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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.