Problem Statement

You are given a string S of even length consisting of lowercase English letters. Let |S| be the length of S, and S_i be the i-th character of S.

Perform the following operation for each i = 1, 2, \ldots, \frac{|S|}{2} in this order, and print the final S.

• Swap S_{2i-1} and S_{2i}.

Constraints

• S is a string of even length consisting of lowercase English letters.
• The length of S is at most 100.

Sample Input 1

abcdef

Sample Output 1

badcfe

Initially, S = abcdef.
Performing the operation for i = 1 swaps S_1 and S_2, making S = bacdef.
Performing the operation for i = 2 swaps S_3 and S_4, making S = badcef.
Performing the operation for i = 3 swaps S_5 and S_6, making S = badcfe.
Thus, badcfe should be printed.

Sample Input 2

aaaa

Sample Output 2

aaaa

Sample Input 3

atcoderbeginnercontest

Sample Output 3

taocedbrgeniencrnoetts

Problem Statement

Takahashi and Aoki decided to jog.
Takahashi repeats the following: "walk at B meters a second for A seconds and take a rest for C seconds."
Aoki repeats the following: "walk at E meters a second for D seconds and take a rest for F seconds."
When X seconds have passed since they simultaneously started to jog, which of Takahashi and Aoki goes ahead?

Constraints

• 1 \leq A, B, C, D, E, F, X \leq 100
• All values in input are integers.

Sample Input 1

4 3 3 6 2 5 10

Sample Output 1

Takahashi

During the first 10 seconds after they started to jog, they move as follows.

• Takahashi walks for 4 seconds, takes a rest for 3 seconds, and walks again for 3 seconds. As a result, he advances a total of (4 + 3) \times 3 = 21 meters.
• Aoki walks for 6 seconds and takes a rest for 4 seconds. As a result, he advances a total of 6 \times 2 = 12 meters.

Since Takahashi goes ahead, Takahashi should be printed.

Sample Input 2

3 1 4 1 5 9 2

Sample Output 2

Aoki

Sample Input 3

1 1 1 1 1 1 1

Sample Output 3

Draw

Problem Statement

AtCoder Kingdom uses a calendar whose year has N months. Month i (1\leq i\leq N) has D _ i days, from day 1 of month i to day D _ i of month i.

How many days in a year of AtCoder have "repdigits" dates?

Here, day j of month i (1\leq i\leq N,1\leq j\leq D _ i) is said to have a repdigit date if and only if all digits in the decimal notations of i and j are the same.

Constraints

• 1\leq N\leq100
• 1\leq D _ i\leq100\ (1\leq i\leq N)
• All input values are integers.

Sample Input 1

12
31 29 31 30 31 30 31 31 30 31 30 31

Sample Output 1

13

In AtCoder Kingdom, the days that have repdigit dates are January 1, January 11, February 2, February 22, March 3, April 4, May 5, June 6, July 7, August 8, September 9, November 1, and November 11, for a total of 13 days.

Sample Input 2

10
10 1 2 3 4 5 6 7 8 100

Sample Output 2

1

In AtCoder Kingdom, only January 1 has a repdigit date.

Sample Input 3

30
73 8 55 26 97 48 37 47 35 55 5 17 62 2 60 23 99 73 34 75 7 46 82 84 29 41 32 31 52 32

Sample Output 3

15

Problem Statement

How many triples of non-negative integers (a, b, c) satisfy a+b+c \leq S and a \times b \times c \leq T?

Constraints

• 0 \leq S \leq 100
• 0 \leq T \leq 10000
• S and T are integers.

Sample Input 1

1 0

Sample Output 1

4

The triples (a,b,c) satisfying the conditions are (0,0,0), (0,0,1), (0,1,0), and (1,0,0) ― there are four of them.

Sample Input 2

2 5

Sample Output 2

10

Sample Input 3

10 10

Sample Output 3

213

Sample Input 4

30 100

Sample Output 4

2471

Problem Statement

You are given an integer sequence A=(A_1,A_2,\dots,A_N) of length N.

Find the maximum value of \displaystyle \sum_{i=1}^{M} i \times B_i for a contiguous subarray B=(B_1,B_2,\dots,B_M) of A of length M.

Notes

A contiguous subarray of a number sequence is a sequence that is obtained by removing 0 or more initial terms and 0 or more final terms from the original number sequence.

For example, (2, 3) and (1, 2, 3) are contiguous subarrays of (1, 2, 3, 4), but (1, 3) and (3,2,1) are not contiguous subarrays of (1, 2, 3, 4).

Constraints

• 1 \le M \le N \le 2 \times 10^5
• - 2 \times 10^5 \le A_i \le 2 \times 10^5
• All values in input are integers.

Sample Input 1

4 2
5 4 -1 8

Sample Output 1

15

When B=(A_3,A_4), we have \displaystyle \sum_{i=1}^{M} i \times B_i = 1 \times (-1) + 2 \times 8 = 15. Since it is impossible to achieve 16 or a larger value, the solution is 15.

Note that you are not allowed to choose, for instance, B=(A_1,A_4).

Sample Input 2

10 4
-3 1 -4 1 -5 9 -2 6 -5 3

Sample Output 2

31

Problem Statement

There are N sticks with several balls stuck onto them. Each ball has a lowercase English letter written on it.

For each i = 1, 2, \ldots, N, the letters written on the balls stuck onto the i-th stick are represented by a string S_i. Specifically, the number of balls stuck onto the i-th stick is the length |S_i| of the string S_i, and S_i is the sequence of letters on the balls starting from one end of the stick.

