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>
using namespace std;
const int MOD=1e9+7;
//const int MOD=998244353;
const long long LINF=1e18;
#define int long long
//template
template <typename T>
void fin(T a){
  cout<<a<<endl;
  exit(0);
}
//main
signed main(){
  int N;cin>>N;
  std::vector<int> v(N+1),ans(10000000,-1);
  for(int i=0;i<N;i++)cin>>v[i],v[i]--;
  typedef pair<int,int> P;
  std::vector<P> w(N);
  for(int i=0;i<N;i++)w[i]=P(v[i],i+1);
  sort(w.begin(),w.end());
  int now=0;
  for(int i=0;i<N;i++){
    int po=w[i].first,num=w[i].second;
    for(int j=1;j<num;j++){
      while(~ans[now])now++;
      ans[now]=num;if(now>=po)fin("No");
    }
    ans[po]=num;
  }
  for(int i=0;i<N;i++){
    int po=w[i].first,num=w[i].second;
    for(int j=0;j<N-num;j++){
      while(~ans[now])now++;
      ans[now]=num;if(now<=po)fin("No");
    }
  }
  bool f=false;
  cout<<"Yes"<<endl;
  for(int i=0;i<N*N;i++){
    if(f)cout<<" ";
    cout<<ans[i];f=true;
  }
  cout<<endl;
}