Problem: You are given an integer sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.

* a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
* For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.

Constraints

* 1 ≤ N ≤ 500
* 1 ≤ x_i ≤ N^2
* All x_i are distinct.

Input

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


N
x_1 x_2 ... x_N


Output

If there does not exist an integer sequence a that satisfies all the conditions, print `No`. If there does exist such an sequence a, print `Yes` in the first line, then print an instance of a in the second line, with spaces inbetween.

Examples

Input

3
1 5 9


Output

Yes
1 1 1 2 2 2 3 3 3


Input

2
4 1


Output

No

Solution (in CPP):

Solution:

#include<cstdio>
#include<algorithm>
using namespace std;
const int N=510;
struct fk{int x,id;}q[N];
int n,a[N*N],cnt[N],flag;
bool cmp(fk a,fk b){return a.x<b.x;}
int main(){
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
        scanf("%d",&q[i].x),q[i].id=i;
    sort(q+1,q+n+1,cmp);
    for(int i=1;i<=n;i++){
        int id=q[i].id;
        a[q[i].x]=id;++cnt[id];
        for(int j=1;j<q[i].x;j++){
            if(cnt[id]==id)break;
            if(!a[j])a[j]=id,++cnt[id];
        }
        if(cnt[id]<id)flag=1;
    }
    if(flag){puts("No");return 0;}
    flag=0;
    for(int i=n;i>=1;i--){
        int id=q[i].id;
        for(int j=n*n;j>q[i].x;j--){
            if(cnt[id]==n)break;
            if(!a[j])a[j]=id,++cnt[id];
        }
        if(cnt[id]<n)flag=1;
    }
    if(flag){puts("No");return 0;}
    puts("Yes");
    for(int i=1;i<=n*n;i++)printf("%d ",a[i]);
    puts("");
}