qyliang/CodeNanoFix huggingface dataset:
Title: Crossing Thin Ice

Problem:
On a cold winter day, JOI Taro decided to play by breaking thin ice spread across a rectangular plaza. The plaza is divided into m by n sections, with some sections having thin ice and others not. Taro follows specific rules while moving through the sections:
- He can start breaking ice from any section with thin ice.
- He can move to an adjacent section (north, south, east, or west) with unbroken thin ice.
- He must break the thin ice in the section he moves to.

Create a program to find the maximum number of sections Taro can move through while breaking thin ice. Constraints: 1 ≤ m ≤ 90, 1 ≤ n ≤ 90. The number of possible movements in the input data does not exceed 200,000.

Input:
The input consists of multiple datasets. Each dataset is in the following format:
- The first line contains the integer m.
- The second line contains the integer n.
- The next n lines (3rd to n+2nd) each contain m integers separated by spaces, representing the presence (1) or absence (0) of thin ice in each section.

The input ends when both m and n are 0. There are at most 5 datasets.

Output:
For each dataset, output the maximum number of sections Taro can move through on a single line.

Input/Output Examples:
(Examples of input and output are provided in the original text.)

Note: The problem description and test data used for automatic judgment are created and published by the Information Olympiad Japan Committee.

# Buggy version:
def s():
 def b(M,x,y,n=1):
  M[x][y]=0;a=n
  if M[x-1][y]:
   t=b(M,x-1,y,n+1)
   if a<t:a=t
  if M[x][y-1]:
   t=b(M,x,y-1,n+1)
   if a<t:a=t
  if M[x+1][y]:
   t=b(M,x+1,y+1,n+1)
   if a<t:a=t
  if M[x][y+1]:
   t=b(M,x,y+1,n+1)
   if a<t:a=t
  M[x][y]=1
  return a
 for e in iter(input,'0'):
  n,m=int(e),int(input())
  P=[[0]*(n+2)for _ in[0]*(m+2)]
  for i in range(m):P[i+1][1:-1]=map(int,input().split())
  print(max(b(P,i,j)for i in range(1,m+1)for j in range(1,n+1)if P[i][j]))
if'__main__'==__name__:s()


# Fixed version:
def s():
 def b(M,x,y,n=1):
  M[x][y]=0;a=n
  if M[x-1][y]:
   t=b(M,x-1,y,n+1)
   if a<t:a=t
  if M[x][y-1]:
   t=b(M,x,y-1,n+1)
   if a<t:a=t
  if M[x+1][y]:
   t=b(M,x+1,y,n+1)
   if a<t:a=t
  if M[x][y+1]:
   t=b(M,x,y+1,n+1)
   if a<t:a=t
  M[x][y]=1
  return a
 for e in iter(input,'0'):
  n,m=int(e),int(input())
  P=[[0]*(n+2)for _ in[0]*(m+2)]
  for i in range(m):
   P[i+1][1:-1]=map(int,input().split())
  a=0
  for i in range(1,m+1):
   for j in range(1,n+1):
    if P[i][j]:
     t=b(P,i,j)
     if a<t:a=t
  print(a)
if'__main__'==__name__:s()
Title: Bingo

Problem:
In a programming contest, it is customary to play a bingo game during the post-competition social gathering. However, the bingo cards used in this game are somewhat special and are created according to the following conditions:
- The bingo card is divided into N rows and N columns, with each cell containing a unique positive integer.
- The integers in the cells range from 1 to M.
- The sum of all N×N integers on the bingo card is S.
- When viewing any column, the integers are arranged in ascending order from top to bottom.
- Each integer in any cell is greater than any integer to its left in the same row.

An example of a bingo card for N = 5, M = 50, and S = 685 is provided.

Objective:
For the social gathering, we want to create as many bingo cards as possible that satisfy the above conditions. However, the same card cannot be created more than twice. Create a program to output the maximum number of bingo cards that can be created, divided by 100000 and the remainder.

