1
time += 1
return (board, ate, time)
def evaluate(dirs, pos_, board):
ate = 0
time = 0
maxate = 0
mintime = 0
pos = pos_.copy()
while (time < len(board)) and ("*" in board):
board, ate, time = step(dirs, pos, board, ate, time)
if ate > maxate:
maxate = ate
mintime = time
return maxate, mintime
#sDirs = []
#sPos = []
#sAte = []
#sBoard = []
#sTime = []
dirs = [-1 for i in range(count)]
maxate = 0
mintime = 0
while count > 0:
p = 0
while dirs[p] > 0:
dirs[p] = -1
p += 1
if p == count:
break
if p == count:
break
dirs[p] = 1
ate, time = evaluate(dirs, pos, init)
if ate > maxate:
maxate = ate
mintime = time
elif (ate == maxate) and (time < mintime):
time = mintime
print(str(maxate) + " " + str(mintime))
```
No
| 1,406 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Game field is represented by a line of n square cells. In some cells there are packmen, in some cells there are asterisks and the rest of the cells are empty. Packmen eat asterisks.
Before the game starts you can choose a movement direction, left or right, for each packman. Once the game begins all the packmen simultaneously start moving according their directions. A packman can't change the given direction.
Once a packman enters a cell containing an asterisk, packman immediately eats the asterisk. Once the packman leaves the cell it becomes empty. Each packman moves at speed 1 cell per second. If a packman enters a border cell, the packman stops. Packmen do not interfere with the movement of other packmen; in one cell there can be any number of packmen moving in any directions.
Your task is to assign a direction to each packman so that they eat the maximal number of asterisks. If there are multiple ways to assign directions to eat the maximal number of asterisks, you should choose the way which minimizes the time to do that.
Input
The first line contains integer number n (2 ≤ n ≤ 1 000 000) — the number of cells in the game field.
The second line contains n characters. If the i-th character is '.', the i-th cell is empty. If the i-th character is '*', the i-th cell contains an asterisk. If the i-th character is 'P', the i-th cell contains a packman.
The field contains at least one asterisk and at least one packman.
Output
Print two integer numbers — the maximal number of asterisks packmen can eat and the minimal time to do it.
Examples
Input
6
*.P*P*
Output
3 4
Input
8
*...P..*
Output
1 3
Note
In the first example the leftmost packman should move to the right, the rightmost packman should move to the left. All the asterisks will be eaten, the last asterisk will be eaten after 4 seconds.
Submitted Solution:
```
size = int(input())
board = input()
pos = []
init = ""
i = 0
for char in board:
if char == "P":
pos.append(i)
init += " "
else:
init += char
i += 1
count = len(pos)
##init : "*. * *"
##pos : [2,4]
##count: 2
#size, count
def charchng(text, pos, new):
return text[:pos] + new + text[pos+1:]
def step(dirs, pos, board, ate):
for i in range(count):
p = pos[i] + dirs[i]
if p < 0 or p >= size:
continue
pos[i] = p
if board[p] == "*":
board = charchng(board, p, ".")
ate += 1
return (board, ate)
def evaluate(dirs, pos_, board):
ate = 0
time = 0
maxate = 0
mintime = 0
pos = pos_.copy()
while (time < size) and ("*" in board):
board, ate = step(dirs, pos, board, ate)
time += 1
if ate > maxate:
maxate = ate
mintime = time
return maxate, mintime
#sDirs = []
#sPos = []
#sAte = []
#sBoard = []
#sTime = []
dirs = [-1 for i in range(count)]
maxate = 0
mintime = 0
while count > 0:
p = 0
while dirs[p] > 0:
dirs[p] = -1
p += 1
if p == count:
break
if p == count:
break
dirs[p] = 1
ate, time = evaluate(dirs, pos, init)
if ate > maxate:
maxate = ate
mintime = time
elif (ate == maxate) and (time < mintime):
mintime = time
print(str(maxate) + " " + str(mintime))
```
No
| 1,407 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Priests of the Quetzalcoatl cult want to build a tower to represent a power of their god. Tower is usually made of power-charged rocks. It is built with the help of rare magic by levitating the current top of tower and adding rocks at its bottom. If top, which is built from k - 1 rocks, possesses power p and we want to add the rock charged with power wk then value of power of a new tower will be {wk}p.
Rocks are added from the last to the first. That is for sequence w1, ..., wm value of power will be
<image>
After tower is built, its power may be extremely large. But still priests want to get some information about it, namely they want to know a number called cumulative power which is the true value of power taken modulo m. Priests have n rocks numbered from 1 to n. They ask you to calculate which value of cumulative power will the tower possess if they will build it from rocks numbered l, l + 1, ..., r.
Input
First line of input contains two integers n (1 ≤ n ≤ 105) and m (1 ≤ m ≤ 109).
Second line of input contains n integers wk (1 ≤ wk ≤ 109) which is the power of rocks that priests have.
Third line of input contains single integer q (1 ≤ q ≤ 105) which is amount of queries from priests to you.
kth of next q lines contains two integers lk and rk (1 ≤ lk ≤ rk ≤ n).
Output
Output q integers. k-th of them must be the amount of cumulative power the tower will have if is built from rocks lk, lk + 1, ..., rk.
Example
Input
6 1000000000
1 2 2 3 3 3
8
1 1
1 6
2 2
2 3
2 4
4 4
4 5
4 6
Output
1
1
2
4
256
3
27
597484987
Note
327 = 7625597484987
Submitted Solution:
```
def build():
num = m
for i in range(n):
mods.append(num)
num = phi(num)
def phi(number):
number = int(number)
res = number
if number % 2 == 0:
while number % 2 == 0:
number //= 2
res -= res // 2
for i in range(3, number + 1):
if number % i == 0:
while number % i == 0:
number //= i
res -= res // i
return res
def chained_pow(w, level):
if len(w) == 1:
return int(w[0] % mods[level])
else:
return int(pow(w[0], chained_pow(w[1:], level+1), mods[level]))
mods = []
_ = [int(x) for x in input().split()]
n = _[0]
m = _[1]
a = [int(x) for x in input().split()]
build()
q = int(input())
for __ in range(q):
_q = [int(x) for x in input().split()]
left = _q[0]
right = _q[1]
print(chained_pow(a[left-1:right], 0))
```
No
| 1,408 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Priests of the Quetzalcoatl cult want to build a tower to represent a power of their god. Tower is usually made of power-charged rocks. It is built with the help of rare magic by levitating the current top of tower and adding rocks at its bottom. If top, which is built from k - 1 rocks, possesses power p and we want to add the rock charged with power wk then value of power of a new tower will be {wk}p.
Rocks are added from the last to the first. That is for sequence w1, ..., wm value of power will be
<image>
After tower is built, its power may be extremely large. But still priests want to get some information about it, namely they want to know a number called cumulative power which is the true value of power taken modulo m. Priests have n rocks numbered from 1 to n. They ask you to calculate which value of cumulative power will the tower possess if they will build it from rocks numbered l, l + 1, ..., r.
Input
First line of input contains two integers n (1 ≤ n ≤ 105) and m (1 ≤ m ≤ 109).
Second line of input contains n integers wk (1 ≤ wk ≤ 109) which is the power of rocks that priests have.
Third line of input contains single integer q (1 ≤ q ≤ 105) which is amount of queries from priests to you.
kth of next q lines contains two integers lk and rk (1 ≤ lk ≤ rk ≤ n).
Output
Output q integers. k-th of them must be the amount of cumulative power the tower will have if is built from rocks lk, lk + 1, ..., rk.
Example
Input
6 1000000000
1 2 2 3 3 3
8
1 1
1 6
2 2
2 3
2 4
4 4
4 5
4 6
Output
1
1
2
4
256
3
27
597484987
Note
327 = 7625597484987
Submitted Solution:
```
MOD = 10**9 + 7
def pow( a, b, mod ):
ret = 1
while b > 0:
if b & 1:
ret = ( ret * a ) % mod
a = ( a * a ) % mod
b //= 2
return ( ret )
def phi( n ):
ans = n
i = 2
while i * i <= n:
if n % i == 0:
ans -= ans//i
while n % i == 0:
n //= i
i += 1
if n != 1:
ans -= ans // n
return ( ans )
x = MOD
P = [ x ]
while True:
x = phi(x)
P.append(x)
if x == 1:
break
n, m = list( map( int, input().split() ) )
w = list( map( int, input().split() ) )
q = int( input() )
def solve( left, right, who ):
if P[who] == 1:
return 1
if left == right:
return w[left] % P[who]
ret = pow( w[left], solve(left+1,right,who+1), P[who] )
return ( ret )
for i in range(q):
l, r = list( map( int, input().split() ) )
print( solve(l-1,r-1, 0) )
```
No
| 1,409 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Priests of the Quetzalcoatl cult want to build a tower to represent a power of their god. Tower is usually made of power-charged rocks. It is built with the help of rare magic by levitating the current top of tower and adding rocks at its bottom. If top, which is built from k - 1 rocks, possesses power p and we want to add the rock charged with power wk then value of power of a new tower will be {wk}p.
Rocks are added from the last to the first. That is for sequence w1, ..., wm value of power will be
<image>
After tower is built, its power may be extremely large. But still priests want to get some information about it, namely they want to know a number called cumulative power which is the true value of power taken modulo m. Priests have n rocks numbered from 1 to n. They ask you to calculate which value of cumulative power will the tower possess if they will build it from rocks numbered l, l + 1, ..., r.
Input
First line of input contains two integers n (1 ≤ n ≤ 105) and m (1 ≤ m ≤ 109).
Second line of input contains n integers wk (1 ≤ wk ≤ 109) which is the power of rocks that priests have.
Third line of input contains single integer q (1 ≤ q ≤ 105) which is amount of queries from priests to you.
kth of next q lines contains two integers lk and rk (1 ≤ lk ≤ rk ≤ n).
Output
Output q integers. k-th of them must be the amount of cumulative power the tower will have if is built from rocks lk, lk + 1, ..., rk.
Example
Input
6 1000000000
1 2 2 3 3 3
8
1 1
1 6
2 2
2 3
2 4
4 4
4 5
4 6
Output
1
1
2
4
256
3
27
597484987
Note
327 = 7625597484987
Submitted Solution:
```
def f(r,l):
s=l-r+1
while len(ar[l])<s:
ar[l].append(pow(w[l-len(ar[l])],ar[l][-1],m))
return(ar[l][s-1])
n,m=map(int,input().split())
w=list(map(int,input().split()))
q=int(input())
ar={}
for i in range(q):
r,l=map(int,input().split())
r,l=r-1,l-1
if l not in ar:
ar[l]=[w[l]]
print(f(r,l))
```
No
| 1,410 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Priests of the Quetzalcoatl cult want to build a tower to represent a power of their god. Tower is usually made of power-charged rocks. It is built with the help of rare magic by levitating the current top of tower and adding rocks at its bottom. If top, which is built from k - 1 rocks, possesses power p and we want to add the rock charged with power wk then value of power of a new tower will be {wk}p.
Rocks are added from the last to the first. That is for sequence w1, ..., wm value of power will be
<image>
After tower is built, its power may be extremely large. But still priests want to get some information about it, namely they want to know a number called cumulative power which is the true value of power taken modulo m. Priests have n rocks numbered from 1 to n. They ask you to calculate which value of cumulative power will the tower possess if they will build it from rocks numbered l, l + 1, ..., r.
Input
First line of input contains two integers n (1 ≤ n ≤ 105) and m (1 ≤ m ≤ 109).
Second line of input contains n integers wk (1 ≤ wk ≤ 109) which is the power of rocks that priests have.
Third line of input contains single integer q (1 ≤ q ≤ 105) which is amount of queries from priests to you.
kth of next q lines contains two integers lk and rk (1 ≤ lk ≤ rk ≤ n).
Output
Output q integers. k-th of them must be the amount of cumulative power the tower will have if is built from rocks lk, lk + 1, ..., rk.
Example
Input
6 1000000000
1 2 2 3 3 3
8
1 1
1 6
2 2
2 3
2 4
4 4
4 5
4 6
Output
1
1
2
4
256
3
27
597484987
Note
327 = 7625597484987
Submitted Solution:
```
class Tower:
def __init__(self, n, m):
self.n = n
self.m = m
self.w = []
self.q = 0
def add_w(self, w):
self.w.append(w)
def set_q(self, q):
self.q = q
def ask(self, left, right):
num = right - left + 1
result = 1
for n in range(num):
result = pow(self.w[right - n], result, self.m)
return result
line = input().split(" ")
tower = Tower(int(line[0]), int(line[1]))
line = input().split(" ")
for item in line:
tower.add_w(int(item))
q = int(input())
for i in range(q):
line = input().split(" ")
print(tower.ask(int(line[0]) - 1, int(line[1]) - 1))
```
No
| 1,411 |
Provide a correct Python 3 solution for this coding contest problem.
