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- Find Digits

# Find Digits

# Find Digits

An integer is a *divisor* of an integer if the remainder of .

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.

**Note:** Each digit is considered to be unique, so each occurrence of the same digit should be counted (e.g. for , is a divisor of each time it occurs so the answer is ).

**Input Format**

The first line is an integer, , indicating the number of test cases.

The subsequent lines each contain an integer, .

**Constraints**

**Output Format**

For every test case, count the number of digits in that are divisors of . Print each answer on a new line.

**Sample Input**

```
2
12
1012
```

**Sample Output**

```
2
3
```

**Explanation**

The number is broken into two digits, and . When is divided by either of those two digits, the remainder is so they are divisors.

The number is broken into four digits, , , , and . is evenly divisible by its digits , , and , but it is *not* divisible by as division by zero is undefined.