Problem: It was the third month of remote learning, Nastya got sick of staying at dormitory, so she decided to return to her hometown. In order to make her trip more entertaining, one of Nastya's friend presented her an integer array a. 

Several hours after starting her journey home Nastya remembered about the present. To entertain herself she decided to check, are there four different indices x, y, z, w such that a_x + a_y = a_z + a_w.

Her train has already arrived the destination, but she still hasn't found the answer. Can you help her unravel the mystery?

Input

The first line contains the single integer n (4 ≤ n ≤ 200 000) — the size of the array.

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 2.5 ⋅ 10^6).

Output

Print "YES" if there are such four indices, and "NO" otherwise.

If such indices exist, print these indices x, y, z and w (1 ≤ x, y, z, w ≤ n).

If there are multiple answers, print any of them.

Examples

Input


6
2 1 5 2 7 4


Output


YES
2 3 1 6 

Input


5
1 3 1 9 20


Output


NO

Note

In the first example a_2 + a_3 = 1 + 5 = 2 + 4 = a_1 + a_6. Note that there are other answer, for example, 2 3 4 6.

In the second example, we can't choose four indices. The answer 1 2 2 3 is wrong, because indices should be different, despite that a_1 + a_2 = 1 + 3 = 3 + 1 = a_2 + a_3

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.stream.IntStream;
import java.io.OutputStream;
import java.util.Arrays;
import java.util.Collection;
import java.util.HashMap;
import java.io.IOException;
import java.io.Reader;
import java.io.InputStreamReader;
import java.util.function.IntPredicate;
import java.io.FileNotFoundException;
import java.util.HashSet;
import java.util.stream.Stream;
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);
        GoingHome solver = new GoingHome();
        solver.solve(1, in, out);
        out.close();
    }

    static class GoingHome {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            var a = in.readIntArray(n);
            var sz = ArrayUtils.max(a) + 1;
            var place = new int[sz][5];
            for (int i = 0; i < a.length; ++i) {
                var e = a[i];
                place[e][++place[e][0]] = i + 1;
                if (place[e][0] == 4) {
                    out.YES();
                    out.println(Arrays.copyOfRange(place[e], 1, 5));
                    return;
                }
            }

            int one = -1, two = -1;
            for (var e : a) {
                if (e != one && place[e][0] > 1) {
                    if (one == -1) {
                        one = e;
                    } else {
                        two = e;
                        break;
                    }
                }
            }

            if (two > 0) {
                out.YES();
                out.printf("%d %d %d %d\n", place[one][1], place[two][1], place[one][2], place[two][2]);
                return;
            }

            if (one != -1) {
                for (int e : a) {
                    var other = 2 * one - e;
                    if (e != one && other > 0 && other < place.length && place[other][0] > 0) {
                        out.YES();
                        out.print(place[one][1]);
                        out.space();
                        out.print(place[one][2]);
                        out.space();
                        out.print(place[e][1]);
                        out.space();
                        out.println(place[other][1]);
                        return;
                    }
                }
            }

            int m = ArrayUtils.firstTrue(1, 10_000, (int k) -> k * (k - 1) / 2 > 5e6);
            var take = new IntSet();
            for (var e : a) {
                take.add(e);
                if (take.size() == m) break;
            }

            var b = take.stream().mapToInt(e -> e).toArray();

            var sums = new IntMap(b.length * (b.length - 1) / 2);

            for (int i = 0; i < b.length - 1; i++) {
                for (int j = i + 1; j < b.length; j++) {
                    int sum = b[i] + b[j];
                    if (!sums.containsKey(sum)) {
                        sums.put(sum, i * b.length + j);
                    } else {
                        int value = sums.get(sum);
                        int j0 = value % b.length;
                        int i0 = value / b.length;
                        out.YES();
                        out.print(place[b[i]][1] + " " + place[b[j]][1] + " ");
                        out.println(place[b[i0]][1] + " " + place[b[j0]][1]);
                        return;
                    }
                }
            }

            out.NO();
        }

    }

    static class ArrayUtils {
        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;
        }

        public static int firstTrue(int low, int high, IntPredicate predicate) {
            while (low <= high) {
                int mid = low + (high - low) / 2;
                if (predicate.test(mid)) {
                    high = mid - 1;
                } else {
                    low = mid + 1;
                }
            }
            return low;
        }

    }

    static class IntSet extends HashSet<Integer> {
        public IntSet() {
            super();
        }

        public IntSet(int initialCapacity) {
            super(initialCapacity);
        }

    }

    static class InputReader extends BufferedReader {
        StringTokenizer tokenizer;

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

        public InputReader(Reader reader) {
            super(reader);
        }

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

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    String line = readLine();
                    if (line == null) continue;
                    tokenizer = new StringTokenizer(line);
                } 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();
//        IntStream.generate(this::nextInt).limit(size).toArray();
            return array;
        }

    }

    static class IntMap extends HashMap<Integer, Integer> {
        public IntMap(int initialCapacity) {
            super(initialCapacity);
        }

        public IntMap() {
            super();
        }

    }

    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 YES() {
            println("YES");
        }

        public void NO() {
            println("NO");
        }

        public void space() {
            print(' ');
        }

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

    }
}