A sum of p rubles is charged from Arkady's mobile phone account every day in the morning. Among the following m days, there are n days when Arkady will top up the account: in the day di he will deposit ti rubles on his mobile phone account. Arkady will always top up the account before the daily payment will be done. There will be no other payments nor tops up in the following m days.
Determine the number of days starting from the 1-st to the m-th such that the account will have a negative amount on it after the daily payment (i. e. in evening). Initially the account's balance is zero rubles.
Input
The first line contains three integers n, p and m (1 ≤ n ≤ 100 000, 1 ≤ p ≤ 109, 1 ≤ m ≤ 109, n ≤ m) — the number of days Arkady will top up the account, the amount of the daily payment, and the number of days you should check.
The i-th of the following n lines contains two integers di and ti (1 ≤ di ≤ m, 1 ≤ ti ≤ 109) — the index of the day when Arkady will make the i-th top up, and the amount he will deposit on this day. It is guaranteed that the indices of the days are distinct and are given in increasing order, i. e. di > di - 1 for all i from 2 to n.
Output
Print the number of days from the 1-st to the m-th such that the account will have a negative amount on it after the daily payment.
Examples
Input
3 6 7
2 13
4 20
7 9
Output
3
Input
5 4 100
10 70
15 76
21 12
30 100
67 85
Output
26
Note
In the first example the balance will change as following (remember, initially the balance is zero):
1. in the first day 6 rubles will be charged, the balance in the evening will be equal to - 6;
2. in the second day Arkady will deposit 13 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 1;
3. in the third day 6 rubles will be charged, the balance in the evening will be equal to - 5;
4. in the fourth day Arkady will deposit 20 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 9;
5. in the fifth day 6 rubles will be charged, the balance in the evening will be equal to 3;
6. in the sixth day 6 rubles will be charged, the balance in the evening will be equal to - 3;
7. in the seventh day Arkady will deposit 9 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 0.
Thus, in the end of the first, third and sixth days the balance will be negative in the end of the day.
"Correct Solution:
```
n, p, m = input().split()
n = int(n)
p = int(p)
m = int(m)
ans = 0
curb = 0
curd = 1
for i in range(0, n):
#print(curb)
tday, tplus = input().split()
tday = int(tday)
tplus = int(tplus)
if curb < 0:
ans += (tday - curd)
curb -= p * (tday - curd)
elif curb - p * (tday - curd) < 0:
curb -= p * (tday - curd)
x = -curb
xx = x // p
if xx * p < x:
xx += 1
x = xx
ans += x
else:
curb -= p * (tday - curd)
curd = tday
#print(curb)
curb += tplus
tday = m + 1
if curb < 0:
ans += (tday - curd)
curb -= p * (tday - curd)
elif curb - p * (tday - curd) < 0:
curb -= p * (tday - curd)
x = -curb
xx = x // p
if xx * p < x:
xx += 1
x = xx
ans += x
print(ans)
```
| 1,412 |
Provide a correct Python 3 solution for this coding contest problem.
A sum of p rubles is charged from Arkady's mobile phone account every day in the morning. Among the following m days, there are n days when Arkady will top up the account: in the day di he will deposit ti rubles on his mobile phone account. Arkady will always top up the account before the daily payment will be done. There will be no other payments nor tops up in the following m days.
Determine the number of days starting from the 1-st to the m-th such that the account will have a negative amount on it after the daily payment (i. e. in evening). Initially the account's balance is zero rubles.
Input
The first line contains three integers n, p and m (1 ≤ n ≤ 100 000, 1 ≤ p ≤ 109, 1 ≤ m ≤ 109, n ≤ m) — the number of days Arkady will top up the account, the amount of the daily payment, and the number of days you should check.
The i-th of the following n lines contains two integers di and ti (1 ≤ di ≤ m, 1 ≤ ti ≤ 109) — the index of the day when Arkady will make the i-th top up, and the amount he will deposit on this day. It is guaranteed that the indices of the days are distinct and are given in increasing order, i. e. di > di - 1 for all i from 2 to n.
Output
Print the number of days from the 1-st to the m-th such that the account will have a negative amount on it after the daily payment.
Examples
Input
3 6 7
2 13
4 20
7 9
Output
3
Input
5 4 100
10 70
15 76
21 12
30 100
67 85
Output
26
Note
In the first example the balance will change as following (remember, initially the balance is zero):
1. in the first day 6 rubles will be charged, the balance in the evening will be equal to - 6;
2. in the second day Arkady will deposit 13 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 1;
3. in the third day 6 rubles will be charged, the balance in the evening will be equal to - 5;
4. in the fourth day Arkady will deposit 20 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 9;
5. in the fifth day 6 rubles will be charged, the balance in the evening will be equal to 3;
6. in the sixth day 6 rubles will be charged, the balance in the evening will be equal to - 3;
7. in the seventh day Arkady will deposit 9 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 0.
Thus, in the end of the first, third and sixth days the balance will be negative in the end of the day.
"Correct Solution:
```
n,p,m=map(int,input().split())
flag,t_neg,t_in,d,tot=0,0,0,1,0
for i in range (n):
ini_d=d
if flag==1:
tot+=(t-p)
if tot<0:
t_neg+=1
d,t=map(int,input().split())
if flag==0:
t_neg=(d-ini_d)
tot=t_neg*-p
flag=1
else:
tot+=(((d-1)-ini_d)*-p)
if tot<0:
if tot<=(((d-1)-ini_d)*-p):
t_neg+=(d-1)-ini_d
else:
x=int(-tot%p)
y=int(-tot/p)
if x!=0:
t_neg+=(y+1)
else:
t_neg+=y
ini_d=d
tot+=(t-p)
if tot<0:
t_neg+=1
tot+=(((m)-ini_d)*-p)
if tot<0:
if tot<=(((m)-ini_d)*-p):
t_neg+=(m)-ini_d
else:
x=int(-tot%p)
y=int(-tot/p)
if x!=0:
t_neg+=(y+1)
else:
t_neg+=y
print (t_neg)
```
| 1,413 |
Provide a correct Python 3 solution for this coding contest problem.
A sum of p rubles is charged from Arkady's mobile phone account every day in the morning. Among the following m days, there are n days when Arkady will top up the account: in the day di he will deposit ti rubles on his mobile phone account. Arkady will always top up the account before the daily payment will be done. There will be no other payments nor tops up in the following m days.
Determine the number of days starting from the 1-st to the m-th such that the account will have a negative amount on it after the daily payment (i. e. in evening). Initially the account's balance is zero rubles.
Input
The first line contains three integers n, p and m (1 ≤ n ≤ 100 000, 1 ≤ p ≤ 109, 1 ≤ m ≤ 109, n ≤ m) — the number of days Arkady will top up the account, the amount of the daily payment, and the number of days you should check.
The i-th of the following n lines contains two integers di and ti (1 ≤ di ≤ m, 1 ≤ ti ≤ 109) — the index of the day when Arkady will make the i-th top up, and the amount he will deposit on this day. It is guaranteed that the indices of the days are distinct and are given in increasing order, i. e. di > di - 1 for all i from 2 to n.
Output
Print the number of days from the 1-st to the m-th such that the account will have a negative amount on it after the daily payment.
Examples
Input
3 6 7
2 13
4 20
7 9
Output
3
Input
5 4 100
10 70
15 76
21 12
30 100
67 85
Output
26
Note
In the first example the balance will change as following (remember, initially the balance is zero):
1. in the first day 6 rubles will be charged, the balance in the evening will be equal to - 6;
2. in the second day Arkady will deposit 13 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 1;
3. in the third day 6 rubles will be charged, the balance in the evening will be equal to - 5;
4. in the fourth day Arkady will deposit 20 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 9;
5. in the fifth day 6 rubles will be charged, the balance in the evening will be equal to 3;
6. in the sixth day 6 rubles will be charged, the balance in the evening will be equal to - 3;
7. in the seventh day Arkady will deposit 9 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 0.
Thus, in the end of the first, third and sixth days the balance will be negative in the end of the day.
"Correct Solution:
```
n, p, m = map(int, input().split())
lastd = 0
acc = 0
output = 0
neg = 0
for i in range(n):
d, t = map(int, input().split())
acc += (d-lastd-1)*-p
if(acc<0):
output += acc//-p -neg
neg = acc//-p
if(acc%p!=0):
output += 1
neg += 1
acc += t-p
if(acc<0):
output += 1
neg = acc//-p
if(acc%p!=0):
neg += 1
else:
neg = 0
lastd = d
if(d<m):
acc += (m-d)*-p
if(acc<0):
output += acc//-p -neg
if(acc%p!=0): output += 1
print(output)
```
| 1,414 |
Provide a correct Python 3 solution for this coding contest problem.
A sum of p rubles is charged from Arkady's mobile phone account every day in the morning. Among the following m days, there are n days when Arkady will top up the account: in the day di he will deposit ti rubles on his mobile phone account. Arkady will always top up the account before the daily payment will be done. There will be no other payments nor tops up in the following m days.
Determine the number of days starting from the 1-st to the m-th such that the account will have a negative amount on it after the daily payment (i. e. in evening). Initially the account's balance is zero rubles.
Input
The first line contains three integers n, p and m (1 ≤ n ≤ 100 000, 1 ≤ p ≤ 109, 1 ≤ m ≤ 109, n ≤ m) — the number of days Arkady will top up the account, the amount of the daily payment, and the number of days you should check.
The i-th of the following n lines contains two integers di and ti (1 ≤ di ≤ m, 1 ≤ ti ≤ 109) — the index of the day when Arkady will make the i-th top up, and the amount he will deposit on this day. It is guaranteed that the indices of the days are distinct and are given in increasing order, i. e. di > di - 1 for all i from 2 to n.
Output
Print the number of days from the 1-st to the m-th such that the account will have a negative amount on it after the daily payment.
Examples
Input
3 6 7
2 13
4 20
7 9
Output
3
Input
5 4 100
10 70
15 76
21 12
30 100
67 85
Output
26
Note
In the first example the balance will change as following (remember, initially the balance is zero):
1. in the first day 6 rubles will be charged, the balance in the evening will be equal to - 6;
2. in the second day Arkady will deposit 13 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 1;
3. in the third day 6 rubles will be charged, the balance in the evening will be equal to - 5;
4. in the fourth day Arkady will deposit 20 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 9;
5. in the fifth day 6 rubles will be charged, the balance in the evening will be equal to 3;
6. in the sixth day 6 rubles will be charged, the balance in the evening will be equal to - 3;
7. in the seventh day Arkady will deposit 9 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 0.
Thus, in the end of the first, third and sixth days the balance will be negative in the end of the day.
"Correct Solution:
```
rd = lambda: map(int, input().split())
n, p, m = rd()
q, l, r = 0, 0, 0
for i in range(n):
d, t = rd()
c = d - q - 1
r += max(min(c - l // p, c), 0)
l -= p * (c + 1) - t
r += l < 0
q = d
c = m - q
print(r + max(min(c - l // p, c), 0))
```
| 1,415 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A sum of p rubles is charged from Arkady's mobile phone account every day in the morning. Among the following m days, there are n days when Arkady will top up the account: in the day di he will deposit ti rubles on his mobile phone account. Arkady will always top up the account before the daily payment will be done. There will be no other payments nor tops up in the following m days.
Determine the number of days starting from the 1-st to the m-th such that the account will have a negative amount on it after the daily payment (i. e. in evening). Initially the account's balance is zero rubles.
Input
The first line contains three integers n, p and m (1 ≤ n ≤ 100 000, 1 ≤ p ≤ 109, 1 ≤ m ≤ 109, n ≤ m) — the number of days Arkady will top up the account, the amount of the daily payment, and the number of days you should check.
The i-th of the following n lines contains two integers di and ti (1 ≤ di ≤ m, 1 ≤ ti ≤ 109) — the index of the day when Arkady will make the i-th top up, and the amount he will deposit on this day. It is guaranteed that the indices of the days are distinct and are given in increasing order, i. e. di > di - 1 for all i from 2 to n.
Output
Print the number of days from the 1-st to the m-th such that the account will have a negative amount on it after the daily payment.
