Problem Description

Given a sequence of positive integers $A = (A_1, A_2, \dots, A_N)$ of length $ N $. Takahashi will repeat the following operation until the number of positive elements in $ A $ is reduced to 1 or less:

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

Find the number of times Takahashi performs the operation.

Input Format

The input is given from the standard input in the following format:

$ N $ $ A_1 $ $ A_2 $ $\cdots$ $ A_N $

Output Format

Output the answer.

Sample Input and Output

Sample Input #1

4
1 2 3 3

Sample Output #1

4

Sample Input #2

3
1 1 100

Sample Output #2

2

Notes/Hints

Constraints

• $2 \leq N \leq 100$
• $1 \leq A_i \leq 100$
• All inputs are integers

Sample Explanation 1

The operations proceed as follows:
- After the 1st operation, $ A = (2, 2, 2, 1) $.
- After the 2nd operation, $ A = (1, 1, 2, 1) $.
- After the 3rd operation, $ A = (1, 0, 1, 1) $.
- After the 4th operation, $ A = (0, 0, 1, 0) $. The number of positive elements in $ A $ is reduced to 1 or less, so the operations end here.

见题面 Input 部分

见题面 Output 部分