Input:
The input consists of multiple datasets. Each dataset is given in the following format:
A single line containing three positive integers separated by spaces: N (1≤N≤7), the upper limit of integers written in the cells M (1≤M≤2000), and the total sum of integers written on the bingo card S (1≤S≤3000). For any given input data, it is possible to create at least one bingo card that satisfies the conditions.
The input ends when N, M, and S are all 0. The number of datasets does not exceed 5.

Output:
For each dataset, output the maximum number of bingo cards that can be created, divided by 100000 and the remainder, on a single line.

Input/Output Example:
Input:
3 9 45
3 100 50
5 50 685
0 0 0

Output:
1
7
74501

For the third input example, the maximum number of bingo cards that can be created is 642499974501, so the output is the remainder when divided by 100000, which is 74501.

# Buggy version:
def listrep(n,m,s):
    tab = [[[0]*(s+1) for j in range(n+1)]
    tab[0][0] = 1
    for i in range(1,n+1):
        for k in range(s+1):
            if i <= k:
                tab[i][k] += tab[i][k-i] + tab[i-1][k-i]
            if j-1 >= m:
                tab[i][k] -= tab[i-1][j-1-m]
    return tab[n][m][s]

while True:
    n,m,s = map(int,input().split())
    if n == 0 : break
    n *= n
    print(listrep(n,m,s))

# Fixed version:
def listrep(n,m,s):
    tab = [[0]*(s+1) for j in range(n+1)]
    tab[0][0] = 1
    for i in range(1,n+1):
        for k in range(s+1):
            if i <= k:
                tab[i][k] += tab[i][k-i] + tab[i-1][k-i]
            if k-1 >= m:
                tab[i][k] -= tab[i-1][k-1-m]
            tab[i][k] %= 100000
    return tab[n][s]

while True:
    n,m,s = map(int,input().split())
    if n == 0 : break
    n *= n
    print(listrep(n,m,s))
Title: Card Arrangement

Problem:
Hanako is playing with n cards (4 ≤ n ≤ 10). Each card has a unique integer between 1 and 99 written on it. Hanako selects k cards (2 ≤ k ≤ 4) from the set and arranges them in a row to form an integer. How many different integers can Hanako create in total?

For example, given 5 cards with numbers 1, 2, 3, 13, 21, and selecting 3 cards, Hanako can create the integer 2113 by arranging 2, 1, 13 or 21, 1, 3. Different combinations of cards may produce the same integer.

Write a program to determine the total number of integers that can be formed by selecting k cards from the given n cards and arranging them in a row.

Input:
The input consists of multiple datasets. Each dataset is formatted as follows:
- Each dataset consists of 2+n lines.
- The first line contains the number of cards, n (4 ≤ n ≤ 10).
- The second line contains the number of cards to be selected, k (2 ≤ k ≤ 4).
- The following n lines (2+i, where 1 ≤ i ≤ n) contain integers (1 to 99) written on the i-th card.

The input ends when both n and k are 0. The number of datasets does not exceed 5.

Output:
For each dataset, output the total number of integers Hanako can create on a single line.

Input/Output Example:
Input:
4
2
1
2
12
1
6
3
72
2
12
7
2
1
0
0

Output:
7
68

In the first example, from the 4 cards with numbers 1, 2, 12, 1, Hanako can select 2 cards and create 7 different integers: 11, 12, 21, 112, 121, 122, 212.

# Buggy version:
from itertools import permutations as P
import sys
r=sys.stdin.readline
for e in iter(r,'0\n'):
 n,k=int(e),int(r())
 C=[r()for _ in[0]*n]
 print(len(set(''.join(s)for s in P(C,k))))


# Fixed version:
from itertools import permutations as P
import sys
r=sys.stdin.readline
for e in iter(r,'0\n'):
 n,k=int(e),int(r())
 C=[r()[:-1]for _ in[0]*n]
 print(len(set(''.join(s)for s in P(C,k))))
Title: Soccer

Problem:
In the JOI country, soccer is popular, and the JOI League, a weekly league, is held. N teams are part of the JOI League, numbered from 1 to N. Each team plays every other team exactly once, resulting in N × (N - 1) / 2 matches. The outcome of each match is determined by the points earned by each team. A winning team earns 3 points, a losing team earns 0 points, and in case of a draw, both teams earn 1 point. Rankings are based on the total points earned by each team, without considering goal differences. In case of equal points, teams are ranked higher. Given the results of all matches, create a program to determine the ranking of each team.