Examples
Input
3 6 7
2 13
4 20
7 9
Output
3
Input
5 4 100
10 70
15 76
21 12
30 100
67 85
Output
26
Note
In the first example the balance will change as following (remember, initially the balance is zero):
1. in the first day 6 rubles will be charged, the balance in the evening will be equal to - 6;
2. in the second day Arkady will deposit 13 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 1;
3. in the third day 6 rubles will be charged, the balance in the evening will be equal to - 5;
4. in the fourth day Arkady will deposit 20 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 9;
5. in the fifth day 6 rubles will be charged, the balance in the evening will be equal to 3;
6. in the sixth day 6 rubles will be charged, the balance in the evening will be equal to - 3;
7. in the seventh day Arkady will deposit 9 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 0.
Thus, in the end of the first, third and sixth days the balance will be negative in the end of the day.
Submitted Solution:
```
n, p, m = map(int, input().split())
lastd = 0
acc = 0
output = 0
neg = 0
for i in range(n):
d, t = map(int, input().split())
acc += (d-lastd-1)*-p
if(acc<0):
output += acc//-p -neg
neg = acc//-p
if(acc%p!=0):
output += 1
neg += 1
acc += t-p
if(acc<0):
output += 1
neg = acc//-p
if(acc%p!=0):
output += 1
neg += 1
else:
neg = 0
lastd = d
if(d<m):
acc += (m-d)*-p
if(acc<0):
output += acc//-p -neg
if(acc%p!=0): output += 1
print(output)
```
No
| 1,416 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A sum of p rubles is charged from Arkady's mobile phone account every day in the morning. Among the following m days, there are n days when Arkady will top up the account: in the day di he will deposit ti rubles on his mobile phone account. Arkady will always top up the account before the daily payment will be done. There will be no other payments nor tops up in the following m days.
Determine the number of days starting from the 1-st to the m-th such that the account will have a negative amount on it after the daily payment (i. e. in evening). Initially the account's balance is zero rubles.
Input
The first line contains three integers n, p and m (1 ≤ n ≤ 100 000, 1 ≤ p ≤ 109, 1 ≤ m ≤ 109, n ≤ m) — the number of days Arkady will top up the account, the amount of the daily payment, and the number of days you should check.
The i-th of the following n lines contains two integers di and ti (1 ≤ di ≤ m, 1 ≤ ti ≤ 109) — the index of the day when Arkady will make the i-th top up, and the amount he will deposit on this day. It is guaranteed that the indices of the days are distinct and are given in increasing order, i. e. di > di - 1 for all i from 2 to n.
Output
Print the number of days from the 1-st to the m-th such that the account will have a negative amount on it after the daily payment.
Examples
Input
3 6 7
2 13
4 20
7 9
Output
3
Input
5 4 100
10 70
15 76
21 12
30 100
67 85
Output
26
Note
In the first example the balance will change as following (remember, initially the balance is zero):
1. in the first day 6 rubles will be charged, the balance in the evening will be equal to - 6;
2. in the second day Arkady will deposit 13 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 1;
3. in the third day 6 rubles will be charged, the balance in the evening will be equal to - 5;
4. in the fourth day Arkady will deposit 20 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 9;
5. in the fifth day 6 rubles will be charged, the balance in the evening will be equal to 3;
6. in the sixth day 6 rubles will be charged, the balance in the evening will be equal to - 3;
7. in the seventh day Arkady will deposit 9 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 0.
Thus, in the end of the first, third and sixth days the balance will be negative in the end of the day.
Submitted Solution:
```
# -*- coding: utf-8 -*-
"""
Created on Wed Mar 21 21:25:18 2018
@author: Asus
"""
n,p,m = map(int,input().split())
day = [i for i in range(n)]
topup = [i for i in range(n)]
for i in range(n):
day[i],topup[i] = map(int, input().split())
balance = [i for i in range(m)]
for i in range(m):
balance[i] = (i)*(-1*p)
for i in range(n):
for j in range(day[i],m):
balance[j] += topup[i]
ans = 0
for i in range(m):
if(balance[i] < 0):
ans += 1
print(ans)
```
No
| 1,417 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A sum of p rubles is charged from Arkady's mobile phone account every day in the morning. Among the following m days, there are n days when Arkady will top up the account: in the day di he will deposit ti rubles on his mobile phone account. Arkady will always top up the account before the daily payment will be done. There will be no other payments nor tops up in the following m days.
Determine the number of days starting from the 1-st to the m-th such that the account will have a negative amount on it after the daily payment (i. e. in evening). Initially the account's balance is zero rubles.
Input
The first line contains three integers n, p and m (1 ≤ n ≤ 100 000, 1 ≤ p ≤ 109, 1 ≤ m ≤ 109, n ≤ m) — the number of days Arkady will top up the account, the amount of the daily payment, and the number of days you should check.
The i-th of the following n lines contains two integers di and ti (1 ≤ di ≤ m, 1 ≤ ti ≤ 109) — the index of the day when Arkady will make the i-th top up, and the amount he will deposit on this day. It is guaranteed that the indices of the days are distinct and are given in increasing order, i. e. di > di - 1 for all i from 2 to n.
Output
Print the number of days from the 1-st to the m-th such that the account will have a negative amount on it after the daily payment.
Examples
Input
3 6 7
2 13
4 20
7 9
Output
3
Input
5 4 100
10 70
15 76
21 12
30 100
67 85
Output
26
Note
In the first example the balance will change as following (remember, initially the balance is zero):
1. in the first day 6 rubles will be charged, the balance in the evening will be equal to - 6;
2. in the second day Arkady will deposit 13 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 1;
3. in the third day 6 rubles will be charged, the balance in the evening will be equal to - 5;
4. in the fourth day Arkady will deposit 20 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 9;
5. in the fifth day 6 rubles will be charged, the balance in the evening will be equal to 3;
6. in the sixth day 6 rubles will be charged, the balance in the evening will be equal to - 3;
7. in the seventh day Arkady will deposit 9 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 0.
Thus, in the end of the first, third and sixth days the balance will be negative in the end of the day.
Submitted Solution:
```
n, p, m = map(int, input().split())
lastd = 0
acc = 0
output = 0
neg = 0
for i in range(n):
d, t = map(int, input().split())
acc += (d-lastd-1)*-p
if(acc<0):
output += acc//-p -neg
neg = acc//-p
if(acc%p!=0):
output += 1
neg += 1
acc += t-p
if(acc<0):
output += 1
neg = acc//-p
else:
neg = 0
lastd = d
if(d<m):
acc += (m-d)*-p
if(acc<0):
output += acc//-p -neg
if(acc%p!=0): output += 1
print(output)
```
No
| 1,418 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A sum of p rubles is charged from Arkady's mobile phone account every day in the morning. Among the following m days, there are n days when Arkady will top up the account: in the day di he will deposit ti rubles on his mobile phone account. Arkady will always top up the account before the daily payment will be done. There will be no other payments nor tops up in the following m days.
Determine the number of days starting from the 1-st to the m-th such that the account will have a negative amount on it after the daily payment (i. e. in evening). Initially the account's balance is zero rubles.
Input
The first line contains three integers n, p and m (1 ≤ n ≤ 100 000, 1 ≤ p ≤ 109, 1 ≤ m ≤ 109, n ≤ m) — the number of days Arkady will top up the account, the amount of the daily payment, and the number of days you should check.
The i-th of the following n lines contains two integers di and ti (1 ≤ di ≤ m, 1 ≤ ti ≤ 109) — the index of the day when Arkady will make the i-th top up, and the amount he will deposit on this day. It is guaranteed that the indices of the days are distinct and are given in increasing order, i. e. di > di - 1 for all i from 2 to n.
Output
Print the number of days from the 1-st to the m-th such that the account will have a negative amount on it after the daily payment.
Examples
Input
3 6 7
2 13
4 20
7 9
Output
3
Input
5 4 100
10 70
15 76
21 12
30 100
67 85
Output
26
Note
In the first example the balance will change as following (remember, initially the balance is zero):
1. in the first day 6 rubles will be charged, the balance in the evening will be equal to - 6;
2. in the second day Arkady will deposit 13 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 1;
3. in the third day 6 rubles will be charged, the balance in the evening will be equal to - 5;
4. in the fourth day Arkady will deposit 20 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 9;
5. in the fifth day 6 rubles will be charged, the balance in the evening will be equal to 3;
6. in the sixth day 6 rubles will be charged, the balance in the evening will be equal to - 3;
7. in the seventh day Arkady will deposit 9 rubles, then 6 rubles will be charged, the balance in the evening will be equal to 0.
Thus, in the end of the first, third and sixth days the balance will be negative in the end of the day.
Submitted Solution:
```
# -*- coding: utf-8 -*-
"""
Created on Wed Mar 21 21:25:18 2018
@author: Asus
"""
n,p,m = map(int,input().split())
day = [i for i in range(n)]
topup = [i for i in range(n)]
balance = [i for i in range(m)]
ans = 0
for i in range(n):
day[i],topup[i] = map(int, input().split())
for j in range(day[i]-1,m):
balance[j] += topup[i]
for i in range(m):
balance[i] += (i)*(-1*p)
if(balance[i] < 0):
ans += 1
print(ans)
```
No
| 1,419 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jenya has recently acquired quite a useful tool — k-scissors for cutting strings. They are generally used for cutting out two non-intersecting substrings of length k from an arbitrary string s (its length should be at least 2·k in order to perform this operation) and concatenating them afterwards (preserving the initial order). For example, with the help of 2-scissors you can cut ab and de out of abcde and concatenate them into abde, but not ab and bc since they're intersecting.
It's a nice idea to test this tool before using it in practice. After looking through the papers, Jenya came up with two strings s and t. His question is whether it is possible to apply his scissors to string s such that the resulting concatenation contains t as a substring?
Input
The first line contains three integers n, m, k (2 ≤ m ≤ 2·k ≤ n ≤ 5·105) — length of s, length of t and the aforementioned scissors' parameter correspondingly.
The next two lines feature s and t consisting of lowercase latin letters.
Output
If there is no answer, print «No».
Otherwise print «Yes» and two integers L and R denoting the indexes where cutted substrings start (1-indexed). If there are several possible answers, output any.
Examples
Input
7 4 3
baabaab
aaaa
Output
Yes
1 5
Input
6 3 2
cbcbcb
bcc
Output
Yes
2 5
Input
7 5 3
aabbaaa
aaaaa
Output
No
Note
In the first sample case you can cut out two substrings starting at 1 and 5. The resulting string baaaab contains aaaa as a substring.
In the second sample case the resulting string is bccb.
Submitted Solution:
```
n,m,k=map(int,input().split(' '))
line = input()
goal = input()
found = False
for i in range(len(line) - k + 1):
if not found:
for j in range(i + 3, len(line) - k + 1):
test = line[i:i + k] + line[j:j + k]
if goal in test:
print('Yes')
print("%d %d" % (i + 1, j + 1))
found = True
break
if not found:
print('No')
```
No
| 1,420 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jenya has recently acquired quite a useful tool — k-scissors for cutting strings. They are generally used for cutting out two non-intersecting substrings of length k from an arbitrary string s (its length should be at least 2·k in order to perform this operation) and concatenating them afterwards (preserving the initial order). For example, with the help of 2-scissors you can cut ab and de out of abcde and concatenate them into abde, but not ab and bc since they're intersecting.
It's a nice idea to test this tool before using it in practice. After looking through the papers, Jenya came up with two strings s and t. His question is whether it is possible to apply his scissors to string s such that the resulting concatenation contains t as a substring?
Input
The first line contains three integers n, m, k (2 ≤ m ≤ 2·k ≤ n ≤ 5·105) — length of s, length of t and the aforementioned scissors' parameter correspondingly.
The next two lines feature s and t consisting of lowercase latin letters.
Output
If there is no answer, print «No».
Otherwise print «Yes» and two integers L and R denoting the indexes where cutted substrings start (1-indexed). If there are several possible answers, output any.
Examples
Input
7 4 3
baabaab
aaaa
Output
Yes
1 5
Input
6 3 2
cbcbcb
bcc
Output
Yes
2 5
Input
7 5 3
aabbaaa
aaaaa
Output
No
Note
In the first sample case you can cut out two substrings starting at 1 and 5. The resulting string baaaab contains aaaa as a substring.
In the second sample case the resulting string is bccb.
