Problem Statement

There is one humidifier in the AtCoder company office. The current time is 0, and the humidifier has no water inside.

You will add water to this humidifier N times. The i-th addition of water (1 \leq i \leq N) takes place at time T_i, and you add V_i liters of water. It is guaranteed that T_i < T_{i+1} for all 1 \leq i \leq N-1.

However, the humidifier has a leak, and as long as there is water inside, the amount of water decreases by 1 liter per unit time.

Find the amount of water remaining in the humidifier immediately after you finish adding water at time T_N.

Constraints

• 1 \leq N \leq 100
• 1 \leq T_i \leq 100 (1 \leq i \leq N)
• 1 \leq V_i \leq 100 (1 \leq i \leq N)
• T_i < T_{i+1} (1 \leq i \leq N-1)
• All input values are integers.

Sample Input 1

4
1 3
3 1
4 4
7 1

Sample Output 1

3

At each point in time, water is added as follows:

• Time 1: Before adding, the humidifier has 0 liters. After adding 3 liters, it has 3 liters.
• Time 3: Before adding, it has 1 liter. After adding 1 liter, it has 2 liters total.
• Time 4: Before adding, it has 1 liter. After adding 4 liters, it has 5 liters total.
• Time 7: Before adding, it has 2 liters. After adding 1 liter, it has 3 liters total.

After finishing the addition at time 7, the humidifier contains 3 liters. Thus, the answer is 3.

Sample Input 2

3
1 8
10 11
21 5

Sample Output 2

5

Sample Input 3

10
2 1
22 10
26 17
29 2
45 20
47 32
72 12
75 1
81 31
97 7

Sample Output 3

57

Problem Statement

There are N items. You are given strings T and A of length N that represent which items Takahashi and Aoki want, respectively. Let T_i and A_i be the i-th (1\leq i\leq N) characters of T and A, respectively.

Takahashi wants the i-th item when T_i is o, and does not want the i-th item when T_i is x. Similarly, Aoki wants the i-th item when A_i is o, and does not want the i-th item when A_i is x.

Determine whether there exists an item that both of them want.

Constraints

• 1\leq N\leq 100
• N is an integer.
• T and A are strings of length N consisting of o and x.

Sample Input 1

4
oxoo
xoox

Sample Output 1

Yes

The third item is wanted by both of them, so output Yes.

Sample Input 2

5
xxxxx
ooooo

Sample Output 2

No

There is no item that both of them want, so output No.

Sample Input 3

10
xoooxoxxxo
ooxooooxoo

Sample Output 3

Yes

Problem Statement

There is a rectangular chocolate consisting of H rows and W columns of blocks.

You are given Q queries; process them in order and find the answer to each query. Each query is in one of the following formats:

• Type 1: An integer R is given. Find the number of chocolate blocks in the bottom R rows, then eat them.

• Type 2: An integer C is given. Find the number of chocolate blocks in the rightmost C columns, then eat them.

When the queries are processed in order, the chocolate remains rectangular after each query is processed, and it has at least R + 1 rows immediately before processing a type 1 query and has at least C + 1 columns immediately before processing a type 2 query.

Constraints

• 2 \leq H, W \leq 100
• 1 \leq Q \leq 100
• For type 1 queries, 1 \leq R.
• When the queries are processed in order, the chocolate has at least R + 1 rows immediately before processing a type 1 query.
• For type 2 queries, 1 \leq C.
• When the queries are processed in order, the chocolate has at least C + 1 columns immediately before processing a type 2 query.
• All input values are integers.

Sample Input 1

7 9 5
2 4
1 3
2 1
2 1
1 3

Sample Output 1

28
15
4
4
9

Initially, the chocolate is a rectangle with 7 rows and 9 columns.

For the first query, the number of chocolate blocks in the rightmost 4 columns is 28, so output 28. The chocolate becomes 7 rows and 5 columns.

For the second query, the number of chocolate blocks in the bottom 3 rows is 15, so output 15. The chocolate becomes 4 rows and 5 columns.

For the third query, the number of chocolate blocks in the rightmost 1 column is 4, so output 4. The chocolate becomes 4 rows and 4 columns.

For the fourth query, the number of chocolate blocks in the rightmost 1 column is 4, so output 4. The chocolate becomes 4 rows and 3 columns.

For the fifth query, the number of chocolate blocks in the bottom 3 rows is 9, so output 9. The chocolate becomes 1 row and 3 columns.

Problem Statement

You have an empty sequence A. There are Q queries given, and you need to process them in the order they are given.
The queries are of the following two types:

• 1 x: Append x to the end of A.
• 2 k: Find the k-th value from the end of A. It is guaranteed that the length of A is at least k when this query is given.

Constraints

• 1 \leq Q \leq 100
• In the first type of query, x is an integer satisfying 1 \leq x \leq 10^9.
• In the second type of query, k is a positive integer not greater than the current length of sequence A.

Sample Input 1

5
1 20
1 30
2 1
1 40
2 3

Sample Output 1

30
20

• Initially, A is empty.
• The first query appends 20 to the end of A, making A=(20).
• The second query appends 30 to the end of A, making A=(20,30).
• The answer to the third query is 30, which is the 1-st value from the end of A=(20,30).
• The fourth query appends 40 to the end of A, making A=(20,30,40).
• The answer to the fifth query is 20, which is the 3-rd value from the end of A=(20,30,40).