Two sticks are considered the same when the sequence of letters on the balls starting from one end of one stick is equal to the sequence of letters starting from one end of the other stick. More formally, for integers i and j between 1 and N, inclusive, the i-th and j-th sticks are considered the same if and only if S_i equals S_j or its reversal.

Print the number of different sticks among the N sticks.

Constraints

• N is an integer.
• 2 \leq N \leq 2 \times 10^5
• S_i is a string consisting of lowercase English letters.
• |S_i| \geq 1
• \sum_{i = 1}^N |S_i| \leq 2 \times 10^5

Sample Input 1

6
a
abc
de
cba
de
abc

Sample Output 1

3

• S_2 = abc equals the reversal of S_4 = cba, so the second and fourth sticks are considered the same.
• S_2 = abc equals S_6 = abc, so the second and sixth sticks are considered the same.
• S_3 = de equals S_5 = de, so the third and fifth sticks are considered the same.

Therefore, there are three different sticks among the six: the first, second (same as the fourth and sixth), and third (same as the fifth).

Problem Statement

You are given a string S that is a permutation of atcoder.
On this string S, you will perform the following operation 0 or more times:

• Choose two adjacent characters of S and swap them.

Find the minimum number of operations required to make S equal atcoder.

Constraints

• S is a string that is a permutation of atcoder

Sample Input 1

catredo

Sample Output 1

8

You can make S equal atcoder in 8 operations as follows:
catredo \rightarrow [ac]tredo \rightarrow actre[od] \rightarrow actr[oe]d \rightarrow actro[de] \rightarrow act[or]de \rightarrow acto[dr]e \rightarrow a[tc]odre \rightarrow atcod[er]
This is the minimum number of operations achievable.

Sample Input 2

atcoder

Sample Output 2

0

In this case, the string S is already atcoder.

Sample Input 3

redocta

Sample Output 3

21

Problem Statement

We have a variable X and N kinds of operations that change the value of X. Operation i is represented as a pair of integers (T_i,A_i), and is the following operation:

• if T_i=1, it replaces the value of X with X\ {\rm and}\ A_i;
• if T_i=2, it replaces the value of X with X\ {\rm or}\ A_i;
• if T_i=3, it replaces the value of X with X\ {\rm xor}\ A_i.

Initialize X with the value of C and execute the following procedures in order:

• Perform Operation 1, and then print the resulting value of X.
• Next, perform Operation 1, 2 in this order, and then print the value of X.
• Next, perform Operation 1, 2, 3 in this order, and then print the value of X.
• \vdots
• Next, perform Operation 1, 2, \ldots, N in this order, and then print the value of X.

Constraints

• 1 \leq N \leq 2\times 10^5
• 1\leq T_i \leq 3
• 0\leq A_i \lt 2^{30}
• 0\leq C \lt 2^{30}
• All values in input are integers.

Sample Input 1

3 10
3 3
2 5
1 12

Sample Output 1

9
15
12

The initial value of X is 10.

• Operation 1 changes X to 9.
• Next, Operation 1 changes X to 10, and then Operation 2 changes it to 15.
• Next, Operation 1 changes X to 12, and then Operation 2 changes it to 13, and then Operation 3 changes it to 12.

Sample Input 2

9 12
1 1
2 2
3 3
1 4
2 5
3 6
1 7
2 8
3 9

Sample Output 2

0
2
1
0
5
3
3
11
2

Problem Statement

The Republic of AtCoder has N islands. Initially, none of the islands has an airport or harbor, and there is no road between any two of them. Takahashi, the king, will provide some means of transportation between these islands. Specifically, he can do the following operations any number of times in any order.

• Choose an integer i such that 1\leq i\leq N and pay a cost of X_i to build an airport on island i.
• Choose an integer i such that 1\leq i\leq N and pay a cost of Y_i to build a harbor on island i.
• Choose an integer i such that 1\leq i\leq M and pay a cost of Z_i to build a road that bidirectionally connects island A_i and island B_i.

Takahashi's objective is to make it possible, for every pair of different islands U and V, to reach island V from island U when one can perform the following actions any number of times in any order.

• When islands S and T both have airports, go from island S to island T.
• When islands S and T both have harbors, go from island S to island T.
• When islands S and T are connected by a road, go from island S to island T.

Find the minimum total cost Takahashi needs to pay to achieve his objective.

Constraints

• 2 \leq N \leq 2\times 10^5
• 1 \leq M \leq 2\times 10^5
• 1\leq X_i\leq 10^9
• 1\leq Y_i\leq 10^9
• 1\leq A_i<B_i\leq N
• 1\leq Z_i\leq 10^9
• (A_i,B_i)\neq (A_j,B_j), if i\neq j.
• All values in the input are integers.

Sample Input 1

4 2
1 20 4 7
20 2 20 3
1 3 5
1 4 6

Sample Output 1

16

Takahashi will build the following infrastructure.

• Pay a cost of X_1=1 to build an airport on island 1.
• Pay a cost of X_3=4 to build an airport on island 3.
• Pay a cost of Y_2=2 to build a harbor on island 2.
• Pay a cost of Y_4=3 to build a harbor on island 4.
• Pay a cost of Z_2=6 to build a road connecting island 1 and island 4.

Then, the objective will be achieved at a cost of 16. There is no way to achieve the objective for a cost of 15 or less, so 16 should be printed.

Sample Input 2

3 1
1 1 1
10 10 10
1 2 100

Sample Output 2

3

It is not mandatory to build all three types of facilities at least once.

Sample Input 3

7 8
35 29 36 88 58 15 25
99 7 49 61 67 4 57
2 3 3
2 5 36
2 6 89
1 6 24
5 7 55
1 3 71
3 4 94
5 6 21

Sample Output 3

160