Submitted Solution:
```
n, m, k = map( int, input().split() )
s = input()
t = input()
lt = len(t)
Lmatch = {}
for i in range(0, min(len(t), k) +1):
if i == lt:
p = s.find( t[:i] )
else:
p = s.find( t[:i], k-i )
if p >= 0:
Lmatch[i] = p
else:
break
#print(list(Lmatch.items()))
s_ = s[::-1]
t_ = t[::-1]
Rmatch = {}
for i in range(0, min(len(t_), k) +1):
if i == lt:
p = s_.find( t_[:i] )
else:
p = s_.find( t_[:i], k-i )
if p >= 0:
Rmatch[i] = len(s) -1 -p
else:
break
#print(list(Rmatch.items()))
L, R = None, None
for mL in Lmatch.keys():
#print(mL)
if lt - mL in Rmatch:
#print(' ', lt-mL)
if mL == lt:
a = k - lt
L = max(0, Lmatch[mL] - a)
else:
L = Lmatch[mL] - (k-mL)
R = Rmatch[lt - mL] - (lt -mL) + 1
if R + k > len(s):
R -= R+k - len(s) +1
if R < L + k:
L, R = None, None
else:
break
if not R:
print('No')
else:
print('Yes')
print(L+1, R+1)
```
No
| 1,421 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jenya has recently acquired quite a useful tool — k-scissors for cutting strings. They are generally used for cutting out two non-intersecting substrings of length k from an arbitrary string s (its length should be at least 2·k in order to perform this operation) and concatenating them afterwards (preserving the initial order). For example, with the help of 2-scissors you can cut ab and de out of abcde and concatenate them into abde, but not ab and bc since they're intersecting.
It's a nice idea to test this tool before using it in practice. After looking through the papers, Jenya came up with two strings s and t. His question is whether it is possible to apply his scissors to string s such that the resulting concatenation contains t as a substring?
Input
The first line contains three integers n, m, k (2 ≤ m ≤ 2·k ≤ n ≤ 5·105) — length of s, length of t and the aforementioned scissors' parameter correspondingly.
The next two lines feature s and t consisting of lowercase latin letters.
Output
If there is no answer, print «No».
Otherwise print «Yes» and two integers L and R denoting the indexes where cutted substrings start (1-indexed). If there are several possible answers, output any.
Examples
Input
7 4 3
baabaab
aaaa
Output
Yes
1 5
Input
6 3 2
cbcbcb
bcc
Output
Yes
2 5
Input
7 5 3
aabbaaa
aaaaa
Output
No
Note
In the first sample case you can cut out two substrings starting at 1 and 5. The resulting string baaaab contains aaaa as a substring.
In the second sample case the resulting string is bccb.
Submitted Solution:
```
def getSubString(s, pos1, pos2, k):
return s[pos1 :pos1 + k], s[pos2: pos2 + k]
def solve(n, m, k, s, t):
for i in range(n - 2*k):
for j in range(i + k, n - 1):
s1, s2 = getSubString(s, i, j, k)
if t in s1 + s2: return i, j
return -1
n, m, k = [int(i) for i in input().split()]
s = input()
t = input()
if solve(n, m, k, s, t) == -1: print("No")
else:
print("Yes")
num1, num2 = solve(n, m, k, s, t)
print(str(num1 + 1) + " " + str(num2 + 1))
```
No
| 1,422 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jenya has recently acquired quite a useful tool — k-scissors for cutting strings. They are generally used for cutting out two non-intersecting substrings of length k from an arbitrary string s (its length should be at least 2·k in order to perform this operation) and concatenating them afterwards (preserving the initial order). For example, with the help of 2-scissors you can cut ab and de out of abcde and concatenate them into abde, but not ab and bc since they're intersecting.
It's a nice idea to test this tool before using it in practice. After looking through the papers, Jenya came up with two strings s and t. His question is whether it is possible to apply his scissors to string s such that the resulting concatenation contains t as a substring?
Input
The first line contains three integers n, m, k (2 ≤ m ≤ 2·k ≤ n ≤ 5·105) — length of s, length of t and the aforementioned scissors' parameter correspondingly.
The next two lines feature s and t consisting of lowercase latin letters.
Output
If there is no answer, print «No».
Otherwise print «Yes» and two integers L and R denoting the indexes where cutted substrings start (1-indexed). If there are several possible answers, output any.
Examples
Input
7 4 3
baabaab
aaaa
Output
Yes
1 5
Input
6 3 2
cbcbcb
bcc
Output
Yes
2 5
Input
7 5 3
aabbaaa
aaaaa
Output
No
Note
In the first sample case you can cut out two substrings starting at 1 and 5. The resulting string baaaab contains aaaa as a substring.
In the second sample case the resulting string is bccb.
Submitted Solution:
```
n,m,k=map(int,input().split(' '))
line = input()
goal = input()
found = False
for i in range(len(line) - k + 1):
for j in range(i + 3, len(line) - k + 1):
test = line[i:i + k] + line[j:j + k]
if goal in test:
print('Yes')
print("%d %d" % (i + 1, j + 1))
found = True
break
if not found:
print('No')
```
No
| 1,423 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It's marriage season in Ringland!
Ringland has a form of a circle's boundary of length L. There are n bridegrooms and n brides, and bridegrooms decided to marry brides.
Of course, each bridegroom should choose exactly one bride, and each bride should be chosen by exactly one bridegroom.
All objects in Ringland are located on the boundary of the circle, including the capital, bridegrooms' castles and brides' palaces. The castle of the i-th bridegroom is located at the distance a_i from the capital in clockwise direction, and the palace of the i-th bride is located at the distance b_i from the capital in clockwise direction.
Let's define the inconvenience of a marriage the maximum distance that some bride should walk along the circle from her palace to her bridegroom's castle in the shortest direction (in clockwise or counter-clockwise direction).
Help the bridegrooms of Ringland to choose brides in such a way that the inconvenience of the marriage is the smallest possible.
Input
The first line contains two integers n and L (1 ≤ n ≤ 2 ⋅ 10^{5}, 1 ≤ L ≤ 10^{9}) — the number of bridegrooms and brides and the length of Ringland.
The next line contains n integers a_1, a_2, …, a_n (0 ≤ a_i < L) — the distances from the capital to the castles of bridegrooms in clockwise direction.
The next line contains n integers b_1, b_2, …, b_n (0 ≤ b_i < L) — the distances from the capital to the palaces of brides in clockwise direction.
Output
In the only line print the smallest possible inconvenience of the wedding, where the inconvenience is the largest distance traveled by a bride.
Examples
Input
2 4
0 1
2 3
Output
1
Input
10 100
3 14 15 92 65 35 89 79 32 38
2 71 82 81 82 84 5 90 45 23
Output
27
Note
In the first example the first bridegroom should marry the second bride, the second bridegroom should marry the first bride. This way, the second bride should walk the distance of 1, and the first bride should also walk the same distance. Thus, the inconvenience is equal to 1.
In the second example let p_i be the bride the i-th bridegroom will marry. One of optimal p is the following: (6,8,1,4,5,10,3,2,7,9).
Submitted Solution:
```
print(1)
```
No
| 1,424 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It's marriage season in Ringland!
Ringland has a form of a circle's boundary of length L. There are n bridegrooms and n brides, and bridegrooms decided to marry brides.
Of course, each bridegroom should choose exactly one bride, and each bride should be chosen by exactly one bridegroom.
All objects in Ringland are located on the boundary of the circle, including the capital, bridegrooms' castles and brides' palaces. The castle of the i-th bridegroom is located at the distance a_i from the capital in clockwise direction, and the palace of the i-th bride is located at the distance b_i from the capital in clockwise direction.
Let's define the inconvenience of a marriage the maximum distance that some bride should walk along the circle from her palace to her bridegroom's castle in the shortest direction (in clockwise or counter-clockwise direction).
Help the bridegrooms of Ringland to choose brides in such a way that the inconvenience of the marriage is the smallest possible.
Input
The first line contains two integers n and L (1 ≤ n ≤ 2 ⋅ 10^{5}, 1 ≤ L ≤ 10^{9}) — the number of bridegrooms and brides and the length of Ringland.
The next line contains n integers a_1, a_2, …, a_n (0 ≤ a_i < L) — the distances from the capital to the castles of bridegrooms in clockwise direction.
The next line contains n integers b_1, b_2, …, b_n (0 ≤ b_i < L) — the distances from the capital to the palaces of brides in clockwise direction.
Output
In the only line print the smallest possible inconvenience of the wedding, where the inconvenience is the largest distance traveled by a bride.
Examples
Input
2 4
0 1
2 3
Output
1
Input
10 100
3 14 15 92 65 35 89 79 32 38
2 71 82 81 82 84 5 90 45 23
Output
27
Note
In the first example the first bridegroom should marry the second bride, the second bridegroom should marry the first bride. This way, the second bride should walk the distance of 1, and the first bride should also walk the same distance. Thus, the inconvenience is equal to 1.
In the second example let p_i be the bride the i-th bridegroom will marry. One of optimal p is the following: (6,8,1,4,5,10,3,2,7,9).
Submitted Solution:
```
n,l=map(int,input().split())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
c=[]
d=[]
a.sort()
b.sort()
for i in range(1,n):
x=a[i]-a[i-1]
c.append(x)
for j in range(1,n):
y=b[i]-b[i-1]
d.append(y)
print(max(max(d),max(c)))
```
No
| 1,425 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It's marriage season in Ringland!
Ringland has a form of a circle's boundary of length L. There are n bridegrooms and n brides, and bridegrooms decided to marry brides.
Of course, each bridegroom should choose exactly one bride, and each bride should be chosen by exactly one bridegroom.
All objects in Ringland are located on the boundary of the circle, including the capital, bridegrooms' castles and brides' palaces. The castle of the i-th bridegroom is located at the distance a_i from the capital in clockwise direction, and the palace of the i-th bride is located at the distance b_i from the capital in clockwise direction.
Let's define the inconvenience of a marriage the maximum distance that some bride should walk along the circle from her palace to her bridegroom's castle in the shortest direction (in clockwise or counter-clockwise direction).
Help the bridegrooms of Ringland to choose brides in such a way that the inconvenience of the marriage is the smallest possible.
Input
The first line contains two integers n and L (1 ≤ n ≤ 2 ⋅ 10^{5}, 1 ≤ L ≤ 10^{9}) — the number of bridegrooms and brides and the length of Ringland.
The next line contains n integers a_1, a_2, …, a_n (0 ≤ a_i < L) — the distances from the capital to the castles of bridegrooms in clockwise direction.
The next line contains n integers b_1, b_2, …, b_n (0 ≤ b_i < L) — the distances from the capital to the palaces of brides in clockwise direction.
Output
In the only line print the smallest possible inconvenience of the wedding, where the inconvenience is the largest distance traveled by a bride.
Examples
Input
2 4
0 1
2 3
Output
1
Input
10 100
3 14 15 92 65 35 89 79 32 38
2 71 82 81 82 84 5 90 45 23
Output
27
Note
In the first example the first bridegroom should marry the second bride, the second bridegroom should marry the first bride. This way, the second bride should walk the distance of 1, and the first bride should also walk the same distance. Thus, the inconvenience is equal to 1.
In the second example let p_i be the bride the i-th bridegroom will marry. One of optimal p is the following: (6,8,1,4,5,10,3,2,7,9).
Submitted Solution:
```
L = 100
n = 10
boys = '3 14 15 92 65 35 89 79 32 38'
girls = '2 71 82 81 82 84 5 90 45 23'
boys = boys.split(' ')
girls = girls.split(' ')
boys = sorted([int(i) for i in boys])
girls = sorted([int(i) for i in girls])
out = []
for j in range(n):
out.append(max([min(abs(boys[i] - girls[(i + j) % n]), L - abs(boys[i] - girls[(i + j) % n])) for i in range(n)]))
print(min(out))
```
No
| 1,426 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It's marriage season in Ringland!
Ringland has a form of a circle's boundary of length L. There are n bridegrooms and n brides, and bridegrooms decided to marry brides.
Of course, each bridegroom should choose exactly one bride, and each bride should be chosen by exactly one bridegroom.
All objects in Ringland are located on the boundary of the circle, including the capital, bridegrooms' castles and brides' palaces. The castle of the i-th bridegroom is located at the distance a_i from the capital in clockwise direction, and the palace of the i-th bride is located at the distance b_i from the capital in clockwise direction.
Let's define the inconvenience of a marriage the maximum distance that some bride should walk along the circle from her palace to her bridegroom's castle in the shortest direction (in clockwise or counter-clockwise direction).
Help the bridegrooms of Ringland to choose brides in such a way that the inconvenience of the marriage is the smallest possible.
Input
The first line contains two integers n and L (1 ≤ n ≤ 2 ⋅ 10^{5}, 1 ≤ L ≤ 10^{9}) — the number of bridegrooms and brides and the length of Ringland.
The next line contains n integers a_1, a_2, …, a_n (0 ≤ a_i < L) — the distances from the capital to the castles of bridegrooms in clockwise direction.
The next line contains n integers b_1, b_2, …, b_n (0 ≤ b_i < L) — the distances from the capital to the palaces of brides in clockwise direction.
Output
In the only line print the smallest possible inconvenience of the wedding, where the inconvenience is the largest distance traveled by a bride.
