Factorial Yen Coin

AtCoder

IDabc208_b

Time2000ms

Memory256MB

Difficulty—

The coins used in the Kingdom of Takahashi are $1!$\-yen coins, $2!$\-yen coins, $\dots$, and $10!$\-yen coins. Here, $N! = 1 \times 2 \times \dots \times N$. Takahashi has $100$ of every kind of coin, and he is going to buy a product worth $P$ yen **by giving the exact amount without receiving change**. We can prove that there is always such a way to make payment. At least how many coins does he need to use in his payment? ## Constraints * $1 \leq P \leq 10^7$ * $P$ is an integer. ## Input Input is given from Standard Input in the following format: $P$ [samples]

Samples

Input #1

Output #1

3

By giving one $(1! =) 1$\-yen coin, one $(2! =) 2$\-yen coin, and one $(3! =) 6$\-yen coin, we can make the exact payment for the product worth $9$ yen. There is no way to pay this amount using fewer coins.

Input #2

Output #2

10

We should use one $1!$\-yen coin, two $2!$\-yen coins, three $3!$\-yen coins, and four $4!$\-yen coins.

Input #3

10000000

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Factorial Yen Coin",
    "description": {
      "content": "The coins used in the Kingdom of Takahashi are $1!$\\-yen coins, $2!$\\-yen coins, $\\dots$, and $10!$\\-yen coins. Here, $N! = 1 \\times 2 \\times \\dots \\times N$. Takahashi has $100$ of every kind of coin",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc208_b"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "The coins used in the Kingdom of Takahashi are $1!$\\-yen coins, $2!$\\-yen coins, $\\dots$, and $10!$\\-yen coins. Here, $N! = 1 \\times 2 \\times \\dots \\times N$.\nTakahashi has $100$ of every kind of coin...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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