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 Template {
	static long[] mods = {1000000007, 998244353, 1000000009};
	static long mod = mods[0];
	public static MyScanner sc;
    public static PrintWriter out;
	public static void main(String[] omkar) throws Exception{
		// TODO Auto-generated method stub
 		sc = new MyScanner();
 		out = new PrintWriter(System.out);
 		int n = sc.nextInt();
 		int [] arr = readArrayInt1(n);
 		ArrayList<ArrayList<Integer>> freq = new ArrayList<>();
 		for(int j = 0;j<=2500000;j++){
 			freq.add(new ArrayList<>());
 		}
 		for(int j = 1;j<=n;j++){
 			freq.get(arr[j]).add(j);
 		}
 		int count4 = 0;
 		int count2 = 0;
 		int ind41 = -1;
 		int ind21 = -1;
 		int ind22 = -1;
 		for(int j = 0;j<=2500000;j++){
 			if (freq.get(j).size() >= 4){
 				count4++;
 				if(ind41 == -1){
 					ind41 = j;
 				}
 			}
 			else if (freq.get(j).size() >=2){
 				count2++;
 				if (ind21 == -1){
 					ind21 = j;
 				}
 				else if (ind22 == -1){
 					ind22 = j;
 				}
 			}
 		}
 		if (count4 >=1){
 			out.println("YES");
 			for(int j = 0;j<4;j++){
 				out.print(freq.get(ind41).get(j) + " ");
 			}
 			out.println();
 		}
 		else if (count2 >=2){
 			out.println("YES");
 			out.print(freq.get(ind21).get(0) + " ");
 			out.print(freq.get(ind22).get(0) + " ");
 			out.print(freq.get(ind21).get(1) + " ");
 			out.println(freq.get(ind22).get(1) + " ");
 		}
 		else{
 			int[] pair1 = new int[5000001];
	 		int[] pair2 = new int[5000001];
 			if (n <= 5000){
 	 			boolean found = false;
 	 			for(int i = 1;i<=n;i++){
 	 				for(int j = i+1;j<=n;j++){
 	 					if (pair1[arr[i]+arr[j]] == 0){
 	 						pair1[arr[i]+arr[j]] = i;
 	 						pair2[arr[i]+arr[j]] = j;
 	 					}
 	 					else{
 	 						Set<Integer> set = new HashSet<>();
 	 						set.add(pair1[arr[i]+arr[j]]);
 	 						set.add(pair2[arr[i]+arr[j]]);
 	 						set.add(i);
 	 						set.add(j);
 	 						if (set.size() != 4)
 	 							continue;
 	 						found = true;
 	 						out.println("YES");
 	 						out.println(pair1[arr[i]+arr[j]] + " " + pair2[arr[i]+arr[j]] + " " + i + " " + j);
 	 						break;
 	 					}
 	 				}
 	 				if (found)
 	 					break;
 	 			}
 	 			if (!found)
 	 				out.println("NO");
 			}
 			else{
 				boolean found = false;
 				for(int i = 1;i<=n;i++){
 	 				for(int j = i+1;j<=n;j++){
 	 					if (pair1[arr[i]+arr[j]] == 0){
 	 						pair1[arr[i]+arr[j]] = i;
 	 						pair2[arr[i]+arr[j]] = j;
 	 					}
 	 					else{
 	 						found = true;
 	 						out.println("YES");
 	 						out.println(pair1[arr[i]+arr[j]] + " " + pair2[arr[i]+arr[j]] + " " + i + " " + j);
 	 						break;
 	 					}
 	 				}
 	 				if (found)
 	 					break;
 	 			}
 			}
 			
 			
 		}
 		
	 		
 		out.close();
 	}
	public static void sort(int[] array){
		ArrayList<Integer> copy = new ArrayList<>();
		for (int i : array)
			copy.add(i);
		Collections.sort(copy);
		for(int i = 0;i<array.length;i++)
			array[i] = copy.get(i);
	}
	static String[] readArrayString(int n){
		String[] array = new String[n];
		for(int j =0 ;j<n;j++)
			array[j] = sc.next();
		return array;
	}
	static int[] readArrayInt(int n){
    	int[] array = new int[n];
    	for(int j = 0;j<n;j++)
    		array[j] = sc.nextInt();
    	return array;
    }
	static int[] readArrayInt1(int n){
		int[] array = new int[n+1];
		for(int j = 1;j<=n;j++){
			array[j] = sc.nextInt();
		}
		return array;
	}
	static long[] readArrayLong(int n){
		long[] array = new long[n];
		for(int j =0 ;j<n;j++)
			array[j] = sc.nextLong();
		return array;
	}
	static double[] readArrayDouble(int n){
		double[] array = new double[n];
		for(int j =0 ;j<n;j++)
			array[j] = sc.nextDouble();
		return array;
	}
	static int minIndex(int[] array){
		int minValue = Integer.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	static int minIndex(long[] array){
		long minValue = Long.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	static int minIndex(double[] array){
		double minValue = Double.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	static long power(long x, long y){
		if (y == 0)
			return 1;
		if (y%2 == 1)
			return (x*power(x, y-1))%mod;
		return power((x*x)%mod, y/2)%mod;
	}
	static void verdict(boolean a){
        out.println(a ? "YES" : "NO");
    }
    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;
        }
        
    }	
}

//StringJoiner sj = new StringJoiner(" "); 
//sj.add(strings)
//sj.toString() gives string of those stuff w spaces or whatever that sequence is