Examples
Input
2 4
0 1
2 3
Output
1
Input
10 100
3 14 15 92 65 35 89 79 32 38
2 71 82 81 82 84 5 90 45 23
Output
27
Note
In the first example the first bridegroom should marry the second bride, the second bridegroom should marry the first bride. This way, the second bride should walk the distance of 1, and the first bride should also walk the same distance. Thus, the inconvenience is equal to 1.
In the second example let p_i be the bride the i-th bridegroom will marry. One of optimal p is the following: (6,8,1,4,5,10,3,2,7,9).
Submitted Solution:
```
n,l=map(int,input().split())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
c=[]
d=[]
for i in range(1,n):
x=a[i]-a[i-1]
c.append(x)
for j in range(1,n):
y=b[i]-b[i-1]
d.append(y)
print(max(max(d),max(c)))
```
No
| 1,427 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
"Correct Solution:
```
s = int(input())
mod = 10**9 + 7
dp = [0]*(s+1)
dp[0] = 1
x = 0
for i in range(1,s+1):
if i >= 3:
x += dp[i-3]
dp[i] = x
print(dp[s]%mod)
```
| 1,428 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
"Correct Solution:
```
ans = [0]*2001
for i in range(3, 6):
ans[i] = 1
for i in range(6, 2001):
tmp = i - 3
ans[i] = (sum(ans[3:tmp+1])+1)%(10**9+7)
print(ans[int(input())])
```
| 1,429 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
"Correct Solution:
```
s = int(input())
mod = 1000000007
dp = [0]*(s+1)
dp[0] = 1
for i in range(3,s+1):
for j in range(i-2):
dp[i] += dp[j]
dp[i] %= mod
print(dp[s])
```
| 1,430 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
"Correct Solution:
```
s = int(input())
MOD = 10**9+7
dp = [0] * (s+1)
dp[0] = 1
for i in range(s+1):
for j in range(0, i-3+1):
dp[i] += dp[j]
dp[i] %= MOD
print(dp[s])
```
| 1,431 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
"Correct Solution:
```
S=int(input())
f=[1,0,0]
for i in range(S-2):f.append(f[i]+f[i+2])
print(f[S]%(10**9+7))
```
| 1,432 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
"Correct Solution:
```
s = int(input())
dp = [0 for _ in range(s+1)]
MOD = 10**9+7
for i in range(3,s+1):
dp[i] = 1
for j in range(3,i-2):
dp[i] += dp[i-j]
dp[i] %= MOD
print(dp[s])
```
| 1,433 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
"Correct Solution:
```
s = int(input())
m = 10**9+7
a = [1,0,0,1,1,1,2]
if s < 7:
print(a[s])
exit()
for i in range(7,s+1):
a.append((sum(a[3:i-2])+1)%m)
print(a[s])
```
| 1,434 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
"Correct Solution:
```
n=int(input())
M=10**9+7
F=[1]
for i in range(1,2001): F+=[i*F[-1]%M]
c=lambda n,r: F[n]*pow(F[r]*F[n-r],M-2,M)%M
a=0
for i in range(n//3):
n-=3
a=(a+c(n+i,n))%M
print(a)
```
| 1,435 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
Submitted Solution:
```
s = int(input())
MOD = 10**9+7
ans = [0 for _ in range(2000)]
for i in range(2, 2000):
ans[i] = (sum(ans[2:i-2]) + 1) % MOD
print(ans[s-1])
```
Yes
| 1,436 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
Submitted Solution:
```
s=int(input())
m=10**9+7
dp=[0]*(s+1)
dp[0]=1
for i in range(1,s+1):
for j in range(0,(i-3)+1):
dp[i]+=dp[j]
dp[i]%=m
print(dp[s])
```
Yes
| 1,437 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
Submitted Solution:
```
S = int(input())
mod = 10 ** 9 + 7
dp = [1, 0, 0]
cnt = 0
for i in range(3, S+1):
cnt = dp[i-1] + dp[i-3]
cnt %= mod
dp.append(cnt)
ans = dp[S]
print(ans)
```
Yes
| 1,438 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
Submitted Solution:
```
N = int(input())
dp=[0]*(N+1)
dp[0]=1
for i in range(1,N+1):
for u in range(i-2):
dp[i]+=dp[u]
print(dp[N]%(10**9+7))
```
Yes
| 1,439 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
Submitted Solution:
```
import sys
n = int(input())
ans = [0]*(n+1) #ans[k]:入力値kでの答え
#初期値３、４、５
ans[3] = 1
ans[4] = 1
ans[5] = 1
if n == 1 or n == 2:
print(0)
sys.exit()
if 3<= n <=5:
print(1)
sys.exit()
for i in range(6,n+1):
start = 3
stop = i-3
s = 1
for j in range(start,stop+1):
s = (s+ans[j]) % (10**9+7)
ans[i] = s
print(ans[-1])
```
No
| 1,440 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
Submitted Solution:
```
M = 10**9+7
S = int(input())
num_list = [0]*(S+1)
num_list[-1] = 1
for idx in reversed(range(S+1)):
if idx-9 > -1:
num_list[idx-9] += num_list[idx]
if idx-8 > -1:
num_list[idx-8] += num_list[idx]
if idx-7 > -1:
num_list[idx-7] += num_list[idx]
if idx-6 > -1:
num_list[idx-6] += num_list[idx]
if idx-5 > -1:
num_list[idx-5] += num_list[idx]
if idx-4 > -1:
num_list[idx-4] += num_list[idx]
if idx-3 > -1:
num_list[idx-3] += num_list[idx]
ans = num_list[0]%M
print(ans)
```
No
| 1,441 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
Submitted Solution:
```
import sys
input=sys.stdin.readline
s=int(input())
INF=10**9+7
def modcomb(n,k,m):
fac=[0]*(n+1)
finv=[0]*(n+1)
inv=[0]*(n+1)
fac[0]=fac[1]=1
finv[0]=finv[1]=1
inv[1]=1
for i in range(2,n+1):
fac[i]=fac[i-1]*i%m
inv[i]=m-inv[m%i]*(m//i)%m
finv[i]=finv[i-1]*inv[i]%m
return fac[n]*(finv[k]*finv[n-k]%m)%m
ans=0
for n in range(1,667):
if s-3*n>=0:
ans=(ans+modcomb(s-2*n-1,n-1,INF))%INF
print(ans)
```
No
| 1,442 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
Submitted Solution:
```
import sys
sys.setrecursionlimit(10**9)
def mi(): return map(int,input().split())
def ii(): return int(input())
def isp(): return input().split()
def deb(text): print("-------\n{}\n-------".format(text))
INF=10**20
class Counting():
def __init__(self,maxim,mod):
maxim += 1
self.mod = mod
self.fact = [0]*maxim
self.fact[0] = 1
for i in range(1,maxim):
self.fact[i] = self.fact[i-1] * i % mod
self.invfact = [0]*maxim
self.invfact[maxim-1] = pow(self.fact[maxim-1],mod-2,mod)
for i in reversed(range(maxim-1)):
self.invfact[i] = self.invfact[i+1] * (i+1) % mod
def nCk(self,n,r):
if n < 0 or n < r: return 0
return self.fact[n] * self.invfact[r] * self.invfact[n-r] % self.mod
def nPk(self,n,r):
if n < 0 or n < r: return 0
return self.fact[n] * self.invfact[n-r] % self.mod
def main():
S=ii()
MOD = 10**9+7
k = 1
ans = 0
C = Counting(10**6,MOD)
while S-3*k > 0:
ans += C.nCk(S-2*k-1,k-1)
ans %= MOD
k += 1
print(ans%MOD)
if __name__ == "__main__":
main()
```
No
| 1,443 |
Provide a correct Python 3 solution for this coding contest problem.
A bracket sequence is a string that is one of the following:
1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /
Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?
Constraints
* 1 \leq N \leq 10^6
* The total length of the strings S_i is at most 10^6.
* S_i is a non-empty string consisting of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S_1
:
S_N
Output
If a bracket sequence can be formed by concatenating all the N strings in some order, print `Yes`; otherwise, print `No`.
Examples
Input
2
)
(()
Output
Yes
Input
2
)(
()
Output
No
Input
4
((()))
((((((
))))))
()()()
Output
Yes
Input
3
(((
)
)
Output
No
"Correct Solution:
```
def f():
N = int(input())
UP = []
DOWN = []
for _ in range(N):
S = input()
c = 0
minC = 0
for s in S:
if s == '(':
c += 1
else:
c -= 1
minC = min(minC, c)
if c >= 0:
UP.append((minC, c))
else:
DOWN.append((c - minC, c))
c = 0
for up in sorted(UP, reverse=True):
if c + up[0] < 0:
return False
c += up[1]
for down in sorted(DOWN, reverse=True):
if c + down[1] - down[0] < 0:
return False
c += down[1]
if c != 0:
return False
return True
if f():
print('Yes')
else:
print('No')
```
| 1,444 |
Provide a correct Python 3 solution for this coding contest problem.
A bracket sequence is a string that is one of the following:
1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /
Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?
Constraints
* 1 \leq N \leq 10^6
* The total length of the strings S_i is at most 10^6.
* S_i is a non-empty string consisting of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S_1
:
S_N
Output
If a bracket sequence can be formed by concatenating all the N strings in some order, print `Yes`; otherwise, print `No`.
Examples
Input
2
)
(()
Output
Yes
Input
2
)(
()
Output
No
Input
4
((()))
((((((
))))))
()()()
Output
Yes
Input
3
(((
)
)
Output
No
"Correct Solution:
```
import sys
input = sys.stdin.readline
n = int(input())
br = [input().rstrip() for i in range(n)]
ls = []
numsum = 0
charge = 0
for i in range(n):
s = br[i]
need = 0
num = 0
for t in s:
if t == "(":
num += 1
else:
num -= 1
need = max(need,-num)
numsum += num
if need == 0:
charge += num
else:
ls.append([need,num])
if numsum != 0:
print("No")
exit()
ls.sort()
l = len(ls)
vis = [0]*l
for i,x in enumerate(ls):
need,num = x
if need <= charge and num >= 0:
charge += num
ls[i][0] = -1
ls.sort(key = lambda x:x[0]+x[1],reverse=True)
for i in range(l):
need,num = ls[i]
if need == -1:
continue
if need > charge:
print("No")
exit()
charge += num
print("Yes")
```
| 1,445 |
Provide a correct Python 3 solution for this coding contest problem.
A bracket sequence is a string that is one of the following:
1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /
Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?
Constraints
* 1 \leq N \leq 10^6
* The total length of the strings S_i is at most 10^6.
* S_i is a non-empty string consisting of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S_1
:
S_N
Output
If a bracket sequence can be formed by concatenating all the N strings in some order, print `Yes`; otherwise, print `No`.
Examples
Input
2
)
(()
Output
Yes
Input
2
)(
()
Output
No
Input
4
((()))
((((((
))))))
()()()
Output
Yes
Input
3
(((
)
)
Output
No
"Correct Solution:
```
N = int(input())
Up = []
Down = []
for _ in range(N):
S = input()
L = [0]
mi = 0
now = 0
for __ in range(len(S)):
if S[__] == '(':
now += 1
else:
now -= 1
mi = min(mi, now)
if now > 0:
Up.append((mi, now))
else:
Down.append((mi - now, mi, now))
Up.sort(reverse=True)
Down.sort()
now = 0
for i, j in Up:
if now + i < 0:
print('No')
exit()
else:
now += j
for _, i, j in Down:
if now + i < 0:
print('No')
exit()
else:
now += j
if now == 0:
print('Yes')
else:
print('No')
```
| 1,446 |
Provide a correct Python 3 solution for this coding contest problem.
A bracket sequence is a string that is one of the following:
1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /
Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?
Constraints
* 1 \leq N \leq 10^6
* The total length of the strings S_i is at most 10^6.
* S_i is a non-empty string consisting of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S_1
:
S_N
Output
If a bracket sequence can be formed by concatenating all the N strings in some order, print `Yes`; otherwise, print `No`.
Examples
Input
2
)
(()
Output
Yes
Input
2
)(
()
Output
No
Input
4
((()))
((((((
))))))
()()()
Output
Yes
Input
3
(((
)
)
Output
No
"Correct Solution:
```
N=int(input())
S=[]
L=0
R=0
for i in range(N):
s=input()
n=len(s)
data=[s[j] for j in range(n)]
l=0
r=0
yabai=float("inf")
for j in range(n):
l+=(s[j]=="(")
r+=(s[j]==")")
yabai=min(l-r,yabai)
S.append([yabai,l-r])
L+=l
R+=r
if L!=R:
print("No")
else:
first=[]
last=[]
for i in range(N):
yabai,gap=S[i]
if gap>0:
first.append(S[i])
else:
last.append([gap-yabai,yabai])
first.sort(reverse=True)
last.sort(reverse=True)
G=0
for i in range(len(first)):
yabai,gap=first[i]
if 0>G+yabai:
print("No")
exit()
else:
G+=gap
for j in range(len(last)):
gapminus,yabai=last[j]
if 0>G+yabai:
print("No")
break
else:
G+=gapminus+yabai
else:
print("Yes")
```
| 1,447 |
Provide a correct Python 3 solution for this coding contest problem.
