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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class TP {

    public static PrintWriter out = new PrintWriter(System.out);
    public static FastReader in = new FastReader();

    public static void main(String[] args) {
        long s = System.currentTimeMillis();
        int t = 1;
//        t = ni();
        while (t-- > 0) solve();
        out.flush();
        tr(System.currentTimeMillis() - s + "ms");
    }


    private static void solve() {
        int n = ni();
        int[] a = na(n);
        int[][] val = new int[5000001][2];
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                int sum = a[i] + a[j];
                if (val[sum][0] != 0) {
                    if (val[sum][0] == (i + 1) || val[sum][0] == (j + 1) || val[sum][1] == (i + 1) || val[sum][1] == (j + 1))
                        continue;
                    out.println("YES");
                    out.println(val[sum][0] + " " + val[sum][1] + " " + (i + 1) + " " + (j + 1));
                    return;

                } else {
                    val[sum][0] = i + 1;
                    val[sum][1] = j + 1;
                }
            }
        }
        out.println("No");
    }

    private static long lcm(long a, long b) {
        return a * b / gcd(a, b);
    }

    public static int[][] enumPrimesAndLPF(int n) {
        int[] lpf = new int[n + 1];
        double lu = Math.log(n + 32);

        int tot = 0;
        int[] primes = new int[(int) ((n + 32) / lu + (n + 32) / lu / lu * 1.5)];

        for (int i = 2; i <= n; i++) {
            lpf[i] = i;
        }

        for (int p = 2, tmp; p <= n; p++) {
            if (lpf[p] == p) {
                primes[tot++] = p;
            }
            for (int i = 0; i < tot && primes[i] <= lpf[p] && (tmp = primes[i] * p) <= n; i++) {
                lpf[tmp] = primes[i];
            }
        }

        return new int[][]{Arrays.copyOf(primes, tot), lpf};
    }

    static boolean isPrime(int n) {
        for (int i = 2; i * i <= n; i++) if (n % i == 0) return false;
        return true;
    }

    static boolean sorted(int[] a) {
        for (int i = 0; i < a.length - 1; i++) {
            if (a[i] > a[i + 1]) return false;
        }
        return true;
    }

    public static long gcd(long a, long b) {
        while (b != 0) {
            a %= b;
            long t = a;
            a = b;
            b = t;
        }
        return a;
    }

    private static int ni() {
        return in.nextInt();
    }

    private static String ns() {
        return in.next();
    }

    private static int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = ni();
        return a;
    }

    private static long[] nal(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = nl();
        return a;
    }

    private static long nl() {
        return in.nextLong();
    }

    private float nf() {
        return (float) in.nextDouble();
    }

    private static double nd() {
        return in.nextDouble();
    }

    public static int[] facs(int n, int[] primes) {
        int[] ret = new int[9];
        int rp = 0;
        for (int p : primes) {
            if (p * p > n) break;
            int i;
            i = 0;
            while (n % p == 0) {
                n /= p;
                i++;
            }
            if (i > 0) ret[rp++] = p;
        }
        if (n != 1) ret[rp++] = n;
        return Arrays.copyOf(ret, rp);
    }

    public static int[] sieveEratosthenes(int n) {
        if (n <= 32) {
            int[] primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
            for (int i = 0; i < primes.length; i++) {
                if (n < primes[i]) {
                    return Arrays.copyOf(primes, i);
                }
            }
            return primes;
        }

        int u = n + 32;
        double lu = Math.log(u);
        int[] ret = new int[(int) (u / lu + u / lu / lu * 1.5)];
        ret[0] = 2;
        int pos = 1;

        int[] isnp = new int[(n + 1) / 32 / 2 + 1];
        int sup = (n + 1) / 32 / 2 + 1;

        int[] tprimes = {3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
        for (int tp : tprimes) {
            ret[pos++] = tp;
            int[] ptn = new int[tp];
            for (int i = (tp - 3) / 2; i < tp << 5; i += tp) ptn[i >> 5] |= 1 << (i & 31);
            for (int j = 0; j < sup; j += tp) {
                for (int i = 0; i < tp && i + j < sup; i++) {
                    isnp[j + i] |= ptn[i];
                }
            }
        }

        // 3,5,7
        // 2x+3=n
        int[] magic = {
                0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4, 13, 31, 22, 28, 18, 26, 10, 7, 12, 21,
                17, 9, 6, 16, 5, 15, 14
        };
        int h = n / 2;
        for (int i = 0; i < sup; i++) {
            for (int j = ~isnp[i]; j != 0; j &= j - 1) {
                int pp = i << 5 | magic[(j & -j) * 0x076be629 >>> 27];
                int p = 2 * pp + 3;
                if (p > n) break;
                ret[pos++] = p;
                if ((long) p * p > n) continue;
                for (int q = (p * p - 3) / 2; q <= h; q += p) isnp[q >> 5] |= 1 << q;
            }
        }

        return Arrays.copyOf(ret, pos);
    }


    private static final boolean oj = System.getProperty("ONLINE_JUDGE") != null;

    private static void tr(Object... o) {
        if (!oj) System.out.println(Arrays.deepToString(o));
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

    static class Pair<K, V> {
        private K key;
        private V value;

        public Pair(K key, V value) {
            this.key = key;
            this.value = value;
        }

        public K getKey() {
            return key;
        }

        public V getValue() {
            return value;
        }

        public void setKey(K key) {
            this.key = key;
        }

        public void setValue(V value) {
            this.value = value;
        }

    }
}