Triple Attack

AtCoder

IDabc368_c

Time2000ms

Memory256MB

Difficulty—

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. ## Constraints * $1 \leq N \leq 2\times 10^5$ * $1 \leq H_i \leq 10^9$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $H_1$ $H_2$ $\ldots$ $H_N$ [samples]

Samples

Input #1

3
6 2 2

Output #1

8

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 $1-1=0$.

Input #2

9
1 12 123 1234 12345 123456 1234567 12345678 123456789

Output #2

82304529

Input #3

5
1000000000 1000000000 1000000000 1000000000 1000000000

Output #3

3000000000

Beware of integer overflow.

API Response (JSON)

{
  "problem": {
    "name": "Triple Attack",
    "description": {
      "content": "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 becom",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc368_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are playing a game.\nThere are $N$ enemies lined up in a row, and the $i$\\-th enemy from the front has a health of $H_i$.\nYou will repeat the following action until the healths of all enemies becom...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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