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 JAVA):

Solution:
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;

public class Main {
	InputStream is;

	int __t__ = 1;
	int __f__ = 0;
	int __FILE_DEBUG_FLAG__ = __f__;
	String __DEBUG_FILE_NAME__ = "src/D4";

	FastScanner in;
	PrintWriter out;

	class Pair implements Comparable<Pair> {
		int v;
		int idx;

		Pair(int v, int idx) {
			this.v = v;
			this.idx = idx;
		}

		public int compareTo(Pair s) {
			return idx - s.idx;
		}

		public String toString() {
			return "(" + v + ", " + idx + ")";
		}
	}
	
	public void solve() {
		int n = in.nextInt(), n2 = n * n;
		int[] a = new int[n+1];
		for (int i = 1; i <= n; i++) {
			a[i] = in.nextInt();
		}
		
		int[] res = new int[n2+1];
		int[] cnt = new int[n+1];
		Arrays.fill(res, -1);
		for (int i = 1; i <= n; i++) {
			res[a[i]] = i;
			cnt[i]++;
		}
		
		PriorityQueue<Pair> pq = new PriorityQueue<>();
		Queue<Integer> free = new LinkedList<>();
		
		for (int i = 1; i <= n; i++) {
			pq.add(new Pair(i, a[i]));
		}
		
		for (int i = 1; i <= n2; i++) {
			if (res[i] != -1) {
				if (cnt[res[i]] == res[i]) {
					free.add(res[i]);
					continue;
				} else {
					System.out.println("No");
					return;
				}
			}
			if (!pq.isEmpty()) {
				Pair next = pq.peek();
				if (cnt[next.v] == next.v) {
					pq.poll(); i--;
					continue;
				} else {
					cnt[next.v]++;
					res[i] = next.v;
				}
			} else {
				while (!free.isEmpty()) {
					int next = free.peek();
					if (cnt[next] == n) {
						free.poll();
						continue;
					}
					res[i] = next;
					cnt[next]++;
					break;
				}
				
				if (res[i] == -1) {
					System.out.println("No");
					return;
				}
			}
		}
		out.println("Yes");
		for (int i = 1; i <= n2; i++) {
			out.print(res[i]);
			if (i != n2) out.print(" ");
		}
		out.println();
		out.close();
	}

	public void run() {
		if (__FILE_DEBUG_FLAG__ == __t__) {
			try {
				is = new FileInputStream(__DEBUG_FILE_NAME__);
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
			System.out.println("FILE_INPUT!");
		} else {
			is = System.in;
		}
		in = new FastScanner(is);
		out = new PrintWriter(System.out);
		Thread t = new Thread(null, new Runnable() {

			@Override
			public void run() {
				solve();
			}
		}, "lul", 1 << 30);
		t.start();
	}

	public static void main(String[] args) {
		new Main().run();
	}

	public void mapDebug(int[][] a) {
		System.out.println("--------map display---------");

		for (int i = 0; i < a.length; i++) {
			for (int j = 0; j < a[i].length; j++) {
				System.out.printf("%3d ", a[i][j]);
			}
			System.out.println();
		}

		System.out.println("----------------------------");
		System.out.println();
	}

	public void debug(Object... obj) {
		System.out.println(Arrays.deepToString(obj));
	}

	class FastScanner {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public FastScanner(InputStream stream) {
			this.stream = stream;
			// stream = new FileInputStream(new File("dec.in"));

		}

		int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

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

		int[] nextIntArray(int n) {
			int[] array = new int[n];
			for (int i = 0; i < n; i++)
				array[i] = nextInt();

			return array;
		}

		int[][] nextIntMap(int n, int m) {
			int[][] map = new int[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextIntArray(m);
			}
			return map;
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		long[] nextLongArray(int n) {
			long[] array = new long[n];
			for (int i = 0; i < n; i++)
				array[i] = nextLong();

			return array;
		}

		long[][] nextLongMap(int n, int m) {
			long[][] map = new long[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextLongArray(m);
			}
			return map;
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		double[] nextDoubleArray(int n) {
			double[] array = new double[n];
			for (int i = 0; i < n; i++)
				array[i] = nextDouble();

			return array;
		}

		double[][] nextDoubleMap(int n, int m) {
			double[][] map = new double[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextDoubleArray(m);
			}
			return map;
		}

		String next() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		String[] nextStringArray(int n) {
			String[] array = new String[n];
			for (int i = 0; i < n; i++)
				array[i] = next();

			return array;
		}

		String nextLine() {
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}
	}
}