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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author ilyakor
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            ArrayList<ii> a = new ArrayList<>();
            for (int i = 0; i < n; ++i) {
                int x = in.nextInt();
                a.add(new ii(x - 1, i));
            }
            Collections.sort(a);
            int[] d = new int[n * n];
            Arrays.fill(d, -1);
            int l = 0, sum = 0;
            for (ii entry : a) {
                int pos = entry.first;
                int x = entry.second;
                if (pos - sum + 1 < x + 1) {
                    out.printLine("No");
                    return;
                }
                for (int i = 0; i < x; ++i) {
                    while (d[l] != -1) ++l;
                    d[l] = x;
                    ++sum;
                }
                Assert.assertTrue(d[pos] == -1);
                d[pos] = x;
                ++sum;
            }
            int[] need = new int[n];
            for (int i = 0; i < n; ++i)
                need[i] = n - a.get(n - i - 1).second - 1;
            l = 0;
            for (int i = d.length - 1; i >= 0; --i) {
                if (d[i] != -1) continue;
                while (l < need.length && need[l] == 0) ++l;
                ii entry = a.get(n - l - 1);
                int pos = entry.first;
                int x = entry.second;
                if (i <= pos) {
                    out.printLine("No");
                    return;
                }
                --need[l];
                d[i] = x;
            }
            out.printLine("Yes");
            for (int i = 0; i < d.length; ++i)
                out.print((d[i] + 1) + " ");
            out.printLine();
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buffer = new byte[10000];
        private int cur;
        private int count;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

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

        public int read() {
            if (count == -1) {
                throw new InputMismatchException();
            }
            try {
                if (cur >= count) {
                    cur = 0;
                    count = stream.read(buffer);
                    if (count <= 0)
                        return -1;
                }
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            return buffer[cur++];
        }

        public int readSkipSpace() {
            int c;
            do {
                c = read();
            } while (isSpace(c));
            return c;
        }

        public int nextInt() {
            int sgn = 1;
            int c = readSkipSpace();
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res = res * 10 + c - '0';
                c = read();
            } while (!isSpace(c));
            res *= sgn;
            return res;
        }

    }

    static class Assert {
        public static void assertTrue(boolean flag) {
//        if (!flag)
//        while (true);
            if (!flag)
                throw new AssertionError();
        }

    }

    static class ii implements Comparable<ii> {
        public int first;
        public int second;

        public ii() {
        }

        public ii(int first, int second) {
            this.first = first;
            this.second = second;
        }

        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;

            ii ii = (ii) o;

            if (first != ii.first) return false;
            if (second != ii.second) return false;

            return true;
        }

        public int hashCode() {
            int result = first;
            result = 31 * result + second;
            return result;
        }

        public int compareTo(ii o) {
            if (first != o.first) {
                return first < o.first ? -1 : 1;
            }
            if (second != o.second) {
                return second < o.second ? -1 : 1;
            }
            return 0;
        }


        public String toString() {
            return "{" +
                    "first=" + first +
                    ", second=" + second +
                    '}';
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

    }
}