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C - All Pair Digit Sums /

Time Limit: 4 sec / Memory Limit: 1024 MB

### 制約

• 1\leq N\leq 2\times 10^5
• 1\leq A_i < 10^{15}

### 入力

N
A_1 \ldots A_N


### 出力

\sum_{i=1}^N\sum_{j=1}^N f(A_i + A_j) を出力してください．

### 入力例 1

2
53 28


### 出力例 1

36


\sum_{i=1}^N\sum_{j=1}^N f(A_i + A_j) = f(A_1+A_1)+f(A_1+A_2)+f(A_2+A_1)+f(A_2+A_2)=7+9+9+11=36 です．

### 入力例 2

1
999999999999999


### 出力例 2

135


\sum_{i=1}^N\sum_{j=1}^N f(A_i + A_j) = f(A_1+A_1) = 135 です．

### 入力例 3

5
123 456 789 101 112


### 出力例 3

321


Score : 500 points

### Problem Statement

For a positive integer x, let f(x) denote the sum of its digits. For instance, f(158) = 1 + 5 + 8 = 14, f(2023) = 2 + 0 + 2 + 3 = 7, and f(1) = 1.

You are given a sequence of positive integers A = (A_1, \ldots, A_N). Find \sum_{i=1}^N\sum_{j=1}^N f(A_i + A_j).

### Constraints

• 1\leq N\leq 2\times 10^5
• 1\leq A_i < 10^{15}

### Input

The input is given from Standard Input in the following format:

N
A_1 \ldots A_N


### Output

Print \sum_{i=1}^N\sum_{j=1}^N f(A_i + A_j).

### Sample Input 1

2
53 28


### Sample Output 1

36


We have \sum_{i=1}^N\sum_{j=1}^N f(A_i + A_j) = f(A_1+A_1)+f(A_1+A_2)+f(A_2+A_1)+f(A_2+A_2)=7+9+9+11=36.

### Sample Input 2

1
999999999999999


### Sample Output 2

135


We have \sum_{i=1}^N\sum_{j=1}^N f(A_i + A_j) = f(A_1+A_1) = 135.

### Sample Input 3

5
123 456 789 101 112


### Sample Output 3

321