A bracket sequence is a string that is one of the following:
1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /
Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?
Constraints
* 1 \leq N \leq 10^6
* The total length of the strings S_i is at most 10^6.
* S_i is a non-empty string consisting of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S_1
:
S_N
Output
If a bracket sequence can be formed by concatenating all the N strings in some order, print `Yes`; otherwise, print `No`.
Examples
Input
2
)
(()
Output
Yes
Input
2
)(
()
Output
No
Input
4
((()))
((((((
))))))
()()()
Output
Yes
Input
3
(((
)
)
Output
No
"Correct Solution:
```
n = int(input())
left = []
mid = []
midminus = []
right = []
L = []
R = []
for i in range(n):
s = input()
l = 0
r = 0
for x in s:
if x == '(':
l += 1
else:
if l > 0:
l -= 1
else:
r += 1
if l > 0 and r == 0:
left.append((l, r))
elif l > 0 and r > 0:
if l > r:
mid.append((r, l)) # a,b-a
else:
midminus.append((r,l))
elif l == 0 and r > 0:
right.append((l, r))
L.append(l)
R.append(r)
if sum(L) != sum(R):
print('No')
exit()
A = 0
B = 0
for x in left:
A += x[0]
for x in right:
B += x[1]
mid = sorted(mid, key=lambda x: (x[0],-x[1]))
midminus = sorted(midminus,key= lambda x:x[0]-x[1])
mid += midminus
l = A
r = 0
for a, b in mid:
if l < a:
print('No')
exit()
l -= a
l += b
print('Yes')
```
| 1,448 |
Provide a correct Python 3 solution for this coding contest problem.
A bracket sequence is a string that is one of the following:
1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /
Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?
Constraints
* 1 \leq N \leq 10^6
* The total length of the strings S_i is at most 10^6.
* S_i is a non-empty string consisting of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S_1
:
S_N
Output
If a bracket sequence can be formed by concatenating all the N strings in some order, print `Yes`; otherwise, print `No`.
Examples
Input
2
)
(()
Output
Yes
Input
2
)(
()
Output
No
Input
4
((()))
((((((
))))))
()()()
Output
Yes
Input
3
(((
)
)
Output
No
"Correct Solution:
```
N = int(input())
#INF = float('inf')
def check(A):
th = 0 #高さの合計
for i in range(len(A)):
b = A[i][0]
h = A[i][1]
if th + b < 0:
return False
else:
th += h
return True
L = []
R = []
goukei = 0
for i in range(N):
temp = str(input())
b= 0 #最下点
h = 0 #ゴールの位置
for j in range(len(temp)):
if temp[j] == "(":
h += 1
else:
h -= 1
b = min(b,h)
if h > 0:
L.append([b,h])
else:
R.append([b-h,-h])
goukei += h
L.sort(reverse=True)
R.sort(reverse=True)
#print(L,R)
if check(L) and check(R) and goukei == 0:
print("Yes")
else:
print("No")
```
| 1,449 |
Provide a correct Python 3 solution for this coding contest problem.
A bracket sequence is a string that is one of the following:
1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /
Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?
Constraints
* 1 \leq N \leq 10^6
* The total length of the strings S_i is at most 10^6.
* S_i is a non-empty string consisting of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S_1
:
S_N
Output
If a bracket sequence can be formed by concatenating all the N strings in some order, print `Yes`; otherwise, print `No`.
Examples
Input
2
)
(()
Output
Yes
Input
2
)(
()
Output
No
Input
4
((()))
((((((
))))))
()()()
Output
Yes
Input
3
(((
)
)
Output
No
"Correct Solution:
```
import sys
input = sys.stdin.readline
N = int(input())
D, E = [], []
t,l = 0, 0
res = 0
for _ in range(N):
S = input().rstrip()
x,y = 0,0
for s in S:
if s=="(": x+=1
else: x=max(x-1,0)
for s in reversed(S):
if s==")": y+=1
else: y=max(y-1,0)
D.append((x,y))
D.sort(key=lambda x:x[1])
t = 0
for x,y in D:
if x-y>=0:
if t>=y: t+=x-y
else: print("No"); exit()
D.sort(key=lambda x:x[0])
s = 0
for x,y in D:
if y-x>=0:
if s>=x: s+=y-x
else: print("No"); exit()
if t!=s: print("No")
else: print("Yes")
```
| 1,450 |
Provide a correct Python 3 solution for this coding contest problem.
A bracket sequence is a string that is one of the following:
1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /
Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?
Constraints
* 1 \leq N \leq 10^6
* The total length of the strings S_i is at most 10^6.
* S_i is a non-empty string consisting of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S_1
:
S_N
Output
If a bracket sequence can be formed by concatenating all the N strings in some order, print `Yes`; otherwise, print `No`.
Examples
Input
2
)
(()
Output
Yes
Input
2
)(
()
Output
No
Input
4
((()))
((((((
))))))
()()()
Output
Yes
Input
3
(((
)
)
Output
No
"Correct Solution:
```
n = int(input())
ls, rs = [], []
def check(sl):
h = 0
for t in sl:
b = h + t[0]
if b < 0:
return False
h += t[1]
return True
total = 0
for i in range(n):
b, h = 0, 0
S = input()
for s in S:
if s == '(':
h += 1
else:
h -= 1
b = min(b, h)
if h > 0:
ls.append((b, h))
else:
rs.append((b - h, -h))
total += h
ls.sort(key=lambda x: x[0], reverse=True)
rs.sort(key=lambda x: x[0], reverse=True)
print('Yes' if check(ls) and check(rs) and total == 0 else 'No')
```
| 1,451 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A bracket sequence is a string that is one of the following:
1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /
Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?
Constraints
* 1 \leq N \leq 10^6
* The total length of the strings S_i is at most 10^6.
* S_i is a non-empty string consisting of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S_1
:
S_N
Output
If a bracket sequence can be formed by concatenating all the N strings in some order, print `Yes`; otherwise, print `No`.
Examples
Input
2
)
(()
Output
Yes
Input
2
)(
()
Output
No
Input
4
((()))
((((((
))))))
()()()
Output
Yes
Input
3
(((
)
)
Output
No
Submitted Solution:
```
from sys import exit
from itertools import accumulate,chain
n,*s=open(0).read().split()
t=[2*(i.count("("))-len(i) for i in s]
if sum(t)!=0:
print("No");exit()
#pypyではinitialだめ
st=[[t_,min(accumulate(s_,lambda a,b: a+(1 if b=="(" else -1),initial=0))] for s_,t_ in zip(s,t)]
now=0
v=list(filter(lambda x:x[0]>=0,st))
w=list(filter(lambda x:x[0]<0,st))
v.sort(reverse=True,key=lambda z:z[1])
w.sort(key=lambda z:z[0]-z[1],reverse=True)
for sub in chain(v,w):
if now+sub[1]<0:
print("No");exit()
now+=sub[0]
print("Yes")
```
Yes
| 1,452 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A bracket sequence is a string that is one of the following:
1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /
Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?
Constraints
* 1 \leq N \leq 10^6
* The total length of the strings S_i is at most 10^6.
* S_i is a non-empty string consisting of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S_1
:
S_N
Output
If a bracket sequence can be formed by concatenating all the N strings in some order, print `Yes`; otherwise, print `No`.
Examples
Input
2
)
(()
Output
Yes
Input
2
)(
()
Output
No
Input
4
((()))
((((((
))))))
()()()
Output
Yes
Input
3
(((
)
)
Output
No
Submitted Solution:
```
N=int(input())
if N==0:
print("Yes")
exit()
P=[]
M=[]
for i in range(N):
s=input()
f=0
m=0
cnt=0
for j in range(len(s)):
if s[j]=="(":
cnt+=1
else:
cnt-=1
if cnt<m:
m=cnt
if cnt>=0:
P.append([m,cnt])
else:
M.append([m-cnt,-cnt])
P.sort(reverse=True)
M.sort(reverse=True)
#print(P)
#print(M)
SUM=0
for i,j in P:
SUM+=j
for i,j in M:
SUM-=j
if SUM!=0:
print("No")
exit()
SUMP=0
for i,j in P:
if SUMP>=(-i):
SUMP+=j
else:
print("No")
exit()
SUMM=0
for i,j in M:
if SUMM>=(-i):
SUMM+=j
else:
print("No")
exit()
print("Yes")
```
Yes
| 1,453 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A bracket sequence is a string that is one of the following:
1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /
Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?
Constraints
* 1 \leq N \leq 10^6
* The total length of the strings S_i is at most 10^6.
* S_i is a non-empty string consisting of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S_1
:
S_N
Output
If a bracket sequence can be formed by concatenating all the N strings in some order, print `Yes`; otherwise, print `No`.
Examples
Input
2
)
(()
Output
Yes
Input
2
)(
()
Output
No
Input
4
((()))
((((((
))))))
()()()
Output
Yes
Input
3
(((
)
)
Output
No
Submitted Solution:
```
n = int(input())
s = [input() for _ in range(n)]
def bracket(x):
# f: final sum of brackets '(':+1, ')': -1
# m: min value of f
f = m = 0
for i in range(len(x)):
if x[i] == '(':
f += 1
else:
f -= 1
m = min(m, f)
# m <= 0
return f, m
def func(l):
# l = [(f, m)]
l.sort(key=lambda x: -x[1])
v = 0
for fi, mi in l:
if v + mi >= 0:
v += fi
else:
return -1
return v
l1 = []
l2 = []
for i in range(n):
fi, mi = bracket(s[i])
if fi >= 0:
l1.append((fi, mi))
else:
l2.append((-fi, mi - fi))
v1 = func(l1)
v2 = func(l2)
if v1 == -1 or v2 == -1:
ans = 'No'
else:
ans = 'Yes' if v1 == v2 else 'No'
print(ans)
```
Yes
| 1,454 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A bracket sequence is a string that is one of the following:
1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /
Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?
Constraints
* 1 \leq N \leq 10^6
* The total length of the strings S_i is at most 10^6.
* S_i is a non-empty string consisting of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S_1
:
S_N
Output
If a bracket sequence can be formed by concatenating all the N strings in some order, print `Yes`; otherwise, print `No`.
Examples
Input
2
)
(()
Output
Yes
Input
2
)(
()
Output
No
Input
4
((()))
((((((
))))))
()()()
Output
Yes
Input
3
(((
)
)
Output
No
Submitted Solution:
```
import sys
input = lambda: sys.stdin.readline().rstrip()
N = int(input())
def I():
s = input()
mi = 0
su = 0
t = 0
for a in s:
if a == "(":
t += 1
else:
t -= 1
mi = min(mi, t)
return (mi, t)
X = [I() for _ in range(N)]
if sum([x[1] for x in X]):
print("No")
exit()
X = sorted(X, key = lambda x: -10**10 if x[0] == 0 else -10**9 - x[0] if x[1] > 0 else x[0] - x[1])
T = 0
for mi, t in X:
if T + mi < 0:
print("No")
exit()
T += t
print("Yes")
```
Yes
| 1,455 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A bracket sequence is a string that is one of the following:
1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /
Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?
Constraints
* 1 \leq N \leq 10^6
* The total length of the strings S_i is at most 10^6.
* S_i is a non-empty string consisting of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S_1
:
S_N
Output
If a bracket sequence can be formed by concatenating all the N strings in some order, print `Yes`; otherwise, print `No`.
Examples
Input
2
)
(()
Output
Yes
Input
2
)(
()
Output
No
Input
4
((()))
((((((
))))))
()()()
Output
Yes
Input
3
(((
)
)
Output
No
Submitted Solution:
```
# import sys
# input = sys.stdin.readline
def solve():
N = int(input())
brackets_gen = (input() for _ in range(N))
grads_positive = list()
grads_negative = list()
for brackets in brackets_gen:
elevation, bottom = 0, 0
for bk in brackets:
elevation += 1 if bk == '(' else -1
bottom = min(bottom, elevation)
if elevation >= 0:
grads_positive.append((bottom, elevation))
elif elevation < 0:
grads_negative.append((bottom - elevation, -elevation))
grads_positive.sort(reverse=True)
grads_negative.sort()
def is_good(grads):
elevation, bottom = 0, 0
for grad in grads:
bottom = elevation + grad[0]
if bottom < 0:
return False
elevation += grad[1]
if elevation == 0:
return True
else:
return False
if is_good(grads_positive) and is_good(grads_negative):
return True
else:
return False
def main():
ok = solve()
if ok:
print('Yes')
else:
print('No')
if __name__ == "__main__":
main()
```
No
| 1,456 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A bracket sequence is a string that is one of the following:
1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /
Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?
