Problem Statement

You are given a sequence of N positive integers A = (A_1, A_2, \dots ,A_N). Takahashi repeats the following operation until A contains one or fewer positive elements:

• Sort A in descending order. Then, decrease both A_1 and A_2 by 1.

Find the number of times he performs this operation.

Constraints

• 2 \leq N \leq 100
• 1 \leq A_i \leq 100
• All input values are integers.

Sample Input 1

4
1 2 3 3

Sample Output 1

4

The process goes as follows:

• After the 1st operation, A is (2, 2, 2, 1).
• After the 2nd operation, A is (1, 1, 2, 1).
• After the 3rd operation, A is (1, 0, 1, 1).
• After the 4th operation, A is (0, 0, 1, 0). A no longer contains more than one positive elements, so the process ends here.

Sample Input 2

3
1 1 100

Sample Output 2

2

Problem Statement

N players numbered 1 to N will play a soccer game.
When a player commits an offense, that player will receive a yellow card or a red card.
A player who satisfies one of the following conditions will be removed from the game.

• Accumulates two yellow cards.
• Receives a red card.

Once a player is removed, that player will no longer receive any cards.

You will watch this game. Initially, the players have not received any cards.
There will be Q events. Correctly answer the questions asked in the events.
There are three kinds of events, which are given in the format c x from the input, where c is 1, 2, or 3. The events are as follows.

• 1 x: Player x receives a yellow card.
• 2 x: Player x receives a red card.
• 3 x: You are asked whether player x has been removed from the game. Answer Yes or No.

Constraints

• 1 \leq N \leq 100
• 1 \leq Q \leq 100
• 1 \leq x \leq N in all events.
• There is at least one event of the third kind.
• A player who has been removed will no longer receive any cards.
• All values in the input are integers.

Sample Input 1

3 9
3 1
3 2
1 2
2 1
3 1
3 2
1 2
3 2
3 3

Sample Output 1

No
No
Yes
No
Yes
No

Here are all the events in chronological order.

In the 1-st event, you are asked whether player 1 has been removed from the game. Player 1 has not been removed, so you should print No.
In the 2-nd event, you are asked whether player 2 has been removed from the game. Player 2 has not been removed, so you should print No.
In the 3-rd event, player 2 receives a yellow card.
In the 4-th event, player 1 receives a red card and is removed from the game.
In the 5-th event, you are asked whether player 1 has been removed from the game. Player 1 has been removed, so you should print Yes.
In the 6-th event, you are asked whether player 2 has been removed from the game. Player 2 has not been removed, so you should print No.
In the 7-th event, player 2 receives a yellow card and is removed from the game.
In the 8-th event, you are asked whether player 2 has been removed from the game. Player 2 has been removed, so you should print Yes.
In the 9-th event, you are asked whether player 3 has been removed from the game. Player 3 has not been removed, so you should print No.

Problem Statement

The AtCoder Kingdom holds a festival for N days. On M of these days, namely on the A_1-th, A_2-th, \dots, A_M-th days, fireworks will be launched. It is guaranteed that fireworks will be launched on the last day of the festival. (In other words, A_M=N is guaranteed.)

For each i=1,2,\dots,N, solve the following problem.

• How many days later from the i-th day will fireworks be launched for the first time on or after the i-th day? If fireworks are launched on the i-th day, it is considered to be 0 days later.

Constraints

• 1 \le M \le N \le 2 \times 10^5
• 1 \le A_1 < A_2 < \dots < A_M = N
• All input values are integers.

Sample Input 1

3 2
2 3

Sample Output 1

1
0
0

The kingdom holds a festival for 3 days, and fireworks are launched on the 2-nd and 3-rd days.

• From the 1-st day, the first time fireworks are launched is the 2-nd day of the festival, which is 1 day later.
• From the 2-nd day, the first time fireworks are launched is the 2-nd day of the festival, which is 0 days later.
• From the 3-rd day, the first time fireworks are launched is the 3-rd day of the festival, which is 0 days later.

Sample Input 2

8 5
1 3 4 7 8

Sample Output 2

0
1
0
0
2
1
0
0

Problem Statement

N people numbered 1 through N tossed a coin several times. We know that person i's tosses resulted in A_i heads and B_i tails.

Person i's success rate of the tosses is defined by \displaystyle\frac{A_i}{A_i+B_i}. Sort people 1,\ldots,N in descending order of their success rates, with ties broken in ascending order of their assigned numbers.

Constraints

• 2\leq N \leq 2\times 10^5
• 0\leq A_i, B_i\leq 10^9
• A_i+B_i \geq 1
• All input values are integers.

Sample Input 1

3
1 3
3 1
2 2

Sample Output 1

2 3 1

Person 1's success rate is 0.25, person 2's is 0.75, and person 3's is 0.5.

Sort them in descending order of their success rates to obtain the order in Sample Output.

Sample Input 2

2
1 3
2 6

Sample Output 2

1 2

Note that person 1 and 2 should be printed in ascending order of their numbers, as they have the same success rates.

Sample Input 3

4
999999999 1000000000
333333333 999999999
1000000000 999999997
999999998 1000000000

Sample Output 3

3 1 4 2

Problem Statement

Find the number of positive integers not greater than N that have exactly 9 positive divisors.

Constraints

• 1 \leq N \leq 4 \times 10^{12}
• All input values are integers.

Sample Input 1

200

Sample Output 1

3

Three positive integers 36,100,196 satisfy the condition.

Sample Input 2

4000000000000

Sample Output 2

407073