Input:
The first line of the input file contains the number of teams, N (2 ≤ N ≤ 100). The following N × (N - 1) / 2 lines contain the results of each match. Each line (1 ≤ i ≤ N × (N - 1) / 2) contains integers A_i, B_i, C_i, D_i (1 ≤ A_i ≤ N, 1 ≤ B_i ≤ N, 0 ≤ C_i ≤ 100, 0 ≤ D_i ≤ 100), representing a match between teams A_i and B_i, where A_i scored C_i points and B_i scored D_i points. No match is repeated.

Output:
The output consists of N lines, each containing a single integer representing the ranking of each team.

Example:
Input
4
1 2 0 1
1 3 2 1
1 4 2 2
2 3 1 1
2 4 3 0
3 4 1 3

Output
2
1
4
2

# Buggy version:
t = int(input())
point_l = [0 for i in range(t)]
for i in range((t*(t-1))/2):
    input_line = input()
    tmp = [int(x) for x in input_line.rstrip().split(' ')]
    if tmp[2] > tmp[3]:
        point_l[tmp[0]-1] += 3
    elif tmp[3] > tmp[2]:
        point_l[tmp[1]-1] += 3
    elif tmp[2] == tmp[3]:
        point_l[tmp[0]-1] += 1
        point_l[tmp[1]-1] += 1

rank_l = [0 for i in range(t)]
rank = 1
for l in sorted(point_l, reverse=True):
    dup = point_l.count(l)
    for j in range(dup):
        rank_l[point_l.index(l)] += rank
        point_l[point_l.index(l)] = -1
    rank += dup

for l in rank_l:
    print(l)

# Fixed version:
t = int(input())
point_l = [0 for i in range(t)]
for i in range(int(t*(t-1)/2)):
    tmp = [int(x) for x in input().split()]
    if tmp[2] > tmp[3]:
        point_l[tmp[0]-1] += 3
    elif tmp[3] > tmp[2]:
        point_l[tmp[1]-1] += 3
    elif tmp[2] == tmp[3]:
        point_l[tmp[0]-1] += 1
        point_l[tmp[1]-1] += 1

rank_l = [0 for i in range(t)]
rank = 1
for l in sorted(point_l, reverse=True):
    dup = point_l.count(l)
    for j in range(dup):
        rank_l[point_l.index(l)] += rank
        point_l[point_l.index(l)] = -1
    rank += dup

for l in rank_l:
    print(l)
Title: Pasta

Problem:
You love pasta and have it for dinner every day. You can make three types of pasta: tomato sauce, cream sauce, and basil sauce.

You want to plan dinner for N days. Each day, you choose one type of pasta. However, you shouldn't choose the same pasta for more than three consecutive days. Also, K days of pasta are already decided within the N days.

Input:
The input consists of K + 1 lines.
The first line contains two integers N and K (3 ≤ N ≤ 100, 1 ≤ K ≤ N).
The following K lines each contain two integers Ai and Bi (1 ≤ Ai ≤ N, 1 ≤ Bi ≤ 3), where Ai represents the day and Bi represents the type of pasta (1 for tomato, 2 for cream, 3 for basil). All Ai values are distinct.

Output:
Output the number of possible dinner plans that satisfy the conditions, modulo 10000.

Example:
Input
5 3
3 1
1 1
4 2

Output
6

In this example, you need to plan dinner for 5 days. On days 1 and 3, you have tomato sauce, and on day 4, you have cream sauce. There are 6 possible dinner plans that satisfy the conditions.

