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:
/**
 * BaZ :D
 */

import java.util.*;
import java.io.*;

import static java.lang.Math.*;

public class Main
{
    static MyScanner scan;
    static PrintWriter pw;
    static long MOD = 1_000_000_007;
    static long INF = 2_000_000_000_000_000_000L;
    static long inf = 2_000_000_000;
    public static void main(String[] args) {
        new Thread(null, null, "BaZ", 1 << 27) {
            public void run() {
                try {
                    solve();
                } catch (Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }


    static void solve() throws java.lang.Exception {
        //initIo(true, "");
        initIo(false, "");
        StringBuilder sb = new StringBuilder();

        int n = ni(), MAX = 3_000_000;
        int arr[] = new int[n];
        int freq[] = new int[MAX];
        for(int i=0;i<n;i++) {
            arr[i] = ni();
            // arr[i] = 1 + (int)(random()*25_000_00);
            ++freq[arr[i]];
        }

        int freq4 = -1, freq2_1 = -1, freq_2_2 = -1;
        for(int i=1;i<MAX;i++) {
            if(freq[i]>=4) {
                freq4 = i;
                break;
            }
            else if(freq[i]>=2) {
                if(freq2_1==-1) {
                    freq2_1 = i;
                }
                else {
                    freq_2_2 = i;
                }
            }
        }

        if(freq4!=-1) {
            pl("YES");
            // pl("trivial 4");
            for(int e : getIndexes(arr, freq4, 4)) {
                p(e);
            }
            pl();
        }
        else {
            if(freq_2_2!=-1) {
                pl("YES");
                // pl("trivial 2");
                ArrayList<Integer> l1 = getIndexes(arr, freq2_1, 2);
                ArrayList<Integer> l2 = getIndexes(arr, freq_2_2, 2);
                p(l1.get(0)+" "+l2.get(0)+" "+l1.get(1)+" "+l2.get(1));
                pl();
            }
            else {

                ArrayList<Integer> distinct_elements = new ArrayList<>();
                Arrays.fill(freq, -1);


               for(int i=0;i<n;i++) {
                   if(freq[arr[i]]==-1) {
                       freq[arr[i]] = i;
                       distinct_elements.add(i);
                   }
               }

                // pa("dis ele", distinct_elements);


               int pairx[] = new int[5_000_001];
               int pairy[] = new int[5_000_001];
               for(int i=0;i<=5_000_000;i++) {
                   pairx[i] = pairy[i] = -1;
               }

               for(int i=0;i<distinct_elements.size();i++) {
                   for(int j=0;j<i;j++) {
                       int sum = arr[distinct_elements.get(i)] + arr[distinct_elements.get(j)];
                       if(pairx[sum]!=-1) {
                            pl("YES");
                            pl(pairx[sum]+" "+pairy[sum]+" "+(distinct_elements.get(i)+1)+" "+(distinct_elements.get(j)+1));
                            System.exit(0);
                       }
                       else {
                           pairx[sum] = distinct_elements.get(i) + 1;
                           pairy[sum] = distinct_elements.get(j) + 1;
                       }
                   }
               }

               if(freq2_1!=-1) {
                   if(pairx[2*freq2_1]!=-1) {
                       ArrayList<Integer> list_2 = getIndexes(arr, freq2_1, 2);
                       pl("YES");
                       // pl("two of a kind");
                       pl(pairx[2*freq2_1]+" "+pairy[2*freq2_1]+" "+list_2.get(0)+" "+list_2.get(1));
                       System.exit(0);
                   }
               }

                pl("NO");
            }
        }

        pw.flush();
        pw.close();
    }

    static ArrayList<Integer> getIndexes(int arr[], int val, int times) {
        ArrayList<Integer> ans = new ArrayList<>();
        for(int i=0;i<arr.length;i++) {
            if(arr[i]==val) {
                ans.add((i+1));
                times--;
                if(times==0) {
                    return ans;
                }
            }
        }
        return ans;
    }


    static void assert_in_range(String varName, int n, int l, int r) {
        if (n >=l && n<=r) return;
        System.out.println(varName + " is not in range. Actual: "+n+" l : "+l+" r: "+r);
        System.exit(1);
    }
    static void assert_in_range(String varName, long n, long l, long r) {
        if (n>=l && n<=r) return;
        System.out.println(varName + " is not in range. Actual: "+n+" l : "+l+" r: "+r);
        System.exit(1);
    }