Problem Statement

Takahashi can combine a head part and a body part to create a robot. A robot falls over if the weight of the head part is greater than the weight of the body part.

Currently, he has N head parts and M body parts. The weight of the i-th (1\le i\le N) head part is H _ i grams, and the weight of the i-th (1\le i\le M) body part is B _ i grams.

He wants to create a total of K robots that do not fall over by appropriately combining the parts he has. Determine whether he can achieve his goal by combining the parts well.

Here, a part cannot be used to create multiple robots, and two or more head parts (or two or more body parts) cannot be used to create one robot.

Constraints

• 1\le N\le2\times10 ^ 5
• 1\le M\le2\times10 ^ 5
• 1\le K\le\min\lbrace N,M\rbrace
• 1\le H _ i\le10 ^ 9\ (1\le i\le N)
• 1\le B _ i\le10 ^ 9\ (1\le i\le M)
• All input values are integers.

Sample Input 1

6 6 3
2 7 1 8 2 8
1 8 2 8 4 5

Sample Output 1

Yes

If we denote combining the i-th head part and the j-th body part as (i,j), then Takahashi can create three robots that do not fall over by combining them as (1,2),(2,4),(3,6), for example.

Thus, print Yes.

Sample Input 2

1 1 1
43
1

Sample Output 2

No

His head part is too heavy, so he cannot create any robot that does not fall over.

Sample Input 3

1 1 1
100
100

Sample Output 3

Yes

Note that a robot does not fall over if the head and body have equal weights.

Sample Input 4

12 15 12
748 169 586 329 972 529 432 519 408 587 138 249
656 114 632 299 984 755 404 772 155 506 832 854 353 465 387

Sample Output 4

Yes

Problem Statement

For two strings A and B, let A+B denote the concatenation of A and B in this order.

You are given N strings S_1,\ldots,S_N. Modify and print them as follows, in the order i=1, \ldots, N:

• if none of S_1,\ldots,S_{i-1} is equal to S_i, print S_i;
• if X (X>0) of S_1,\ldots,S_{i-1} are equal to S_i, print S_i+ ( +X+ ), treating X as a string.

Constraints

• 1 \leq N \leq 2\times 10^5
• S_i is a string of length between 1 and 10 (inclusive) consisting of lowercase English letters.

Sample Input 1

5
newfile
newfile
newfolder
newfile
newfolder

Sample Output 1

newfile
newfile(1)
newfolder
newfile(2)
newfolder(1)

Sample Input 2

11
a
a
a
a
a
a
a
a
a
a
a

Sample Output 2

a
a(1)
a(2)
a(3)
a(4)
a(5)
a(6)
a(7)
a(8)
a(9)
a(10)

Problem Statement

Let us regard an integer k as "similar to 250" if the following condition is satisfied:

• k is represented as k=p \times q^3 with primes p<q.

How many integers less than or equal to N are "similar to 250"?

Constraints

• N is an integer between 1 and 10^{18} (inclusive)

Sample Input 1

250

Sample Output 1

2

• 54 = 2 \times 3^3 is "similar to 250".
• 250 = 2 \times 5^3 is "similar to 250".

The two integers above are all the integers "similar to 250".

Sample Input 2

1

Sample Output 2

0

Sample Input 3

123456789012345

Sample Output 3

226863

Problem Statement

You are given an integer sequence of length N, (A_1,\dots,A_N), and a positive integer D.

Find the number of pairs of integers (L,R) that satisfy both of the following conditions:

• 1 \leq L \leq R \leq N
• Any two elements of (A_L,A_{L+1},\dots,A_R) have a difference of at least D.
  • That is, |A_i-A_j|\geq D for all pairs of integers (i,j) satisfying L \leq i < j \leq R.

Constraints

• 2\leq N \leq 4\times 10^5
• 1 \leq A_i \leq 10^9
• 1 \leq D \leq 10^9

Sample Input 1

5 3
3 1 4 1 5

Sample Output 1

8

The eight pairs (1,1),(2,2),(3,3),(4,4),(5,5),(2,3),(3,4),(4,5) satisfy the conditions.

Sample Input 2

9 1
1 2 3 4 5 6 7 8 9

Sample Output 2

45

Sample Input 3

6 1000000000
123456789 234567891 987654321 321987654 1000000000 1

Sample Output 3

6

Problem Statement

You are given a sequence of integers A=(A_1,\ldots,A_N). For a tree T with N vertices, define f(T) as follows:

• Let d_i be the degree of vertex i in T. Then, f(T)=\sum_{i=1}^N {d_i}^2 A_i.

Find the minimum possible value of f(T).

The constraints guarantee the answer to be less than 2^{63}.

Constraints

• 2\leq N\leq 2\times 10^5
• 1\leq A_i \leq 10^9
• All input values are integers.

Sample Input 1

4
3 2 5 2

Sample Output 1

24

Consider a tree T with an edge connecting vertices 1 and 2, an edge connecting vertices 2 and 4, and an edge connecting vertices 4 and 3.

Then, f(T) = 1^2\times 3 + 2^2\times 2 + 1^2\times 5 + 2^2\times 2 = 24. It can be proven that this is the minimum value of f(T).

Sample Input 2

3
4 3 2

Sample Output 2

15

Sample Input 3

7
10 5 10 2 10 13 15

Sample Output 3

128