Note: The source of the problem statement and test data used for automatic judgment is provided by the Information Olympiad Japan Committee.

# Buggy version:
N,K=map(int,input().split())
S=[0]*N
for _ in[0]*K:
 a,b=map(int,input().split())
 S[a-1]=b-1
dp=[0]*9
st,nd=S[:2]
if st+1:
 if nd+1:dp[st*3+nd]=1
 else:dp[st*3:-~st*3]=[1]*3
elif nd+1:dp[nd::3]=[1]*3
else:dp=[1]*9
print(dp)
for i in range(2,N):
 cur=S[i];tmp=[0]*9
 if cur+1:
  for k in range(3):tmp[k*3+cur]=sum(dp[k::3])-dp[cur*4]*(k==cur)
 else:
  for cur in range(3):
   for k in range(3):tmp[k*3+cur]=sum(dp[k::3])-dp[cur*4]*(k==cur)
 dp=tmp[:]
print(sum(dp)%10000)


# Fixed version:
N,K=map(int,input().split())
S=[-1]*N
for _ in[0]*K:a,b=map(int,input().split());S[a-1]=b-1
dp=[0]*9
st,nd=S[:2]
if st+1:
 if nd+1:dp[st*3+nd]=1
 else:dp[st*3:st*4]=[1]*3
elif nd+1:dp[nd::3]=[1]*3
else:dp=[1]*9
for i in range(2,N):
 cur=S[i];tmp=[0]*9
 if cur+1:
  for k in range(3):tmp[k*3+cur]=sum(dp[k::3])-dp[cur*4]*(k==cur)
 else:
  for cur in range(3):
   for k in range(3):tmp[k*3+cur]=sum(dp[k::3])-dp[cur*4]*(k==cur)
 dp=tmp[:]
print(sum(dp)%10000)
Title: Homework

Problem:
JOI has always struggled with his winter homework. This time, he plans to execute it systematically. His homework consists of language and math drills, with A pages for language and B pages for math.

JOI can complete a maximum of C pages of language and D pages of math in a day, but he can't play on days when he does homework. Winter break lasts for L days, and JOI must finish his homework during this time. Create a program to determine the maximum number of days JOI can play during the winter break.

Input:
The input consists of 5 lines, each containing a positive integer.
- Line 1: Integer L (2 ≤ L ≤ 40) representing the number of days in winter break.
- Line 2: Integer A (1 ≤ A ≤ 1000) representing the number of pages for the language drill.
- Line 3: Integer B (1 ≤ B ≤ 1000) representing the number of pages for the math drill.
- Line 4: Integer C (1 ≤ C ≤ 100) representing the maximum pages of language drill JOI can do in a day.
- Line 5: Integer D (1 ≤ D ≤ 100) representing the maximum pages of math drill JOI can do in a day.

Output:
Output the maximum number of days JOI can play during the winter break in a single line.

Input/Output Examples:
Input 1:
20
25
30
6
8

Output 1:
15

Input 2:
15
32
48
4
6

Output 2:
7

Note: The input data ensures that JOI will definitely finish his homework during the winter break and will have at least one day to play.

# Buggy version:
import math
l = [input() for i in range(5)]
print l[0] - int(max(math.ceil(l[1]/l[3]), math.ceil(l[2]/l[4])))

# Fixed version:
import math

l = [int(input()) for i in range(5)]
d = max( math.ceil(l[1]/l[3]), math.ceil(l[2]/l[4]))
print(l[0]-d)
Title: Unique Number Game

Problem:
JOI and his friends decide to play a game. The game involves N players. In each round, each player submits an integer between 1 and 100. A player earns points if no one else submits the same number. They play this game three times. Create a program to calculate the total points earned by each player over the three rounds.

Input:
The input consists of 1 + N lines. The first line contains an integer N (2 ≤ N ≤ 200), representing the number of players. The next N lines (1 ≤ i ≤ N) each contain three integers separated by spaces, representing the numbers submitted by the i-th player in the first, second, and third rounds.

