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## 문제

Julia's wedding is going to have a huge one ton cake. All $n$ guests want to taste the cake, so it's going to be cut in $n$ pieces. But this task is not that easy, because all guests are on a special mathematical diet. Guest $i$ is only willing to eat the cake if the weight of his piece in tons $w_i$ has exactly $a_i$ significant digits after the decimal point. In decimal representation all digits up to the last non-zero digit after the decimal point are significant. For example, number 0.007 contains three significant digits after the decimal point, number 1.45 --- two, and number 17.0 has no significant digits after the decimal point.

Your task is to cut the cake for Julia's wedding so that every guest could taste it.

## 입력

First line contains single integer $n$ --- number of guests ($1 \le n \le 10^5$).

Next line contains $n$ integers $a_i$ --- constraint for the weight of $i$-th piece ($1 \le a_i \le 10^5$).

Sum of all $a_i$ doesn't exceed $10^5$.

## 출력

Output should contain "NO", if there is no way to cut the cake.

Otherwise, output "YES" on the first line. Each of the next $n$ lines should contain one single real number $w_i$ --- weight of the piece for the $i$-th guest with exactly $a_i$ digits after the decimal point. All $a_i$ digits after the decimal point have to be significant.

## 서브태스크

번호 배점 제한
1 17

$n \le 100$, $a_i \le 10$

2 21

$n \le 10^5$, all $a_i$ are equal

3 25

$n \le 10^3$, sum of all $a_i$ doesn't exceed $10^3$

4 37

$n \le 10^5$, sum of all $a_i$ doesn't exceed $10^5$

## 예제 입력 1

5
2 4 4 3 2


## 예제 출력 1

YES
0.47
0.1234
0.1326
0.024
0.25


## 채점 및 기타 정보

• 예제는 채점하지 않는다.