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<bits/stdc++.h>
#define N 505
using namespace std;
int n,a[N];
int ans[N*N],arr[N];
bool cmp(int ta,int tb){
    return a[ta]<a[tb];
}
int main(){
    scanf("%d",&n);
    for(int i=1;i<=n;i++) scanf("%d",&a[i]),ans[a[i]]=i,arr[i]=i;
    sort(arr+1,arr+n+1,cmp);
    for(int i=1;i<=n;i++){
        int v=arr[i],cnt=v-1;
        for(int j=1;j<a[v];j++)
            if(ans[j]==0&&cnt!=0) ans[j]=v,cnt--;
        if(cnt!=0) return puts("No"),0;
    }
    for(int i=n;i>=1;i--){
        int v=arr[i],cnt=n-v;
        for(int j=n*n;j>a[v];j--)
            if(ans[j]==0&&cnt!=0) ans[j]=v,cnt--;
        if(cnt!=0) return puts("No"),0;
    }
    puts("Yes");
    for(int i=1;i<=n*n;i++) printf("%d ",ans[i]);
    return 0;
}