Output:
The output consists of N lines. Each line (1 ≤ i ≤ N) contains an integer representing the total points earned by the i-th player over the three rounds.

Example:
Input
5
100 99 98
100 97 92
63 89 63
99 99 99
89 97 98

Output
0
92
215
198
89

In the first example, the total points earned by each player are as follows:
Player 1: 0 + 0 + 0 = 0
Player 2: 0 + 0 + 92 = 92
Player 3: 63 + 89 + 63 = 215
Player 4: 99 + 0 + 99 = 198
Player 5: 89 + 0 + 0 = 89

Input
3
89 92 77
89 92 63
89 63 77

Output
0
63
63

# Buggy version:
n = int(input())

lst = [list(map(int,input().split())) for i in range(n)]
p = [0 for i in range(n)]
for i in range(3):
  dic = [[] for _ in range(101)]
  for j in range(n):
    print(lst)
    dic[lst[j][i]].append(j)
  for x in range(101):
    l = dic[x]
    if lst:
      if len(l) == 1:
        p[l[0]] += x
for i in p:
  print(i)


# Fixed version:
n = int(input())

lst = [list(map(int,input().split())) for i in range(n)]
p = [0 for i in range(n)]
for i in range(3):
  dic = [[] for _ in range(101)]
  for j in range(n):
    dic[lst[j][i]].append(j)
  for x in range(101):
    l = dic[x]
    if lst:
      if len(l) == 1:
        p[l[0]] += x
for i in p:
  print(i)
Title: Signboard

Problem:
JOI decided to create a signboard for his shop. He has N old signboards with characters written at equal intervals. JOI wants to create a signboard by removing some characters from the old signboards. The remaining string should form the name of the shop, and the remaining characters should be equally spaced. He cannot cut or connect old signboards. Given the shop's name and information about N old signboards, create a program to determine the number of signboards JOI can create. If there are multiple ways to create a signboard from one old signboard, it is considered as one signboard.

Input:
The input consists of 2 + N lines.
The first line contains an integer N (1 ≤ N ≤ 100), representing the number of old signboards.
The second line contains a string of 3 to 25 lowercase alphabets, representing the shop's name.
The next N lines (1 ≤ i ≤ N) contain strings of 1 to 100 lowercase alphabets, representing the strings written on the i-th old signboard.

Output:
Output the number of signboards JOI can create as an integer on a single line.

Example:
Input
4
bar
abracadabra
bear
bar
baraxbara

Output
3

Explanation:
The shop's name is "bar".
From the first old signboard, removing characters at positions 2, 6, and 10 creates a signboard.
The second signboard can form "bar" by removing the 2nd character, but the remaining characters are not equally spaced.
The third signboard is already a valid signboard without removing any characters.
For the fourth signboard, there are two ways to create a signboard by removing characters. Thus, JOI can create signboards from the 1st, 3rd, and 4th old signboards, resulting in an output of 3.

# Buggy version:
n = int(input())
s = input()
t = [input() for i in range(n)]
c = 0
for tt in t:
	f = False
	for i in range(len(tt)):
		for j in range(len(tt))[1:]:
			print(tt[i::j][:len(s)])
			f |= s == tt[i::j][:len(s)]
	if f: c += 1
print(c)

# Fixed version:
n = int(input())
s = input()
t = [input() for i in range(n)]
c = 0
for tt in t:
	f = False
	for i in range(len(tt)):
		for j in range(len(tt))[1:]:
			f |= s == tt[i::j][:len(s)]
	if f: c += 1
print(c)
You are given a function f(A, B), where A and B are positive integers. The function returns a string that meets the following conditions: it has a length of A + B, contains A letters "A" and B letters "B", has the smallest possible length of the longest substring of equal letters, and is the lexicographically smallest string satisfying the conditions. You need to answer Q queries, finding the substring of f(Ai, Bi) from position Ci to position Di (1-based). The constraints are: 1 ≤ Q ≤ 10^3, 1 ≤ Ai, Bi ≤ 5 × 10^8, 1 ≤ Ci ≤ Di ≤ Ai + Bi, and Di - Ci + 1 ≤ 100. For each query, print the substring of f(Ai, Bi) from position Ci to position Di.

