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B - Factorial Yen Coin

Score : $200$ points

Problem Statement

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:

$P$

Output

Print the minimum number of coins needed.

9

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.

119

10

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

10000000

24