    static void initIo(boolean isFileIO, String suffix) throws IOException {
        scan = new MyScanner(isFileIO, suffix);
        if(isFileIO) {
            pw = new PrintWriter("/Users/amandeep/Desktop/output"+suffix+".txt");
        }
        else {
            pw = new PrintWriter(System.out, true);
        }
    }
    static int ni() throws IOException
    {
        return scan.nextInt();
    }
    static long nl() throws IOException
    {
        return scan.nextLong();
    }
    static double nd() throws IOException
    {
        return scan.nextDouble();
    }
    static String ne() throws IOException
    {
        return scan.next();
    }
    static String nel() throws IOException
    {
        return scan.nextLine();
    }
    static void pl()
    {
        pw.println();
    }
    static void p(Object o)
    {
        pw.print(o+" ");
    }
    static void pl(Object o)
    {
        pw.println(o);
    }
    static void psb(StringBuilder sb)
    {
        pw.print(sb);
    }
    static void pa(String arrayName, Object arr[])
    {
        pl(arrayName+" : ");
        for(Object o : arr)
            p(o);
        pl();
    }
    static void pa(String arrayName, int arr[])
    {
        pl(arrayName+" : ");
        for(int o : arr)
            p(o);
        pl();
    }
    static void pa(String arrayName, long arr[])
    {
        pl(arrayName+" : ");
        for(long o : arr)
            p(o);
        pl();
    }
    static void pa(String arrayName, double arr[])
    {
        pl(arrayName+" : ");
        for(double o : arr)
            p(o);
        pl();
    }
    static void pa(String arrayName, char arr[])
    {
        pl(arrayName+" : ");
        for(char o : arr)
            p(o);
        pl();
    }
    static void pa(String arrayName, boolean arr[])
    {
        pl(arrayName+" : ");
        for(boolean o : arr)
            p(o);
        pl();
    }
    static void pa(String listName, List list)
    {
        pl(listName+" : ");
        for(Object o : list)
            p(o);
        pl();
    }
    static void pa(String arrayName, Object[][] arr) {
        pl(arrayName+" : ");
        for(int i=0;i<arr.length;++i) {
            for(Object o : arr[i])
                p(o);
            pl();
        }
    }
    static void pa(String arrayName, int[][] arr) {
        pl(arrayName+" : ");
        for(int i=0;i<arr.length;++i) {
            for(int o : arr[i])
                p(o);
            pl();
        }
    }
    static void pa(String arrayName, long[][] arr) {
        pl(arrayName+" : ");
        for(int i=0;i<arr.length;++i) {
            for(long o : arr[i])
                p(o);
            pl();
        }
    }
    static void pa(String arrayName, char[][] arr) {
        pl(arrayName+" : ");
        for(int i=0;i<arr.length;++i) {
            for(char o : arr[i])
                p(o);
            pl();
        }
    }
    static void pa(String arrayName, double[][] arr) {
        pl(arrayName+" : ");
        for(int i=0;i<arr.length;++i) {
            for(double o : arr[i])
                p(o);
            pl();
        }
    }
    static void pa(String arrayName, boolean[][] arr) {
        pl(arrayName+" : ");
        for(int i=0;i<arr.length;++i) {
            for(boolean o : arr[i])
                p(o);
            pl();
        }
    }
    static class MyScanner
    {
        BufferedReader br;
        StringTokenizer st;
        MyScanner(boolean readingFromFile, String suffix) throws IOException
        {
            if(readingFromFile) {
                br = new BufferedReader(new FileReader("/Users/amandeep/Desktop/input"+suffix+".txt"));
            }
            else {
                br = new BufferedReader(new InputStreamReader(System.in));
            }
        }
        String nextLine()throws IOException
        {
            return br.readLine();
        }
        String next() throws IOException
        {
            if(st==null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
        int nextInt() throws IOException
        {
            return Integer.parseInt(next());
        }
        long nextLong() throws IOException
        {
            return Long.parseLong(next());
        }
        double nextDouble() throws IOException
        {
            return Double.parseDouble(next());
        }
    }
}