# Buggy version:
for t in range(int(input())):
  a,b,c,d=map(int,input().split(' '));l,x,y,o=(a+b)//(min(a,b)+1),0,0,""
	if a*l<=b:y=a+b
	elif b*l<=a:x=a+b
	else:x,y=(a*l-b)//(l-1),(b*l-a)//(l-1)
	for i in range(c,d+1):o+="AB"[i%(l+1)==0] if i<=x else "BA"[(a+b-i+1)%(l+1)==0] if a+b-i+1<=y else "AB"[a-x+x//(l+1)-y//(l+1)==0]
	print(o)

# Fixed version:
T=int(input())
for t in range(T):
	a,b,c,d=map(int,input().split(' '))
	l,x,y,o=(a+b)//(min(a,b)+1),0,0,""
	if a*l<=b:y=a+b
	elif b*l<=a:x=a+b
	else:x,y=(a*l-b)//(l-1),(b*l-a)//(l-1)
	for i in range(c,d+1):o+="AB"[i%(l+1)==0] if i<=x else "BA"[(a+b-i+1)%(l+1)==0] if a+b-i+1<=y else "AB"[a-x+x//(l+1)-y//(l+1)==0]
	print(o)
Snuke has a rooted tree with N+1 vertices, numbered 0 through N, where 0 is the root. Snuke also has an initially empty box and marbles. The play begins by placing one marble on some vertices and follows specific rules for moving and removing marbles. The task is to find the total number of marbles in the box at the end of the play for all possible marble placements, and compute the sum modulo 1,000,000,007. Constraints: 1 ≤ N < 2 × 10^5, 0 ≤ p_i < i. For the test set worth 400 points, N < 2,000. Input format: N followed by p_1, p_2, ..., p_N. Output the answer.

# Buggy version:
n, = map(int, input().split())
p = [-1] + [*map(int, input().split())]

MOD = 10**9+7
dp = [[] for _ in range(n+1)]
dep = [0]*(n+1)
nxt = [0]*(n+1)

for v in range(n,0,-1):
    _,nxt[p[v]],dep[p[v]] = sorted([nxt[p[v]],dep[p[v]],dep[v]+1])

tot = [0]*(dep[0]+1)
for i in range(n+1): tot[dep[i]] += 1

def merge(p,v):
    if len(dp[p]) < len(dp[v]):
        dp[p],dp[v]=dp[v],dp[p]
    for i in range(-len(dp[v]),0):
        a,b,c = dp[p][i]
        d,e,f = dp[v][i]
        dp[p][i][:] = [a*d%MOD,(b*d+a*e)%MOD,c*f%MOD]

for v in range(n,-1,-1):
    dp[v].append([1,1,2])
    for i in range(-nxt[v]-1,0):
        dp[v][i][0] = dp[v][i][2] - dp[v][i][1]
    if v: merge(p[v],v)

ans = 0
for d in dp[0]:
    ans += pow(d[2],MOD-2,MOD)*d[1]%MOD
print(ans*pow(2,n+1,MOD)%MOD)
print(1)

# Fixed version:
n, = map(int, input().split())
p = [-1] + [*map(int, input().split())]

MOD = 10**9+7
dp = [[] for _ in range(n+1)]
dep = [0]*(n+1)
nxt = [0]*(n+1)

for v in range(n,0,-1):
    _,nxt[p[v]],dep[p[v]] = sorted([nxt[p[v]],dep[p[v]],dep[v]+1])

tot = [0]*(dep[0]+1)
for i in range(n+1): tot[dep[i]] += 1

def merge(p,v):
    if len(dp[p]) < len(dp[v]):
        dp[p],dp[v]=dp[v],dp[p]
    for i in range(-len(dp[v]),0):
        a,b,c = dp[p][i]
        d,e,f = dp[v][i]
        dp[p][i][:] = [a*d%MOD,(b*d+a*e)%MOD,c*f%MOD]

