Digits in Multiplication

AtCoder

IDabc057_c

Time2000ms

Memory256MB

Difficulty—

You are given an integer $N$. For two positive integers $A$ and $B$, we will define $F(A,B)$ as the larger of the following: the number of digits in the decimal notation of $A$, and the number of digits in the decimal notation of $B$. For example, $F(3,11) = 2$ since $3$ has one digit and $11$ has two digits. Find the minimum value of $F(A,B)$ as $(A,B)$ ranges over all pairs of positive integers such that $N = A \times B$. ## Constraints * $1 \leq N \leq 10^{10}$ * $N$ is an integer. ## Input The input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

3

$F(A,B)$ has a minimum value of $3$ at $(A,B)=(100,100)$.

Input #2

Output #2

7

There are two pairs $(A,B)$ that satisfy the condition: $(1,1000003)$ and $(1000003,1)$. For these pairs, $F(1,1000003)=F(1000003,1)=7$.

Input #3

9876543210

Output #3

API Response (JSON)

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      "content": "You are given an integer $N$.   For two positive integers $A$ and $B$, we will define $F(A,B)$ as the larger of the following: the number of digits in the decimal notation of $A$, and the number of di",
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      "content": "You are given an integer $N$.  \nFor two positive integers $A$ and $B$, we will define $F(A,B)$ as the larger of the following: the number of digits in the decimal notation of $A$, and the number of di...",
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