Problem Statement

You are given an integer sequence of length N: $A=(A_1,A_2,\cdots,A_N)$.
Find the number of pairs of integers $(i,j) (1 \leq i < j \leq N)$ such that calculation of A_i+A_j by column addition does not involve carrying.

Input

Input is given from Standard Input in the following format:
N
$A_1 A_2 \cdots A_N$

Output

Print the answer.

Constraints

• $2 \leq N \leq 10^6$
• $0 \leq A_i \leq 10^6-1$
• All values in input are integers.

Sample Input 1

4
4 8 12 90

Sample Output 1

3

The pairs (i,j) that count are (1,3),(1,4),(2,4).
For example, calculation of A_1+A_3=4+12 does not involve carrying, so (i,j)=(1,3) counts.
On the other hand, calculation of A_3+A_4=12+90 involves carrying, so (i,j)=(3,4) does not count.

Sample Input 2

20
313923 246114 271842 371982 284858 10674 532090 593483 185123 364245 665161 241644 604914 645577 410849 387586 732231 952593 249651 36908

Sample Output 2

6

Sample Input 3

5
1 1 1 1 1

Sample Output 3

10

见题面 Input 部分

见题面 Output 部分