Score : $600$ points

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.

Constraints

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

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $\cdots$ $A_N$

Output

Print the answer.

4
4 8 12 90

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.

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

6

5
1 1 1 1 1

10