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.util.*;

public class CodeForces extends Functions {
    static Scanner sc = new Scanner();
    public static void  solve(){
        int n = sc.nextInt();
        int[] arr = sc.setIntArray(n);
        Map<Integer,List<int[]>> map = new HashMap<>();
        for(int i=0;i<n;i++){
            for(int j=0;j<i;j++){
                int sum = arr[i]+ arr[j];
                if(map.containsKey(sum)){
                    for(int[] ele : map.get(sum))
                        if(ele[0]!=i && ele[0]!=j && ele[1]!=i && ele[1]!=j){
                            System.out.println("YES");
                            System.out.println((ele[0]+1)+" "+(ele[1]+1)+" "+(i+1)+" "+(j+1));
                            return;
                        }
                }
                else map.put(sum,new ArrayList<>());
                map.get(sum).add(new int[]{i,j});
            }
        }
        System.out.println("NO");

    }


    public static void main(String[] args) {
       int testCase = 1;
       // testCase= sc.nextInt();
        while (testCase-->0){
            solve();
        }
        long end = System.currentTimeMillis();
//        System.out.println("time took in ms : "+(end-start));
    }


}

class Functions {
    public static int mod = (int)1e9+7;
    public static int INT_MAX = Integer.MAX_VALUE;
    public static int INT_MIN = Integer.MIN_VALUE;
    public static long LONG_MAX = Long.MAX_VALUE;
    public static long LONG_MIN = Long.MIN_VALUE;
    public static double DOUBLE_MAX = Double.MAX_VALUE;
    public static double DOUBLE_MIN = Double.MIN_VALUE;

    public static void sort(int[] a,boolean isAscending){
        ArrayList<Integer> temp = new ArrayList<>();
        for (int j : a) temp.add(j);
        sort(temp,isAscending);
        for(int i=0;i<a.length;i++)a[i] = temp.get(i);
    }
    public static void sort(List T,boolean isAscending){
        if(isAscending)
            Collections.sort(T);
        else Collections.sort(T,Collections.reverseOrder());
    }
    public static long factorial(int n){
        long fact = 1L;
        for(int i=2;i<=n;i++)fact=  (fact*i)%mod;
        return fact;
    }

    public  static int ncr(int n, int r){
        // time O(n+r)
        if (r > n)
            return 0;
        long[] inv = new long[r + 1];
        inv[1] = 1;
        // Getting the modular inversion
        // for all the numbers
        // from 2 to r with respect to m
        for (int i = 2; i <= r; i++) {
            inv[i] = mod - (mod / i) * inv[(int) (mod % i)] % mod;
        }
        int ans = 1;
        // for 1/(r!) part
        for (int i = 2; i <= r; i++) {
            ans = (int) (((ans % mod) * (inv[i] % mod)) % mod);
        }
           // for (n)*(n-1)*(n-2)*...*(n-r+1) part
        for (int i = n; i >= (n - r + 1); i--) {
            ans = (int) (((ans % mod) * (i % mod)) % mod);
        }
        return ans;
    }

    public static void reverseArray(int[] a){
        int left = 0;
        int right = a.length-1;
        while (left<right){
            int temp =a[left];
            a[left] = a[right];
            a[right] = temp;
            left++;
            right--;
        }
    }
    public static long isPrime(int n){
        for(long i=2;i*i<=n;i++)
            if(n%i==0)return i;
        return -1;
    }
}

class Scanner {
    private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    private StringTokenizer st = new StringTokenizer("");
    public String next(){
        while (!st.hasMoreTokens())
            try {
                st = new StringTokenizer(br.readLine());
            }catch (IOException e){
                e.printStackTrace();
            }
        return st.nextToken();

    }
    public int nextInt(){return Integer.parseInt(next());}
    public long nextLong(){return Long.parseLong(next());}
    public double nextDouble(){return Double.parseDouble(next());}
    public int[] setIntArray(int n){
        int[] arr =new int[n];
        for(int i=0;i<n;i++)arr[i] = nextInt();
        return arr;
    }
    public Integer[] setIntegerArray(int n){
        Integer[] arr =new Integer[n];
        for(int i=0;i<n;i++)arr[i] = nextInt();
        return arr;
    }
    public long[] setlongArray(int n){
        long[] arr =new long[n];
        for(int i=0;i<n;i++)arr[i] = nextLong();
        return arr;
    }
    public int[][] set2DIntegerMatrix(int row,int col){
        int[][] arr = new int[row][col];
        for(int i=0;i<row;i++)
            for(int j= 0;j<col;j++)
                arr[i][j] = nextInt();
        return arr;
    }
}