You are playing a game.

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

You will repeat the following action until the healths of all enemies become $0$ or less, using a variable $T$ initialized to $0$.

• Increase $T$ by $1$. Then, attack the frontmost 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 healths of all enemies become $0$ or less.

The input is given from Standard Input in the following format:

$N$

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

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

The actions are performed as follows:

• $T$ becomes $1$. Attack the 1st enemy, and its health becomes $6-1=5$.
• $T$ becomes $2$. Attack the 1st enemy, and its health becomes $5-1=4$.
• $T$ becomes $3$. Attack the 1st enemy, and its health becomes $4-3=1$.
• $T$ becomes $4$. Attack the 1st enemy, and its health becomes $1-1=0$.
• $T$ becomes $5$. Attack the 2nd enemy, and its health becomes $2-1=1$.
• $T$ becomes $6$. Attack the 2nd enemy, and its health becomes $1-3=-2$.
• $T$ becomes $7$. Attack the 3rd enemy, and its health becomes $2-1=1$.
• $T$ becomes $8$. Attack the 3rd enemy, and its health becomes $1-1=0$.