Contest Duration: - (local time) (120 minutes) Back to Home
D - Without Carry /

Time Limit: 4 sec / Memory Limit: 1024 MB

### 制約

• 2 \leq N \leq 10^6
• 0 \leq A_i \leq 10^6-1
• 入力される値はすべて整数

### 入力

N
A_1 A_2 \cdots A_N


### 入力例 1

4
4 8 12 90


### 出力例 1

3


### 入力例 2

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


### 出力例 2

6


### 入力例 3

5
1 1 1 1 1


### 出力例 3

10


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


### 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