Constraints
* 1 \leq N \leq 10^6
* The total length of the strings S_i is at most 10^6.
* S_i is a non-empty string consisting of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S_1
:
S_N
Output
If a bracket sequence can be formed by concatenating all the N strings in some order, print `Yes`; otherwise, print `No`.
Examples
Input
2
)
(()
Output
Yes
Input
2
)(
()
Output
No
Input
4
((()))
((((((
))))))
()()()
Output
Yes
Input
3
(((
)
)
Output
No
Submitted Solution:
```
def main():
N = int(input())
S = []
for i in range(N):
_ = input()
S.append([ _.count('(') - _.count(')'), _ ])
if sum([S[_][0] for _ in range(N)]) != 0:
print('No')
return
S.sort(reverse=True)
cnt = 0
for s in S:
for c in s[1]:
cnt += c.count('(') - c.count(')')
if cnt < 0:
print('No')
return
print('Yes')
if __name__ == "__main__":
main()
```
No
| 1,457 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A bracket sequence is a string that is one of the following:
1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /
Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?
Constraints
* 1 \leq N \leq 10^6
* The total length of the strings S_i is at most 10^6.
* S_i is a non-empty string consisting of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S_1
:
S_N
Output
If a bracket sequence can be formed by concatenating all the N strings in some order, print `Yes`; otherwise, print `No`.
Examples
Input
2
)
(()
Output
Yes
Input
2
)(
()
Output
No
Input
4
((()))
((((((
))))))
()()()
Output
Yes
Input
3
(((
)
)
Output
No
Submitted Solution:
```
import heapq
N=int(input())
S = [input() for _ in range(N)]
p1 = 0
p2 = []
p3 = []
for i,s in enumerate(S):
depth = 0
max_depth = 0
min_depth = 0
for chr in s:
if chr=='(':
depth += 1
if depth > max_depth:
max_depth = depth
else:
depth -= 1
if depth < min_depth:
min_depth = depth
if depth >= 0 and min_depth >= 0:
p1 += depth
elif depth > 0 and min_depth < 0:
p2.append((min_depth,depth))
else:
p3.append((min_depth,depth))
pp2 = sorted(p2,reverse=True)
pp3 = sorted(p3,reverse=True)
# print(p1)
# print(p2)
# print(p3)
depth = p1
for p in pp2:
if depth+p[0] < 0:
print('No')
exit()
depth += p[1]
for p in pp3:
if depth+p[0] < 0:
print('No')
exit()
depth += p[1]
if depth != 0:
print('No')
else:
print('Yes')
```
No
| 1,458 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A bracket sequence is a string that is one of the following:
1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /
Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?
Constraints
* 1 \leq N \leq 10^6
* The total length of the strings S_i is at most 10^6.
* S_i is a non-empty string consisting of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S_1
:
S_N
Output
If a bracket sequence can be formed by concatenating all the N strings in some order, print `Yes`; otherwise, print `No`.
Examples
Input
2
)
(()
Output
Yes
Input
2
)(
()
Output
No
Input
4
((()))
((((((
))))))
()()()
Output
Yes
Input
3
(((
)
)
Output
No
Submitted Solution:
```
import sys
n=int(input())
s=[input() for i in range(n)]
t=[2*(i.count("("))-len(i) for i in s]
if sum(t)!=0:
print("No")
sys.exit()
st=list(map(list,zip(s,t)))
for i in range(n):
u=st[i][0]
l=len(u)
now,mi=0,0
for j in range(l):
if u[j]=="(":
now+=1
else:
now-=1
mi=min(mi,now)
st[i].append(mi)
st.sort(reverse=True,key=lambda z:z[1])
st.sort(reverse=True,key=lambda z:z[2])
now2=0
for i in range(n):
if now2+st[i][2]<0:
print("No")
break
now2+=st[i][1]
else:
print("Yes")
```
No
| 1,459 |
Provide a correct Python 3 solution for this coding contest problem.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
"Correct Solution:
```
n = int(input())
C = list(map(int, input().split()))
mod = 10**9 + 7
if n == 1:
ans = 2 * C[0]
ans %= mod
print(ans)
exit()
ans = 0
pattern = 2 ** (n-1) % mod
d = 2 ** (n-2) % mod
C.sort(reverse=True)
for c in C:
ans += (c * pattern) % mod
pattern += d
pattern %= mod
ans %= mod
print(ans*(2**n) % mod)
```
| 1,460 |
Provide a correct Python 3 solution for this coding contest problem.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
"Correct Solution:
```
import sys
input = sys.stdin.readline
N = int(input())
a = list(map(int, input().split()))
a.sort(reverse = True)
mod = 10 ** 9 + 7
res = 0
if N == 1:
print(a[0] * 2 % mod)
exit(0)
for i in range(N):
res += a[i] * (pow(2, N - 1, mod) % mod + pow(2, N - 2, mod) * i % mod) % mod
res %= mod
print(res * pow(2, N, mod) % mod)
```
| 1,461 |
Provide a correct Python 3 solution for this coding contest problem.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
"Correct Solution:
```
import sys
readline = sys.stdin.readline
MOD = 10**9+7
N = int(readline())
C = list(map(int, readline().split()))
C.sort()
ans = 0
for i in range(N):
ans = (ans + pow(2, 2*N-2, MOD)*C[i]*(N-i+1))%MOD
print(ans)
```
| 1,462 |
Provide a correct Python 3 solution for this coding contest problem.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
"Correct Solution:
```
import sys,bisect
input = sys.stdin.readline
n = int(input())
c = list(map(int,input().split()))
c.sort()
mod = 10**9+7
se = pow(2,mod-2,mod)
res = 0
for i,e in enumerate(c):
cnt = (pow(4,n,mod)%mod)*se%mod
res = (res + (e*cnt))%mod
res = (res + (e*pow(4,n-1,mod)%mod)*(n-1-i)%mod)%mod
print(res%mod)
```
| 1,463 |
Provide a correct Python 3 solution for this coding contest problem.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
"Correct Solution:
```
MOD = 10 ** 9 + 7
N = int(input())
C = list(map(int, input().split()))
C.sort()
if N == 1:
print (2 * C[0] % MOD)
exit()
lst = [0] * (N + 3)
lst[0] = 1
for i in range(1, N + 3):
lst[i] = (lst[i - 1] * 2) % MOD
ANS = 0
for i, c in enumerate(C):
ANS += c * (N + 1 - i)
ANS *= lst[N - 2]
ANS %= MOD
ANS *= lst[N]
print (ANS % MOD)
```
| 1,464 |
Provide a correct Python 3 solution for this coding contest problem.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
"Correct Solution:
```
mod=10**9+7
n=int(input())
arr=list(map(int,input().split()))
arr=sorted(arr)
ans=0
if n==1:
print((2*arr[0])%mod)
else:
table=[1]
for _ in range(n):
tmp=table[-1]*2
tmp%=mod
table.append(tmp)
for i in range(n):
if i==n-1:
ans+=(table[i-1]*(n-i+1)*arr[i])%mod
else:
ans+=(table[i]*(n-i+1)*table[n-i-2]*arr[i])%mod
print((ans*table[n])%mod)
```
| 1,465 |
Provide a correct Python 3 solution for this coding contest problem.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
"Correct Solution:
```
N = int(input())
C = [int(c) for c in input().split()]
C.sort()
MOD = 10**9+7
p2 = [1]
for i in range(2*N+10):
p2 += [p2[-1]*2%MOD]
ans = 0
for i in range(N):
m = (p2[N-1-i]+(N-i-1)*p2[N-i-2])*C[i]
# print(m)
m = m*p2[N+i]%MOD
ans += m
print(ans%MOD)
```
| 1,466 |
Provide a correct Python 3 solution for this coding contest problem.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
"Correct Solution:
```
mod = 10**9+7
n = int(input())
c = [int(x) for x in input().split()]
c = sorted(c)
ans = 0
pow2 = [1]
for i in range(n+1):
tmp = (pow2[-1]*2)%mod
pow2.append(tmp)
for i in range(n):
ans += pow2[n]*pow2[i]*((n-1-i)*pow2[n-2-i] + pow2[n-1-i])*c[i]
ans %= mod
print(ans)
```
| 1,467 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
Submitted Solution:
```
N = int(input())
C = sorted(list(map(int,input().split())))[::-1]
ans = 0
MOD = 10**9 + 7
for k in range(N):
ans += pow(2,2*N-2,MOD)*(k+2)*C[k]
print(ans%MOD)
```
Yes
| 1,468 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
Submitted Solution:
```
M=1000000007
N=int(input())
C=sorted(map(int,input().split()),reverse=True)
def pow(x,p):
if(p==0):
return 1;
if(p%2):
a=pow(x,p-1)%M;
return x*a%M
else:
a=pow(x,p//2)%M
return a*a%M
ans=0;
p2=pow(2,2*N-2)%M
for k in range(N):
ans=(ans+(C[k]*((p2*k)%M+2*p2))%M)%M
print(ans)
```
Yes
| 1,469 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
Submitted Solution:
```
MOD=10**9+7
N=int(input())
C=sorted(map(int,input().split()))
p=pow(4,N-1,MOD)
ans=0
for i in range(N):
res=p*C[i]*(N-i+1)
ans=(ans+res)%MOD
print(ans)
```
Yes
| 1,470 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
Submitted Solution:
```
MOD=10**9+7
N=int(input())
if N==1:
C=int(input())
print(2*C%MOD)
exit()
C=list(map(int, input().split()))
C.sort(reverse=True)
out=0
tmp1=pow(2, N-1, MOD)
tmp2=pow(2, N-2, MOD)
for i in range(N):
out+=(tmp1+tmp2*i)*C[i]
out%=MOD
out=out*pow(2, N, MOD)
print(int(out%MOD))
```
Yes
| 1,471 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
Submitted Solution:
```
import sys
sys.setrecursionlimit(10**6)
N = int(input())
C = list(map(int, input().split()))
C.sort()
MOD = 10**9 + 7
ans = 0
# どうも公式ドキュメントによると、組み込み関数のpowの第三引数に値渡すとMODとってくれるらしいので、完全に無駄
def pow_mod(x, n, mod):
if n == 0:
return 1 % mod
elif n % 2 == 0:
y = pow_mod(x, n//2, mod)
return y * y % MOD
else:
return x * pow_mod(x, n-1, mod) % mod
for i in range(N):
# 詳細は開設動画の通りだが、i桁目の右にr個の数字、左にlこの数字がある
l = i
r = N - i - 1
# i桁目の寄与が C[i] * 2**l * (2**r + r * 2**(r-1))で、最後に2**Nをかける（Tのとり方が2**Nこあるので）
# -> C[i] * 2**l * (2**(N+r) + r * 2**(r+N-1))
ans += ((C[i] * pow_mod(2, l, MOD)) % MOD * (pow_mod(2, N+r, MOD) + r * pow_mod(2, N+r-1, MOD))) % MOD
ans %= MOD
print(ans)
```
No
| 1,472 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
Submitted Solution:
```
n = int(input())
c = list(map(int, input().split()))
mod = 10**9 + 7
c.sort()
ans = 0
for i in range(n):
ans += c[i] * pow(2, i, mod) % mod * (pow(2, n-i-1, mod) * (n-i) + pow(2, n-i, mod) ) % mod * pow(2, n, mod) % mod
ans %= mod
print(ans)
```
No
| 1,473 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
Submitted Solution:
```
import sys
import math
import fractions
import bisect
import queue
import heapq
from collections import deque
sys.setrecursionlimit(4100000)
MOD = int(1e9+7)
PI = 3.14159265358979323846264338327950288
INF = 1e18
'''
1行のint
N, K = map(int, input().split())
1行のstring
S, T = input().split()
1行の整数配列
P = list(map(int,input().split()))
改行あり
x = []
y = []
for i in range(N):
x1,y1=[int(i) for i in input().split()]
x.append(x1)
y.append(y1)
N行M列の初期化
dp = [[INF] * M for i in range(N)]
'''
N = int(input())
C = list(map(int,input().split()))
# コストの小さいものから更新していけばいい
C.sort()
# 2のべき乗は先に計算しておく
beki = []
for i in range(3*N+20):
beki.append(int(math.pow(2, i))%MOD)
ans = 0
for i in range(N):
ans += (C[i] * beki[2*N-2] * (N-i+1))%MOD
print(ans % MOD)
```
No
| 1,474 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
Submitted Solution:
```
number=10**9+7
n=int(input())
c=list(map(int, input().split()))
c.sort(reverse=True)
sum=0
for i in range(1, n+1):
sum=(sum+(4**(n-1))*(i+1)*c[i-1])%number
print(sum)
```
No
| 1,475 |
Provide a correct Python 3 solution for this coding contest problem.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0
"Correct Solution:
```
a,b,c= map(int,input().split())
t = min(a-b,c)
print(c-t)
```
| 1,476 |
Provide a correct Python 3 solution for this coding contest problem.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0
"Correct Solution:
```
a,b,c=map(int,input().split())
print(b+c-a if b+c-a>=0 else 0)
```
| 1,477 |
Provide a correct Python 3 solution for this coding contest problem.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0
"Correct Solution:
```
A,B,C=map(int,input().split());print(max(0,C-A+B))
```
| 1,478 |
Provide a correct Python 3 solution for this coding contest problem.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0
"Correct Solution:
```
a,b,c=map(int,input().split())
print(b+c-a if a<b+c else 0)
```
| 1,479 |
Provide a correct Python 3 solution for this coding contest problem.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0
"Correct Solution:
```
A,B,C = [int(v) for v in input().split()]
print(max(C-(A-B),0))
```
| 1,480 |
Provide a correct Python 3 solution for this coding contest problem.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0
"Correct Solution:
```
a,b,c=map(int,input().split())
v=b+c-a
print(v if v>0 else 0)
```
| 1,481 |
Provide a correct Python 3 solution for this coding contest problem.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0
"Correct Solution:
```
A,B,C=map(int,input().split())
tmp=max(0,C-(A-B))
print(tmp)
```
| 1,482 |
Provide a correct Python 3 solution for this coding contest problem.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0
"Correct Solution:
```
A, B, C = map(int, input().split(' '))
print(max(C - (A - B), 0))
```
| 1,483 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0
Submitted Solution:
```
a,b,c = list(map(int,input().split(" ")))
print(max(0, c -a+b))
```
Yes
| 1,484 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0
Submitted Solution:
```
a = list(map(int,input().split()))
print(max(0,a[2]-(a[0]-a[1])))
```
Yes
| 1,485 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0
Submitted Solution:
```
a,b,c=map(int,input().split())
print(abs(min(a-b-c,0)))
```
Yes
| 1,486 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0
Submitted Solution:
```
A,B,C=map(int,input().split())
print(C-min(C,A-B))
```
Yes
| 1,487 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0
Submitted Solution:
```
BottleOne = int(input())
BottleTwo = int(input())
BottleThree = int(input())
ans = int((BottleThree+BottleTwo)) - int((BottleOne))
print(int(ans))
```
No
| 1,488 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0
Submitted Solution:
```
# チートシート
a, b, c = map(int, input().split())
tmp = a-b
print(c-tmp)
```
No
| 1,489 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0
Submitted Solution:
```
A, B, C = [int(i) for i in input().split(" ")]
print(C-A+B if C-A+B else 0)
```
No
| 1,490 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0
Submitted Solution:
```
def main():
n = int(input())
h = list(map(int, input().split()))
pre = 0
flag = True
for i in range(n):
if h[i] - 1 >= pre:
h[i] -= -1
if h[i] < pre:
flag = False
break
pre = h[i]
if flag:
print('Yes')
else:
print('No')
if __name__ == '__main__':
main()
```
No
| 1,491 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N consisting of `A`, `C`, `G` and `T`. Answer the following Q queries:
* Query i (1 \leq i \leq Q): You will be given integers l_i and r_i (1 \leq l_i < r_i \leq N). Consider the substring of S starting at index l_i and ending at index r_i (both inclusive). In this string, how many times does `AC` occurs as a substring?
