Problem: Ksenia has an array a consisting of n positive integers a_1, a_2, …, a_n. 

In one operation she can do the following: 

  * choose three distinct indices i, j, k, and then 
  * change all of a_i, a_j, a_k to a_i ⊕ a_j ⊕ a_k simultaneously, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). 



She wants to make all a_i equal in at most n operations, or to determine that it is impossible to do so. She wouldn't ask for your help, but please, help her!

Input

The first line contains one integer n (3 ≤ n ≤ 10^5) — the length of a.

The second line contains n integers, a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — elements of a.

Output

Print YES or NO in the first line depending on whether it is possible to make all elements equal in at most n operations.

If it is possible, print an integer m (0 ≤ m ≤ n), which denotes the number of operations you do.

In each of the next m lines, print three distinct integers i, j, k, representing one operation. 

If there are many such operation sequences possible, print any. Note that you do not have to minimize the number of operations.

Examples

Input


5
4 2 1 7 2


Output


YES
1
1 3 4

Input


4
10 4 49 22


Output


NO

Note

In the first example, the array becomes [4 ⊕ 1 ⊕ 7, 2, 4 ⊕ 1 ⊕ 7, 4 ⊕ 1 ⊕ 7, 2] = [2, 2, 2, 2, 2].

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
public class check3
{
    public static void main(String[] args) throws IOException
    {
       Reader sc=new Reader();
       PrintWriter out = new PrintWriter(System.out);

            int n=sc.nextInt();
            long a[]=new long[n];

            ArrayList<String> ans=new ArrayList<>();
            long t1=0;

            for(int i=0;i<n;i++)
            {
                a[i]=sc.nextLong();
            }
            if(n%2==0)
            {
                int i=0,j=i+2;

                while(j<(n-1))
                {
                    long t2=a[i]^a[i+1]^a[i+2];
                    a[i]=a[i+1]=a[i+2]=t2;

                    ans.add((i+1)+" "+(i+2)+" "+(i+3));
                    i+=2;
                    j+=2;
                }
                if(a[n-2]!=a[n-1])
                {
                    out.println("NO");
                    out.flush();
                    return;
                }

                i=0;
                j=i+1;
                int n1=n-3;

                while(j<n1)
                {
                    ans.add((i+1)+" "+(i+2)+" "+(n));
                    i+=2;
                    j+=2;
                }


            }
            else
            {

                int i=0,j=i+2;

                while(j<n)
                {
                    t1=a[i]^a[i+1]^a[i+2];
                    a[i]=a[i+1]=a[i+2]=t1;
                    ans.add((i+1)+" "+(i+2)+" "+(i+3));
                    i+=2;
                    j+=2;
                }
                i=0;
                j=i+1;
                long val=a[n-1];

                while(j<n-1)
                {
                    ans.add((i+1)+" "+(j+1)+" "+(n));
                    i+=2;
                    j+=2;
                }
            }

            out.println("YES");
            out.println(ans.size());

            for(int i=0;i<ans.size();i++)
            {
                out.println(ans.get(i));
            }
            out.flush();

    }
    public static void shufflearray(long arr[])
    {


        int n=arr.length;
        Random rand=new Random();
        for(int i=0;i<n;i++)
        {
            long temp=arr[i];
            int randomPos=i+rand.nextInt(n-i);
            arr[i]=arr[randomPos];
            arr[randomPos]=temp;
        }
    }
    //       Arrays.sort(arr, new Comparator<pair>() {
//        //@Override
//        public int compare(pair o1, pair o2) {
//            long l1=o1.a-o2.a;
//            if(l1<0L) return -1;
//            if(l1==0) return 0;
//            return 1;
//        }
//    });
    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

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

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

        public String nextLine() throws IOException {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }
        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() throws IOException{
            int c = read();
            while (isSpaceChar(c)) c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }


        public int nextInt() throws IOException {
            int 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;
        }

        public long nextLong() throws IOException {
            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;
        }

        public double nextDouble() throws IOException {
            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;
        }

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

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

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

    }


}