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.*;
import java.util.*;
import java.lang.*;

public class curr {
    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
    static long MOD = (long) (1e9 + 7);
    //    static int MOD = 998244353;
    static long MOD2 = MOD * MOD;
    static FastReader sc = new FastReader();
    static int pInf = Integer.MAX_VALUE;
    static int nInf = Integer.MIN_VALUE;
    static long ded = (long)(1e17)+9;
    public static void main(String[] args) throws Exception {
        int test = 1;
//        test = sc.nextInt();
        for (int i = 1; i <= test; i++){
//            out.print("Case #"+i+": ");
            solve();
        }
        out.flush();
        out.close();
    }
    static void solve()throws Exception{
        int n = sc.nextInt();
        int maxn = 2500000;
        int idxi[] = new int[2*maxn+1];
        int idxj[] = new int[2*maxn+1];
        Arrays.fill(idxi,-1);
        Arrays.fill(idxj,-1);
        int[] a = new int[n];
        for(int i = 0; i < n; i++){
            a[i] = sc.nextInt();
        }
        for(int i = 0 ; i < n ;i++){
            for(int j = i+1; j < n; j++){
                int sum = a[i]+a[j];
                if(idxi[sum]==-1){
                    idxi[sum] = i;
                    idxj[sum] = j;
                }else{
                    if(idxi[sum]==i||idxj[sum]==i||idxi[sum]==j||idxj[sum]==j){
                        continue;
                    }
                    out.println("YES");
                    out.println((i+1)+" "+(j+1)+" "+(idxi[sum]+1)+" "+(idxj[sum]+1));
                    return;
                }
            }
        }
        out.println("NO");
    }
    static class Pair implements Comparable<Pair> {
        int x;
        int y;
        public Pair(int x, int y) {
            this.x = x;
            this.y = y;
//            this.idx = idx;
        }
        @Override
        public int compareTo(Pair o){
            if(this.y==o.y){
                return this.x-o.x;
            }
            return this.y-o.y;
        }
    }
    public static long mul(long a, long b) {
        return ((a % MOD) * (b % MOD)) % MOD;
    }
    public static long add(long a, long b) {
        return ((a % MOD) + (b % MOD)) % MOD;
    }
    public static long c2(long n) {
        if ((n & 1) == 0) {
            return mul(n / 2, n - 1);
        } else {
            return mul(n, (n - 1) / 2);
        }
    }
    //Shuffle Sort
    static final Random random = new Random();
    static void ruffleSort(int[] a) {
        int n = a.length;//shuffle, then sort
        for (int i = 0; i < n; i++) {
            int oi = random.nextInt(n); int temp= a[oi];
            a[oi] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }
    //Brian Kernighans Algorithm
    static long countSetBits(long n) {
        if (n == 0) return 0;
        return 1 + countSetBits(n & (n - 1));
    }
    //Euclidean Algorithm
    static long gcd(long A, long B) {
        if (B == 0) return A;
        return gcd(B, A % B);
    }
    //Modular Exponentiation
    static long fastExpo(long x, long n) {
        if (n == 0) return 1;
        if ((n & 1) == 0) return fastExpo((x * x) % MOD, n / 2) % MOD;
        return ((x % MOD) * fastExpo((x * x) % MOD, (n - 1) / 2)) % MOD;
    }
    //AKS Algorithm
    static boolean isPrime(long n) {
        if (n <= 1) return false;
        if (n <= 3) return true;
        if (n % 2 == 0 || n % 3 == 0) return false;
        for (int i = 5; i <= Math.sqrt(n); i += 6)
            if (n % i == 0 || n % (i + 2) == 0) return false;
        return true;
    }
    public static long modinv(long x) {
        return modpow(x, MOD - 2);
    }
    public static long modpow(long a, long b) {
        if (b == 0) {
            return 1;
        }
        long x = modpow(a, b / 2);
        x = (x * x) % MOD;
        if (b % 2 == 1) {
            return (x * a) % MOD;
        }
        return x;
    }

    static class FastReader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public FastReader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public FastReader(String file_name) throws IOException{
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String nextLine() {
            try{
                byte[] buf = new byte[10000000]; // line length
                int cnt = 0, c;
                while ((c = read()) != -1) {
                    if (c == '\n')
                        break;
                    buf[cnt++] = (byte) c;
                }
                return new String(buf, 0, cnt);
            }catch (Exception e){
                System.out.println(e.getMessage());
                return null;
            }
        }

        public int nextInt()  {
            int ret = 0;
            try {
                byte c = read();
                while (c <= ' ')
                    c = read();
                boolean neg = (c == '-');
                if (neg) c = read();
                do{
                    ret = ret * 10 + c - '0';
                }  while ((c = read()) >= '0' && c <= '9');

                if (neg) return -ret;
                return ret;
            } catch (Exception e) {
                System.out.println(e.getMessage());
                return -1;
            }
        }

        public long nextLong()   {

            try {
                long ret = 0;
                byte c = read();
                while (c <= ' ') c = read();
                boolean neg = (c == '-');
                if (neg)
                    c = read();
                do {
                    ret = ret * 10 + c - '0';
                }
                while ((c = read()) >= '0' && c <= '9');
                if (neg)
                    return -ret;
                return ret;
            } catch (Exception e) {
                System.out.println(e.getMessage());
                return -1;
            }
        }

        public double nextDouble()  {

            try {
                double ret = 0, div = 1;
                byte c = read();
                while (c <= ' ')
                    c = read();
                boolean neg = (c == '-');
                if (neg) c = read();

                do {
                    ret = ret * 10 + c - '0';
                }
                while ((c = read()) >= '0' && c <= '9');
                if (c == '.') {
                    while ((c = read()) >= '0' && c <= '9') {
                        ret += (c - '0') / (div *= 10);
                    }
                }

                if (neg) return -ret;
                return ret;
            } catch (Exception e) {
                System.out.println(e.getMessage());
                return -1;
            }
        }

        private void fillBuffer() throws IOException{
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException  {
            try{
                if (bufferPointer == bytesRead)
                    fillBuffer();
                return buffer[bufferPointer++];
            }catch(Exception e){
                System.out.println(e.getMessage());
                return -1;
            }
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }
}