Problem Description

You are playing a game.

There are $ N $ enemies lined up in a row, and the health of the $ i $-th enemy from the front is $ H_i $.

You use a variable $ T $ initialized to $ 0 $, and repeat the following action until the health of all enemies is $ 0 $ or below.

• Increment $ T $ by $ 1 $. Then, attack the foremost enemy with health $ 1 $ or more. If $ T $ is a multiple of $ 3 $, the enemy's health decreases by $ 3 $, otherwise it decreases by $ 1 $.

Find the value of $ T $ when the health of all enemies is $ 0 $ or below.

Input Format

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

$ N $ $ H_1 $ $ H_2 $ $\ldots$ $ H_N $

Output Format

Output the answer.

Sample Input and Output

Sample Input #1

3
6 2 2

Sample Output #1

8

Sample Input #2

9
1 12 123 1234 12345 123456 1234567 12345678 123456789

Sample Output #2

82304529

Sample Input #3

5
1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output #3

3000000000

Notes/Hints

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq H_i \leq 10^9$
• All inputs are integers

Sample Explanation 1

The actions are performed as follows.
- $ T=1 $. Attack the 1st enemy, its health becomes $ 6-1=5 $.
- $ T=2 $. Attack the 1st enemy, its health becomes $ 5-1=4 $.
- $ T=3 $. Attack the 1st enemy, its health becomes $ 4-3=1 $.
- $ T=4 $. Attack the 1st enemy, its health becomes $ 1-1=0 $.
- $ T=5 $. Attack the 2nd enemy, its health becomes $ 2-1=1 $.
- $ T=6 $. Attack the 2nd enemy, its health becomes $ 1-3=-2 $.
- $ T=7 $. Attack the 3rd enemy, its health becomes $ 2-1=1 $.
- $ T=8 $. Attack the 3rd enemy, its health becomes $ 1-1=0 $.

Sample Explanation 3

Be careful of overflow.

见题面 Input 部分

见题面 Output 部分