Constraints
* 2 \leq N \leq 10^5
* 1 \leq Q \leq 10^5
* S is a string of length N.
* Each character in S is `A`, `C`, `G` or `T`.
* 1 \leq l_i < r_i \leq N
Input
Input is given from Standard Input in the following format:
N Q
S
l_1 r_1
:
l_Q r_Q
Output
Print Q lines. The i-th line should contain the answer to the i-th query.
Example
Input
8 3
ACACTACG
3 7
2 3
1 8
Output
2
0
3
"Correct Solution:
```
n, q = map(int, input().split())
s = input()
a = [0, 0]
for i in range(2, n + 1):
a.append(a[i - 1] + (s[i - 2:i] == 'AC'))
for _ in range(q):
li, ri = map(int, input().split())
print(a[ri] - a[li])
```
| 1,492 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N consisting of `A`, `C`, `G` and `T`. Answer the following Q queries:
* Query i (1 \leq i \leq Q): You will be given integers l_i and r_i (1 \leq l_i < r_i \leq N). Consider the substring of S starting at index l_i and ending at index r_i (both inclusive). In this string, how many times does `AC` occurs as a substring?
Constraints
* 2 \leq N \leq 10^5
* 1 \leq Q \leq 10^5
* S is a string of length N.
* Each character in S is `A`, `C`, `G` or `T`.
* 1 \leq l_i < r_i \leq N
Input
Input is given from Standard Input in the following format:
N Q
S
l_1 r_1
:
l_Q r_Q
Output
Print Q lines. The i-th line should contain the answer to the i-th query.
Example
Input
8 3
ACACTACG
3 7
2 3
1 8
Output
2
0
3
"Correct Solution:
```
n,q = map(int,input().split())
s = input()
t = [0] * (n+1)
for i in range(n):
t[i+1] = t[i] + (1 if s[i:i+2] == 'AC' else 0)
#print (t)
for _ in range(q):
l,r = map(int,input().split())
print (t[r-1]-t[l-1])
```
| 1,493 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N consisting of `A`, `C`, `G` and `T`. Answer the following Q queries:
* Query i (1 \leq i \leq Q): You will be given integers l_i and r_i (1 \leq l_i < r_i \leq N). Consider the substring of S starting at index l_i and ending at index r_i (both inclusive). In this string, how many times does `AC` occurs as a substring?
Constraints
* 2 \leq N \leq 10^5
* 1 \leq Q \leq 10^5
* S is a string of length N.
* Each character in S is `A`, `C`, `G` or `T`.
* 1 \leq l_i < r_i \leq N
Input
Input is given from Standard Input in the following format:
N Q
S
l_1 r_1
:
l_Q r_Q
Output
Print Q lines. The i-th line should contain the answer to the i-th query.
Example
Input
8 3
ACACTACG
3 7
2 3
1 8
Output
2
0
3
"Correct Solution:
```
n,q=map(int,input().split())
s=input()
a = [0] * n
num = 0
for i in range(1, n):
if s[i]=='C' and s[i-1]=='A':
num += 1
a[i] = num
for _ in range(q):
l,r=map(int,input().split())
print(a[r-1] - a[l-1])
```
| 1,494 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N consisting of `A`, `C`, `G` and `T`. Answer the following Q queries:
* Query i (1 \leq i \leq Q): You will be given integers l_i and r_i (1 \leq l_i < r_i \leq N). Consider the substring of S starting at index l_i and ending at index r_i (both inclusive). In this string, how many times does `AC` occurs as a substring?
Constraints
* 2 \leq N \leq 10^5
* 1 \leq Q \leq 10^5
* S is a string of length N.
* Each character in S is `A`, `C`, `G` or `T`.
* 1 \leq l_i < r_i \leq N
Input
Input is given from Standard Input in the following format:
N Q
S
l_1 r_1
:
l_Q r_Q
Output
Print Q lines. The i-th line should contain the answer to the i-th query.
Example
Input
8 3
ACACTACG
3 7
2 3
1 8
Output
2
0
3
"Correct Solution:
```
n, q = (int(x) for x in input().split())
s = input()
t = [0]*(n+1)
for i in range(n):
t[i+1] = t[i] + (1 if s[i : i + 2] == 'AC' else 0)
for i in range(q):
l,r = (int(x) for x in input().split())
print(t[r-1]-t[l-1])
```
| 1,495 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N consisting of `A`, `C`, `G` and `T`. Answer the following Q queries:
* Query i (1 \leq i \leq Q): You will be given integers l_i and r_i (1 \leq l_i < r_i \leq N). Consider the substring of S starting at index l_i and ending at index r_i (both inclusive). In this string, how many times does `AC` occurs as a substring?
Constraints
* 2 \leq N \leq 10^5
* 1 \leq Q \leq 10^5
* S is a string of length N.
* Each character in S is `A`, `C`, `G` or `T`.
* 1 \leq l_i < r_i \leq N
Input
Input is given from Standard Input in the following format:
N Q
S
l_1 r_1
:
l_Q r_Q
Output
Print Q lines. The i-th line should contain the answer to the i-th query.
Example
Input
8 3
ACACTACG
3 7
2 3
1 8
Output
2
0
3
"Correct Solution:
```
n, q = map(int, input().split())
s=input()
d=[0]*n
c=0
for i in range(n-1):
if s[i:i+2]=="AC":
c+=1
d[i+1]=c
for i in range(q):
l,r= map(int, input().split())
print(d[r-1]-d[l-1])
```
| 1,496 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N consisting of `A`, `C`, `G` and `T`. Answer the following Q queries:
* Query i (1 \leq i \leq Q): You will be given integers l_i and r_i (1 \leq l_i < r_i \leq N). Consider the substring of S starting at index l_i and ending at index r_i (both inclusive). In this string, how many times does `AC` occurs as a substring?
Constraints
* 2 \leq N \leq 10^5
* 1 \leq Q \leq 10^5
* S is a string of length N.
* Each character in S is `A`, `C`, `G` or `T`.
* 1 \leq l_i < r_i \leq N
Input
Input is given from Standard Input in the following format:
N Q
S
l_1 r_1
:
l_Q r_Q
Output
Print Q lines. The i-th line should contain the answer to the i-th query.
Example
Input
8 3
ACACTACG
3 7
2 3
1 8
Output
2
0
3
"Correct Solution:
```
n, q = map(int, input().split())
s = input()
a = [list(map(int, input().split())) for i in range(q)]
c = [0] * n
for i in range(1,n):
c[i] = c[i-1] + (s[i-1]+s[i] == 'AC')
for x in a:
print(c[x[1]-1]-c[x[0]-1])
```
| 1,497 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N consisting of `A`, `C`, `G` and `T`. Answer the following Q queries:
* Query i (1 \leq i \leq Q): You will be given integers l_i and r_i (1 \leq l_i < r_i \leq N). Consider the substring of S starting at index l_i and ending at index r_i (both inclusive). In this string, how many times does `AC` occurs as a substring?
Constraints
* 2 \leq N \leq 10^5
* 1 \leq Q \leq 10^5
* S is a string of length N.
* Each character in S is `A`, `C`, `G` or `T`.
* 1 \leq l_i < r_i \leq N
Input
Input is given from Standard Input in the following format:
N Q
S
l_1 r_1
:
l_Q r_Q
Output
Print Q lines. The i-th line should contain the answer to the i-th query.
Example
Input
8 3
ACACTACG
3 7
2 3
1 8
Output
2
0
3
"Correct Solution:
```
n,q=map(int,input().split())
s=input()
l=[list(map(int,input().split())) for i in range(q)]
L=[0];ct=0
for i in range(n-1):
if s[i:i+2]=='AC':
ct+=1
L.append(ct)
for j in range(q):
print(L[l[j][1]-1]-L[l[j][0]-1])
```
| 1,498 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N consisting of `A`, `C`, `G` and `T`. Answer the following Q queries:
* Query i (1 \leq i \leq Q): You will be given integers l_i and r_i (1 \leq l_i < r_i \leq N). Consider the substring of S starting at index l_i and ending at index r_i (both inclusive). In this string, how many times does `AC` occurs as a substring?
Constraints
* 2 \leq N \leq 10^5
* 1 \leq Q \leq 10^5
* S is a string of length N.
* Each character in S is `A`, `C`, `G` or `T`.
* 1 \leq l_i < r_i \leq N
Input
Input is given from Standard Input in the following format:
N Q
S
l_1 r_1
:
l_Q r_Q
Output
Print Q lines. The i-th line should contain the answer to the i-th query.
Example
Input
8 3
ACACTACG
3 7
2 3
1 8
Output
2
0
3
"Correct Solution:
```
n, q = map(int, input().split())
S = input()
t = [0] * (n + 1)
for i in range(n):
t[i + 1] = t[i] + (1 if S[i : i+2] == "AC" else 0)
for i in range(q):
l, r = map(int, input().split())
print(t[r-1] - t[l-1])
```
| 1,499 |
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