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:
// package com.company;
import java.util.*;
import java.io.*;
import java.lang.*;
public class Main{
    /*
     ** || ॐ श्री गणेशाय नमः ||
     ** @𝙖𝙪𝙩𝙝𝙤𝙧 𝙅𝙞𝙜𝙖𝙧_𝙉𝙖𝙞𝙣𝙪𝙟𝙞
     ** 𝙎𝙑𝙉𝙄𝙏-𝙎𝙐𝙍𝘼𝙏
     */
    public static void main(String args[]){
        InputReader in=new InputReader(System.in);
        TASK solver = new TASK();
        int t=1;
//        t = in.nextInt();
        for(int i=1;i<=t;i++)
        {
            solver.solve(in,i);
        }
    }
    static class TASK {
        class pair
        {
            int first, second;
            pair(int f,int s)
            {
                first = f; second = s;
            }
        };
        boolean findPairs(int arr[])
        {
            // Create an empty Hash to store mapping from sum to
            // pair indexes
            HashMap<Integer,pair> map = new HashMap<Integer,pair>();
            int n=arr.length;

            // Traverse through all possible pairs of arr[]
            for (int i=0; i<n; ++i)
            {
                for (int j=i+1; j<n; ++j)
                {
                    // If sum of current pair is not in hash,
                    // then store it and continue to next pair
                    int sum = arr[i]+arr[j];
                    if (!map.containsKey(sum))
                        map.put(sum,new pair(i,j));

                    else // Else (Sum already present in hash)
                    {
                        // Find previous pair
                        pair p = map.get(sum);

                        // Since array elements are distinct, we don't
                        // need to check if any element is common among pairs
                        Set<Integer> s = new HashSet<>();
                        s.add(p.first);
                        s.add(i);
                        s.add(j);
                        s.add(p.second);
                        if(s.size()>3) {
                            System.out.println("YES");
                            System.out.println((p.first + 1) + " " + (p.second + 1) + " " + (i + 1) + " " + (j + 1));
                            return true;
                        }
                    }
                }
            }
            System.out.println("NO");
            return false;
        }

        void solve(InputReader in, int testNumber) {
            int n = in.nextInt();
            int a[] = new int[n];
            for(int i=0;i<n;i++)
                a[i]=in.nextInt();
            findPairs(a);





        }
    }


    static class Maths {
        static long gcd(long a, long b) {
            if (a == 0)
                return b;
            return gcd(b % a, a);
        }
        public static long lcm(long a, long b) {
            return (a * b) / gcd(a, b);
        }
        public static long factorial(int n) {
            long fact = 1;
            for (int i = 1; i <= n; i++) {
                fact *= i;
            }
            return fact;
        }
    }
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
        public String nextLine() {
            BufferedReader br = new BufferedReader(new
                    InputStreamReader(System.in));
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }
        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }
        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));
            return res.toString();
        }
        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c
                    == -1;
        }
        public String next() {
            return readString();
        }
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
}