for v in range(n,-1,-1):
    dp[v].append([1,1,2])
    for i in range(-nxt[v]-1,0):
        dp[v][i][0] = dp[v][i][2] - dp[v][i][1]
    if v: merge(p[v],v)

ans = 0
for d in dp[0]:
    ans += pow(d[2],MOD-2,MOD)*d[1]%MOD
print(ans*pow(2,n+1,MOD)%MOD)
In a long narrow forest stretching east-west, there are N beasts. Each beast is located at a specific point and can be sold for a certain amount. You need to choose two points, L and R, and throw a net to capture the beasts within that range. The net costs R - L yen, and your profit is the sum of the selling prices of the captured beasts minus the net cost. Find the maximum profit achievable by throwing the net only once.

Constraints:
- 1 ≤ N ≤ 2 × 10^5
- 1 ≤ x_1 < x_2 < ... < x_N ≤ 10^15
- 1 ≤ s_i ≤ 10^9
- All input values are integers.

Input:
The input consists of N lines, each containing the position and selling price of a beast.

Output:
Print the maximum profit achievable.

Sample Input 1:
5
10 20
40 50
60 30
70 40
90 10

Sample Output 1:
90

Sample Input 2:
5
10 2
40 5
60 3
70 4
90 1

Sample Output 2:
5

Sample Input 3:
4
1 100
3 200
999999999999999 150
1000000000000000 150

Sample Output 3:
299

# Buggy version:
from itertools import accumulate as ac
n=int(input())
a,b=[],[]
for i in range(n):
    x,s=map(int,input().split())
    a.append(x)
    b.append(s)
r=[0]+list(ac(b))
l=b[:]
for i in range(n):
    r[i]+=-a[i]
    l[i+1]+=-a[i]
q,d=0,0
for i in range(1,n+1):
    d=max(l[i]-q,d)
    q=min(q,r[i-1])
print(d)

# Fixed version:
from itertools import accumulate as ac
n=int(input())
a,b=[],[]
for i in range(n):
    x,s=map(int,input().split())
    a.append(x)
    b.append(s)
r=[0]+list(ac(b))
l=r[:]
for i in range(n):
    r[i]+=-a[i]
    l[i+1]+=-a[i]
q,d=r[0],0
for i in range(1,n+1):
    d=max(l[i]-q,d)
    q=min(q,r[i])
print(d)
You are given two strings, s and t, consisting of lowercase English letters, and an integer L. Generate a string of length L by concatenating one or more copies of s and t. The same string can be used more than once. Find the lexicographically smallest string that can be generated in this way. Constraints: 1 ≤ L ≤ 2 × 10^5, 1 ≤ |s|, |t| ≤ L, s and t consist of lowercase English letters, and it is always possible to generate a string of length L. Input is given in the format: N, x_1 s_1, x_2 s_2, ..., x_N s_N. Output the lexicographically smallest string among the ones that can be generated.

# Buggy version:
def main():
    L = int(input())
    S, T = (input() for _ in [0] * 2)

    ans = []
    apnd = ans.append
    a = S
    b = T
    i = 0
    for _ in [0] * 2:
        while 1:
            x = L - (len(b) * i)
            div_, mod_ = divmod(x, len(a))
            if not mod_:
                apnd(a * div_ + b * i)
                break
            i += 1
        a, b = b, a
    print(min(ans))

main()


# Fixed version:
def main():
    L = int(input())
    S, T = (input() for _ in [0] * 2)

    ans = []
    apnd = ans.append
    a = S
    b = T
    i = 0
    for _ in [0] * 2:
        while 1:
            x = L - (len(b) * i)
            div_, mod_ = divmod(x, len(a))
            if not mod_:
                apnd(a * div_ + b * i)
                break
            i += 1
        i = 0
        a, b = b, a
    print(min(ans))

main()