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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintStream;
import java.util.Arrays;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;


public class PowerFulKsenia {


    public static void main(String[] args) throws Throwable {
        Thread thread = new Thread (null, new TaskAdapter (), "", 1 << 29);
        thread.start ();
        thread.join ();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput (inputStream);
            FastOutput out = new FastOutput (outputStream);
            Solution solver = new Solution ();
            solver.solve (1, in, out);
            out.close ();
        }
    }

    static class Solution {
        static final Debug debug = new Debug (true);

        public void solve(int testNumber, FastInput in, FastOutput out) {

            int n= in.ri ();
            int[] a=new int[n];
            in.populate (a);
            int xor=a[0];
            for (int i = 1; i <n; i++) {
                xor^=a[i];
            }
            debug.debug ("xor",xor);
            if(n%2==0 && xor!=0) out.prtl ("NO");
            else{
                out.prtl ("YES");
                out.prtl (n%2==0?n-2:n-1);
                for (int i = 0; i < 2; i++) {
                    for (int j = 1; j <n-(n%2==0?1:0) ; j+=2) {
                        out.prtl (j+" "+(j+1)+" "+n);
                    }
                    
                }
            }

        }

    }


    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private static final int THRESHOLD = 32 << 10;
        private final Writer os;
        private StringBuilder cache = new StringBuilder (THRESHOLD * 2);

        public FastOutput append(CharSequence csq) {
            cache.append (csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append (csq, start, end);
            return this;
        }

        private void afterWrite() {
            if (cache.length () < THRESHOLD) {
                return;
            }
            flush ();
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this (new OutputStreamWriter (os));
        }

        public FastOutput append(char c) {
            cache.append (c);
            afterWrite ();
            return this;
        }

        public FastOutput append(String c) {
            cache.append (c);
            afterWrite ();
            return this;
        }

        public FastOutput println(String c) {
            return append (c).println ();
        }

        public FastOutput println() {
            return append ('\n');
        }

        final <T> void prt(T a) {
            append (a + " ");
        }

        final <T> void prtl(T a) {
            append (a + "\n");
        }

        public FastOutput flush() {
            try {
                os.append (cache);
                os.flush ();
                cache.setLength (0);
            } catch (IOException e) {
                throw new UncheckedIOException (e);
            }
            return this;
        }

        public void close() {
            flush ();
            try {
                os.close ();
            } catch (IOException e) {
                throw new UncheckedIOException (e);
            }
        }

        public String toString() {
            return cache.toString ();
        }

        public FastOutput printf(String format, Object... args) {
            return append (String.format (format, args));
        }

        private static int countDigits(long l) {
            if (l >= 1000000000000000000L) return 19;
            if (l >= 100000000000000000L) return 18;
            if (l >= 10000000000000000L) return 17;
            if (l >= 1000000000000000L) return 16;
            if (l >= 100000000000000L) return 15;
            if (l >= 10000000000000L) return 14;
            if (l >= 1000000000000L) return 13;
            if (l >= 100000000000L) return 12;
            if (l >= 10000000000L) return 11;
            if (l >= 1000000000L) return 10;
            if (l >= 100000000L) return 9;
            if (l >= 10000000L) return 8;
            if (l >= 1000000L) return 7;
            if (l >= 100000L) return 6;
            if (l >= 10000L) return 5;
            if (l >= 1000L) return 4;
            if (l >= 100L) return 3;
            if (l >= 10L) return 2;
            return 1;
        }

        private static int countDigits(int l) {
            if (l >= 1000000000) return 10;
            if (l >= 100000000) return 9;
            if (l >= 10000000) return 8;
            if (l >= 1000000) return 7;
            if (l >= 100000) return 6;
            if (l >= 10000) return 5;
            if (l >= 1000) return 4;
            if (l >= 100) return 3;
            if (l >= 10) return 2;
            return 1;
        }

