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.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.List;
 import java.util.*;
  public class realfast implements Runnable 
  {
    private static final int INF = (int) 1e9;
    long in= 1000000007;
    long fac[]= new long[1000001];
    long inv[]=new long[1000001];
    public  void solve() throws IOException 
    {

        //int t = readInt();
         
        int n = readInt();

        int arr[]=new int [n+1];

        for(int i=1;i<=n;i++)
        {
            arr[i]=readInt();
        }
         n=Math.min(n,6000);
         //int fir[]=new int []
         ArrayList<edge> c= new ArrayList<>();

         for(int i =1;i<=n;i++)
         {
             c.add(new edge(i,arr[i]));
         }
         Collections.sort(c);
         boolean check = false;
         int rep=0;
        // int prev1=0;
         //int prev2 =0;
          boolean check1 = false;
          int i =0;
         while(i<(int)c.size())
         {
            int count =0;
            int val =c.get(i).v;
            int j =i;
            while(j<c.size())
            {
                int val1 = c.get(j).v;
                if(val1!=val)
                 break;
                count++;
                j++;

            }
            if(count>=4)
            {
                check = true;
                out.println("YES");
                for(int k =i;k<=i+3;k++)
                {
                    int sal = c.get(k).u;
                    out.print(sal+" ");
                }
                out.println();
                break;
            }
            if(count>=2)
            {
                rep++;
                if(rep==2)
                {
                    check1= true;
                    break;
                }
            }
            i=j;
         }
         if(check1)
         {
            int prev1=0;
            int prev2 =0;
            int prev3 =0;
            int prev4 =0;
            for( i =1;i<c.size();i++)
            {
                int gal = c.get(i).v;
                int pal = c.get(i-1).v;
                if(gal==pal)
                {
                    if(prev1==0){
                     prev1= (int)c.get(i).u;
                     prev3= (int)c.get(i-1).u;
                     i++;
                    }
                    else 
                    {
                        prev2= (int)c.get(i).u;
                        prev4= (int)c.get(i-1).u;
                        break;
                    }
                }
            }
            out.println("YES");
            out.println(prev1+" "+prev2+" "+prev3+" "+prev4);
         }

         if((!check)&&(!check1))
         {
            ArrayList<edge> lo = new ArrayList<edge>();
            int fir[]=new int[5000001];
            int sec[]=new int[5000001];
            for(i =0;i<c.size();i++)
            {
                if(i==0||((int)c.get(i).v!=((int)c.get(i-1).v)))
                {
                    lo.add(new edge((int)c.get(i).u,(int)c.get(i).v));
                }
                else
                {
                    int u =c.get(i).u;
                    int u1 = c.get(i-1).u;
                    int v = c.get(i).v;
                    fir[2*v]=u;
                    sec[2*v]=u1;
                }
            }
            //out.println(lo.size());
            boolean mol= false;
            
            for( i =0;i<lo.size();i++)
            {
                for(int j =i+1;j<lo.size();j++)
                {
                    int u = (int)lo.get(i).u;
                    int v = (int)lo.get(i).v;
                    int u1 = (int)lo.get(j).u;
                    int v1= (int)lo.get(j).v;
                    if(fir[v1+v]==0)
                    {
                        fir[v1+v]=u;
                        sec[v1+v]=u1;
                    }
                    else
                    {
                        out.println("YES");
                        out.println(fir[v+v1]+" "+sec[v+v1]+" "+u+" "+u1);
                        mol = true;
                        break;
                    }
                }
                if(mol)
                    break;
            }
            if(!mol)
                out.println("NO");
         }



        // Collections.sort(c);

       
        

        



        
      

    }
    public boolean check(int a , int b , int c, int d )
    {
        if(a==c||a==d)
            return false;
        if(b==c||b==d)
            return false;

        return true;

    }
    
    public int value (int seg[], int left , int right ,int index, int l, int r)
    {
            
            if(left>right)
            {
              return -100000000;
            }
            if(right<l||left>r)
                return -100000000;
            if(left>=l&&right<=r)
                return seg[index];
            int mid = left+(right-left)/2;
            int val = value(seg,left,mid,2*index+1,l,r);
            int val2 = value(seg,mid+1,right,2*index+2,l,r);
            return Math.max(val,val2);

    }
   
    public int gcd(int a , int b )
    {
      if(a<b)
      {
        int t =a;
        a=b;
        b=t;
      }
      if(a%b==0)
        return b ;
      return gcd(b,a%b);
    }
    public long pow(long n , long p,long m)
    {
         if(p==0)
            return 1;
        long val = pow(n,p/2,m);;
        val= (val*val)%m;
        if(p%2==0)
            return val;
        else
            return (val*n)%m;
    }
    
    
    ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
    public static void main(String[] args) {
        new Thread(null, new realfast(), "", 128 * (1L << 20)).start();
    }
 
    private static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    private BufferedReader reader;
    private StringTokenizer tokenizer;
    private PrintWriter out;
 
    @Override
    public void run() {
        try {
            if (ONLINE_JUDGE || !new File("input.txt").exists()) {
                reader = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                reader = new BufferedReader(new FileReader("input.txt"));
                out = new PrintWriter("output.txt");
            }
            solve();
        } catch (IOException e) {
            throw new RuntimeException(e);
        } finally {
            try {
                reader.close();
            } catch (IOException e) {
                // nothing
            }
            out.close();
        }
    }
 
    private String readString() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
 
    @SuppressWarnings("unused")
    private int readInt() throws IOException {
        return Integer.parseInt(readString());
    }
 
    @SuppressWarnings("unused")
    private long readLong() throws IOException {
        return Long.parseLong(readString());
    }
 
    @SuppressWarnings("unused")
    private double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }
}
class edge implements Comparable<edge>{
    int u ;
    int v;
    
    edge(int u, int v)
    {
       this.u=u;
       this.v=v;
    }
    public int compareTo(edge e)
    {
        return this.v-e.v;
    }
}