Contest Duration: - (local time) (300 minutes) Back to Home
K - Correct Check Digit /

Time Limit: 3 sec / Memory Limit: 1024 MB

### 問題文

• \displaystyle \sum^{N}_{i=1} i \times ( Si 文字目を 1 桁の整数とみなした時の値 )

### 制約

• N1 以上 2 \times 10^5 以下の整数
• S は数字と ? からなる長さ N の文字列

### 入力

N
S


### 出力

そうでない場合、以下の形式に従い置き換え方を出力してください。

Yes
T


まず、 1 行目に Yes と出力してください。

### 入力例 1

5
935?0


### 出力例 1

Yes
93550


935?04 文字目の ? を置き換えることを考えます。

• 4 文字目の ?5 に置き換えた時、置き換えた後の文字列は T= 93550 となります。
• 1 \times 9 + 2 \times 3 + 3 \times 5 + 4 \times 5 + 5 \times 0 = 50 となり、これは確かに 10 の倍数です。

### 入力例 2

5
1?3?5


### 出力例 2

No


1?3?52 つの ? を数字に置き換える方法は全部で 100 通りありますが、どのように置き換えても問題文中の条件を満たすことができません。

### 入力例 3

1
0


### 出力例 3

Yes
0


### Problem Statement

You are given a length-N string S consisting of digits and ?.
Determine if one can replace each occurrence of ? with a digit so that the following value is a multiple of 10. If it is possible, find one such replacement.

• \displaystyle \sum^{N}_{i=1} i \times (the i-th character of S interpreted as a one-digit integer).

### Constraints

• N is an integer between 1 and 2 \times 10^5, inclusive.
• S is a length-N string consisting of digits and ?.

### Input

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

N
S


### Output

Print No in a single line if there is no conforming replacement.
Otherwise, print a replacement in the following format.

Yes
T


The first line should contain Yes.
The second line should contain a string T obtained by a replacement that satisfies the condition in the problem statement.

### Sample Input 1

5
935?0


### Sample Output 1

Yes
93550


Consider what digit should replace the 4-th character ? of 935?0.

• If the 4-th character ? is replaced by 5, the resulting string is T= 93550.
• 1 \times 9 + 2 \times 3 + 3 \times 5 + 4 \times 5 + 5 \times 0 = 50, which is indeed a multiple of 10.

Alternatively, we can also satisfy the condition in the problem statement by replacing the 4-th character ? with 0, thus yielding 93500.

### Sample Input 2

5
1?3?5


### Sample Output 2

No


There are 100 ways to replace the two occurrences of ? in 1?3?5, but none of them satisfies the condition in the problem statement.

### Sample Input 3

1
0


### Sample Output 3

Yes
0


While the string 0 does not contain ? to replace, 1 \times 0 = 0 is already a multiple of 10.