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D - Sum of Sum of Digits /

Time Limit: 5 sec / Memory Limit: 1024 MB

### 制約

• 1\leq N\leq 2\times 10^5
• 1\leq A_i < 10^9

### 入力

N
A_1 \ldots A_N


### 出力

x を非負整数とするとき，\sum_{i=1}^N f(A_i + x) としてありうる最小値を出力してください．

### 入力例 1

4
4 13 8 6


### 出力例 1

14


### 入力例 2

4
123 45 678 90


### 出力例 2

34


### 入力例 3

3
1 10 100


### 出力例 3

3


### 入力例 4

1
153153153


### 出力例 4

1


Score : 800 points

### Problem Statement

For a positive integer x, let f(x) denote the sum of its digits. For instance, we have f(153) = 1 + 5 + 3 = 9, 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 the minimum possible value of \sum_{i=1}^N f(A_i + x) where x is a non-negative integer.

### Constraints

• 1\leq N\leq 2\times 10^5
• 1\leq A_i < 10^9

### Input

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

N
A_1 \ldots A_N


### Output

Print the minimum possible value of \sum_{i=1}^N f(A_i + x) where x is a non-negative integer.

### Sample Input 1

4
4 13 8 6


### Sample Output 1

14


For instance, x = 7 makes \sum_{i=1}^N f(A_i+x) = f(11) + f(20) + f(15) + f(13) = 14.

### Sample Input 2

4
123 45 678 90


### Sample Output 2

34


For instance, x = 22 makes \sum_{i=1}^N f(A_i+x) = f(145) + f(67) + f(700) + f(112) = 34.

### Sample Input 3

3
1 10 100


### Sample Output 3

3


For instance, x = 0 makes \sum_{i=1}^N f(A_i+x) = f(1) + f(10) + f(100) = 3.

### Sample Input 4

1
153153153


### Sample Output 4

1


For instance, x = 9999846846847 makes \sum_{i=1}^N f(A_i+x) = f(10000000000000) = 1.