Problem:
Score : 800 points

Problem Statement

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.

Sample Input 1

3
1 5 9

Sample Output 1

Yes
1 1 1 2 2 2 3 3 3

For example, the second occurrence of the integer 2 from the left in a in the output is the fifth element of a from the left.
Similarly, the condition is satisfied for the integers 1 and 3.

Sample Input 2

2
4 1

Sample Output 2

No

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)



import java.io.*;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            final int n = in.nextInt();
            final int N = n * n;
            final int[] res = new int[N + 1];
            for (int i = 0; i < n; i++) {
                int a = in.nextInt();
                res[a] = i + 1;
            }
            throw new RuntimeException();
//            int sum = 0;
//            for (int i = 1; i <= N; ++i) {
//                if (res[i] > 0)
//                    sum += res[i];
//                if (i < sum) {
//                    out.println("No");
//                    return;
//                }
//            }
//
//            sum = 0;
//            for (int i = N; i > 0; --i) {
//                if (res[i] > 0)
//                    sum += n - res[i];
//                if ((N - i + 1) < sum) {
//                    out.println("No");
//                    return;
//                }
//            }
//
//            List<Integer> order = new ArrayList<>();
//            for (int i = 1; i<=N; ++i) {
//                if (res[i] > 0) order.add(res[i]);
//            }
//            int pos = 0;
//            int cnt = order.get(0) - 1;
//            outerloop:
//            for (int i =1 ; i <=N; ++i) {
//                if (res[i] > 0) continue;
//                while (cnt == 0) {
//                    pos++;
//                    if (pos >= order.size()) break outerloop;
//                    cnt = order.get(pos) - 1;
//                }
//                res[i] = order.get(pos);
//                cnt--;
//            }
//            pos = order.size() - 1;
//            cnt = n - order.get(order.size() - 1);
//            outerloop1:
//            for (int i = N; i > 0; --i) {
//                if (res[i] > 0) continue;
//                while (cnt == 0) {
//                    pos--;
//                    if (pos < 0) break outerloop1;
//                    cnt = n - order.get(pos);
//                }
//                res[i] = order.get(pos);
//                cnt--;
//            }
//
//            out.println("Yes");
//            for (int i = 1; i <= N; ++i) {
//                if (i > 1) out.print(" ");
//                out.print(res[i]);
//            }
//            out.println();

        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}