Counting Pairs with Common Digit

Given N positive integers A₁, A₂, ..., A_N, count the number of pairs (i, j) (with 1 \le i < j &le N) such that A_i and A_j share at least one common digit (the digit can occur in different positions in the two numbers).

The condition can be formally stated in \(\LaTeX\) as follows:

[ 1 \le i < j \le N \quad \text{and} \quad \exists d ; \text{such that} ; d \in \text{digits}(A_i) ; \text{and} ; d \in \text{digits}(A_j). ]

inputFormat

The first line contains an integer N (1 \le N). The second line contains N positive integers A₁, A₂, ..., A_N separated by spaces.

outputFormat

Output a single integer, which is the count of pairs (i, j) that satisfy the condition.

sample

3
11 12 23

2