An integer $\boldsymbol{d}$ is a divisor of an integer $n$ if the remainder of $n\div d=0$.

Given an integer, for each digit that makes up the integer determine whether it is a divisor. Count the number of divisors occurring within the integer.

Example

$n=124$

Check whether $1$, $2$ and $4$ are divisors of $124$. All 3 numbers divide evenly into $124$ so return $3$.

$n=111$

Check whether $1$, $1$, and $1$ are divisors of $\mbox{111}$. All 3 numbers divide evenly into $\mbox{111}$ so return $3$.

$n=10$

Check whether $1$ and $0$ are divisors of $10$. $1$ is, but $0$ is not. Return $1$.

Function Description

Complete the findDigits function in the editor below.

findDigits has the following parameter(s):

int n: the value to analyze

Returns

int: the number of digits in $n$ that are divisors of $n$

Input Format

The first line is an integer, $\boldsymbol{\boldsymbol{t}}$, the number of test cases.

The $\boldsymbol{\boldsymbol{t}}$ subsequent lines each contain an integer, $n$.

Constraints

$1\leq t\leq15$

$0<n<10^9$

Sample Input
2
12
1012

Sample Output
2
3

Explanation

The number $12$ is broken into two digits, $1$ and $2$. When $12$ is divided by either of those two digits, the remainder is $0$ so they are both divisors.

The number $\textbf{1012}$ is broken into four digits, $1$, $0$, $1$, and $2$. $\textbf{1012}$ is evenly divisible by its digits $1$, $1$, and $2$, but it is not divisible by $0$ as division by zero is undefined.

见题面

见题面