Problem: While discussing a proper problem A for a Codeforces Round, Kostya created a cyclic array of positive integers a_1, a_2, …, a_n. Since the talk was long and not promising, Kostya created a new cyclic array b_1, b_2, …, b_{n} so that b_i = (a_i mod a_{i + 1}), where we take a_{n+1} = a_1. Here mod is the [modulo operation](https://en.wikipedia.org/wiki/Modulo_operation). When the talk became interesting, Kostya completely forgot how array a had looked like. Suddenly, he thought that restoring array a from array b would be an interesting problem (unfortunately, not A).

Input

The first line contains a single integer n (2 ≤ n ≤ 140582) — the length of the array a.

The second line contains n integers b_1, b_2, …, b_{n} (0 ≤ b_i ≤ 187126).

Output

If it is possible to restore some array a of length n so that b_i = a_i mod a_{(i mod n) + 1} holds for all i = 1, 2, …, n, print «YES» in the first line and the integers a_1, a_2, …, a_n in the second line. All a_i should satisfy 1 ≤ a_i ≤ 10^{18}. We can show that if an answer exists, then an answer with such constraint exists as well.

It it impossible to restore any valid a, print «NO» in one line.

You can print each letter in any case (upper or lower).

Examples

Input

4
1 3 1 0


Output

YES
1 3 5 2


Input

2
4 4


Output

NO

Note

In the first example:

  * 1 mod 3 = 1 
  * 3 mod 5 = 3 
  * 5 mod 2 = 1 
  * 2 mod 1 = 0 

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.IOException;
import java.io.InputStreamReader;
import java.io.FileNotFoundException;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Asgar Javadov
 */
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);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            int[] b = in.readIntArray(n);

            boolean allEq = true;
            for (int i = 0; i < n; ++i) {
                if (b[i] != b[0]) {
                    allEq = false;
                    break;
                }
            }

            if (allEq) {
                if (b[0] == 0) {
                    out.yes();
                    out.println(ArrayUtils.createArray(n, 1));
                } else {
                    out.no();
                }
                return;
            }

            long[] a = new long[n];

            int m = MathUtils.max(b);
            int index = 0;
            for (; index < n; index++) {
                if (b[index] == m && b[(index - 1 + n) % n] < m) break;
            }

            a[index] = b[index];

            for (int i = index - 1, j = 0; j < n - 1; --i, ++j) {
                int cur = (i + n) % n;
                int next = (i + 1 + n) % n;
                if (j == 0)
                    a[cur] = 2 * a[next] + b[cur];
                else
                    a[cur] = a[next] + b[cur];
            }

            out.yes();
            out.println(a);

//    	for (int i = 1; i < n; ++i) {
//    	    if (b[i - 1] < b[i]) {
//    	        a[i] = b[i];
//    	        continue;
//            }
//        }
        }

    }

    static class InputReader extends BufferedReader {
        StringTokenizer tokenizer;

        public InputReader(InputStream inputStream) {
            super(new InputStreamReader(inputStream), 32768);
        }

        public InputReader(String filename) {
            super(new InputStreamReader(Thread.currentThread().getContextClassLoader().getResourceAsStream(filename)));
        }

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

        public Integer nextInt() {
            return Integer.valueOf(next());
        }

        public int[] readIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++)
                array[i] = nextInt();
            return array;
        }

    }

    static class MathUtils {
        public static int max(int... args) {
            int res = args[0];
            for (int i = 1; i < args.length; ++i)
                if (res < args[i])
                    res = args[i];
            return res;
        }

    }

    static class OutputWriter extends PrintWriter {
        public OutputWriter(OutputStream outputStream) {
            super(outputStream);
        }

        public OutputWriter(Writer writer) {
            super(writer);
        }

        public OutputWriter(String filename) throws FileNotFoundException {
            super(filename);
        }

        public void println(int[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i > 0) print(' ');
                print(array[i]);
            }
            println();
        }

        public void println(long[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i > 0) print(' ');
                print(array[i]);
            }
            println();
        }

        public void yes() {
            println("Yes");
        }

        public void no() {
            println("No");
        }

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

    }

    static class ArrayUtils {
        public static int[] createArray(int count, int value) {
            int[] array = new int[count];
            Arrays.fill(array, value);
            return array;
        }

    }
}