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.util.*;
import java.io.*;

public class _707 {
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        int t = 1;
        int MAX = (int) 5e6 + 2;
        while (t-- > 0) {
            //int n = (int) 2e5;
            int n = sc.nextInt();
            int [] a = new int[n];
            //for (int i = 0; i < n; i++) a[i] = (int) (Math.random() * 2500000) + 1;
            for (int i = 0; i < n; i++) a[i] = sc.nextInt();
            Map<Integer, ArrayList<Integer>> got = new HashMap<>();
            //sort(a);
            for (int i = 0; i < n; i++) {
                if (!got.containsKey(a[i])) {
                    ArrayList<Integer> lst = new ArrayList<>();
                    lst.add(i + 1);
                    got.put(a[i], lst);
                } else got.get(a[i]).add(i + 1);
            }
            Set<Integer> look = new HashSet<>();
            for (int i = 0; i < n; i++) {
                if (got.get(a[i]).size() >= 4) {
                    out.println("YES");
                    for (int j = 0; j < 4; j++) {
                        out.print((got.get(a[i]).get(j)) + " ");
                    }
                    out.close();
                    return;
                }
                if (got.get(a[i]).size() >= 2) {
                    look.add(a[i]);
                }
            }
            if (look.size() >= 2) {
                int ct = 0;
                int first = -1;
                int second = -1;
                for (Integer i: look) {
                    if (ct == 0) first = i;
                    if (ct == 1) {
                        second = i;
                        break;
                    }
                    ++ct;
                }
                out.println("YES");
                out.print(got.get(first).get(0) + " " + got.get(second).get(0) + " " + got.get(first).get(1) + " " + got.get(second).get(1));
                out.close();
                return;
            }
            Map<Integer, ArrayList<Integer>> sums = new HashMap<>();
            int [] idx = new int[n];
            for (int i = 0; i < n; i++) idx[i] = i;
            for (int i = 0; i < n; i++) {
                int first = (int) (Math.random() * n);
                int second = (int) (Math.random() * n);
                int temp = idx[first];
                idx[first] = idx[second];
                idx[second] = temp;
            }
            for (int ii = 0; ii < n; ii++) {
                for (int jj = ii + 1; jj < n; jj++) {
                    int i = idx[ii];
                    int j = idx[jj];
                    int sum = a[i] + a[j];
                    if (!sums.containsKey(sum)) {
                        ArrayList<Integer> insert = new ArrayList<>();
                        insert.add(i + 1);
                        insert.add(j + 1);
                        sums.put(sum, insert);
                    } else {
                        ArrayList<Integer> lst = sums.get(sum);
                        int first = (lst.get(0));
                        int second = (lst.get(1));
                        if (((i + 1) != (first) && (i + 1) != (second) && (j + 1) != (first) && (j + 1) != (second))) {
                            out.println("YES");
                            out.print(first + " " + second + " " + (i + 1) + " " + (j + 1));
                            out.close();
                            return;
                        }
                    }

                }
            }
        }
        out.println("NO");
        out.close();
    }

    static class RangeTree {
        private long[] lazy;
        private long[] sum;
        private int size;
        public RangeTree(int size) {
            this.size = size;
            sum = new long[4*size];
            lazy = new long[4*size];
        }
        public void update(int l, int r, int inc) {
            update(1, 0, size-1, l, r, inc);
        }
        private void pushDown(int index, int l, int r) {
            sum[index] += lazy[index] * (r-l+1);
            if(l != r) {
                lazy[2*index] += lazy[index];
                lazy[2*index+1] += lazy[index];
            }
            lazy[index] = 0;
        }
        private void pullUp(int index, int l, int r) {
            int m = (l+r)/2;
            sum[index] = evaluateSum(2*index, l, m) + evaluateSum(2*index+1, m+1, r);
        }
        private long evaluateSum(int index, int l, int r) {
            return sum[index] + (r-l+1)*lazy[index];
        }
        private void update(int index, int l, int r, int left, int right, int inc) {
            if(r < left || l > right) return;
            if(l >= left && r <= right) {
                lazy[index] += inc;
                return;
            }
            pushDown(index, l, r);
            int m = (l+r)/2;
            update(2*index, l, m, left, right, inc);
            update(2*index+1, m+1, r, left, right, inc);
            pullUp(index, l, r);
        }
        public long sumQuery(int l, int r) {
            return sumQuery(1, 0, size-1, l, r);
        }
        private long sumQuery(int index, int l, int r, int left, int right) {
            if(r < left || l > right) return 0;
            if(l >= left && r <= right) {
                return evaluateSum(index, l, r);
            }
            pushDown(index, l, r);
            int m = (l+r)/2;
            long ret = 0;
            ret += sumQuery(2*index, l, m, left, right);
            ret += sumQuery(2*index+1, m+1, r, left, right);
            pullUp(index, l, r);
            return ret;
        }
    }


    static void sort(int[] a) {
        ArrayList<Integer> q = new ArrayList<>();
        for (int i : a) q.add(i);
        Collections.sort(q);
        for (int i = 0; i < a.length; i++) a[i] = q.get(i);
    }

    static void sort(long[] a) {
        ArrayList<Long> q = new ArrayList<>();
        for (long i : a) q.add(i);
        Collections.sort(q);
        for (int i = 0; i < a.length; i++) a[i] = q.get(i);
    }


    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }


    }

}