    }


    static class FastInput {
        private final InputStream is;
        private StringBuilder defaultStringBuf = new StringBuilder (1 << 13);
        private byte[] buf = new byte[1 << 13];
        private static final int EOF = -1;
        private SpaceCharFilter filter;
        private int bufOffset;
        private int next;
        private int bufLen;

        public FastInput(InputStream is) {
            this.is = is;
        }

        public void populate(int[] data) {
            for (int i = 0; i < data.length; i++) {
                data[i] = readInt ();
            }
        }

        public void populate(long[] data) {
            for (int i = 0; i < data.length; i++) {
                data[i] = readLong ();
            }
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read (buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read ();
            }
        }

        public String next() {
            return readString ();
        }

        public int ri() {
            return readInt ();
        }

        public int readInt() {
            boolean rev = false;

            skipBlank ();
            if (next == '+' || next == '-') {
                rev = next == '-';
                next = read ();
            }

            int val = 0;
            while (next >= '0' && next <= '9') {
                val = val * 10 - next + '0';
                next = read ();
            }

            return rev ? val : -val;
        }

        public long readLong() {
            boolean rev = false;

            skipBlank ();
            if (next == '+' || next == '-') {
                rev = next == '-';
                next = read ();
            }

            long val = 0L;
            while (next >= '0' && next <= '9') {
                val = val * 10 - next + '0';
                next = read ();
            }

            return rev ? val : -val;
        }

        public long rl() {
            return readLong ();
        }

        public String readString(StringBuilder builder) {
            skipBlank ();

            while (next > 32) {
                builder.append ((char) next);
                next = read ();
            }

            return builder.toString ();
        }

        public String readString() {
            defaultStringBuf.setLength (0);
            return readString (defaultStringBuf);
        }

        public int rs(char[] data, int offset) {
            return readString (data, offset);
        }

        public char[] rsc() {
            return readString ().toCharArray ();
        }


        public int rs(char[] data) {
            return rs (data, 0);
        }

        public int readString(char[] data, int offset) {
            skipBlank ();

            int originalOffset = offset;
            while (next > 32) {
                data[offset++] = (char) next;
                next = read ();
            }

            return offset - originalOffset;
        }

        public char rc() {
            return readChar ();
        }

        public char readChar() {
            skipBlank ();
            char c = (char) next;
            next = read ();
            return c;
        }

        public double rd() {
            return nextDouble ();
        }

        public double nextDouble() {
            int c = read ();
            while (isSpaceChar (c))
                c = read ();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read ();
            }
            double res = 0;
            while (!isSpaceChar (c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow (10, readInt ());
                if (c < '0' || c > '9')
                    throw new InputMismatchException ();
                res *= 10;
                res += c - '0';
                c = read ();
            }
            if (c == '.') {
                c = read ();
                double m = 1;
                while (!isSpaceChar (c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow (10, readInt ());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException ();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read ();
                }
            }
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar (c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }


        public boolean hasMore() {
            skipBlank ();
            return next != EOF;
        }


    }


    static class Debug {
        private boolean offline;
        private PrintStream out = System.err;
        static int[] empty = new int[0];

        public Debug(boolean enable) {
            offline = enable && System.getSecurityManager () == null;
        }

        public Debug debug(String name, Object x) {
            return debug (name, x, empty);
        }

        public Debug debug(String name, long x) {
            if (offline) {
                debug (name, "" + x);
            }
            return this;
        }

        public Debug debug(String name, String x) {
            if (offline) {
                out.printf ("%s=%s", name, x);
                out.println ();
            }
            return this;
        }

        public Debug debug(String name, Object x, int... indexes) {
            if (offline) {
                if (x == null || !x.getClass ().isArray ()) {
                    out.append (name);
                    for (int i : indexes) {
                        out.printf ("[%d]", i);
                    }
                    out.append ("=").append ("" + x);
                    out.println ();
                } else {
                    indexes = Arrays.copyOf (indexes, indexes.length + 1);
                    if (x instanceof byte[]) {
                        byte[] arr = (byte[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof short[]) {
                        short[] arr = (short[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof boolean[]) {
                        boolean[] arr = (boolean[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof char[]) {
                        char[] arr = (char[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof int[]) {
                        int[] arr = (int[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof float[]) {
                        float[] arr = (float[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof double[]) {
                        double[] arr = (double[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof long[]) {
                        long[] arr = (long[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else {
                        Object[] arr = (Object[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    }
                }
            }
            return this;
        }

    }
}