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:
// No sorcery shall prevail. //           
import java.util.*;
import java.io.*;
public class InVoker {
	//Variables
	static long mod = 1000000007;
	static long mod2 = 998244353;
	static FastReader inp= new FastReader();
	static PrintWriter out= new PrintWriter(System.out);
	public static void main(String args[]) {		    	
	   	InVoker g=new InVoker();
	   	g.main();
	   	out.close();
	}
	
	
	
	//Main
	void main() {
		
		int n=inp.nextInt();
		int a[]=new int[n];
		input(a,n);
		int xor=0;
		for(int i=0;i<n;i++) xor^=a[i];
		if(n%2==0 && xor!=0) {
			out.println("NO");
			return;
		}
		out.println("YES");
		out.println(2*((n-1)/2));
		for(int i=1;i<n-1;i+=2) {
			out.println(i+" "+(i+1)+" "+n);
		}
		for(int i=1;i<n-1;i+=2) {
			out.println(i+" "+(i+1)+" "+n);
		}
	}
	
	
	
	
	
	
	/*********************************************************************************************************************************************************************************************************
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	 *ti;.                               .:,:i:              .:,;;iii:LLDEEEEEEEEEEEKEEEEEEEEDEEEEEEEEEEEW#WWEEEEEEEKKKKKKKKKKKKKKKKKKKKKKKKKWWKWWWWWWWWWWWWWWKKKKKKKEL    .::.         .:;LijLGGDDDDDDDDEEEEE *
	 *ti;.                               .:,:;:                :,;;ittfDEEEEEEEEEEEEEEEEKEEEGEEEEEEEEEEEKWWWEEEEEEEEEKKKKKKKKKKKKKKKKKKKKKKKKKKWWWWWWWWWWWWWWWKKKKKKKELj   .::.          :,;jffGGDDDDDDDDDEEEE *
	 *ti;.                               .:,:i:                 .,;;tGGDEEEEEEEEEEEKEEEKEEEDEEEEEEEEEEEEWWWEEEEEEEEEEEEKKKKKKKKKKKKKKKKKKKKKKKKKKWWWWWWKWWWWWWKKKKKKKEEL   .::.          .:;itDGGDDDDDDDDDEEEE *
	 *ti;.                               .:::;:                   :;ifDEEEEEEEEEEEEKEEEKEEEEEEEEEEEEEEEWWWEEEEEEEEEEEEEEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKW#WWWKKKKKKKKEEf   .::.           :,itfGEDDDDDDDDDDDEE *
	 *ti;.                               .:::;:                    :GGEEEEEEEEEEEKEKEEKEEEEEEEEEEEEEEEEWWEEEEEEEEEEEEEEEEEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKW#WKKKKKKKKKEEDG  .::.           .,;jfLGKDLDDDDDDEEDD *
	 *ti;.                               .:::;:                     fDEEEEEEKKKKKKKKKEKEEEEEEEEEEEEEEE#WEEEEEEEEEEEEEEEEEEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKW#KKKKKKKKKKEEf .:::.           .,;tfLGDEDDDDDDDDEEE *
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	 *tti.            .....:::..          ...,.           GDEEEKKKKKKKKKWKKKWWW#WWWWWWWWWWWKWKKjiEjitWWWKKWEEEDi...DDLDDDDji;;WEEEEEEEEEEEDEj.iDDEEEEWEEEEEEEEEEEEWWEEDDDDDDGf.          .,;tjfLGGDDDDDDDDDDDD *
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	 *tti.                ....::::..      ...,.          LDEEEKKKKKKKKKKKKKKWWWWWWWWWWWWWWWW####WKiiiWWWKKKEEK,...:E:DDDEii..GWEEEEEEEEDWDDiL.,KDDEEEWEEEEEEEEEEEEWWKEEDDDDDGf:           .,itfLGGDDDDDDDDDDDD *
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	 *tti.                         ....::::::,.        GDEEKKKKKKKKKKKKKWWWW###WWWWWWWWWW#WWWK###W#####WKEKK.....jDDL;;......KKEEEEEEEEEDi.f...;KDEEEWWEEEEEEEEEEEWWWWEEEEEDDGf           .,;tjLLGGDDDDDDDDDDD *
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	 *jti.                                ...:...,,;GEEKKKKKWWKKKKKWWWWWWWW###WWWWWWWWWKKKWWKiLGGEDEDEKGKKiEG..;...........jKEEEKK;:.G....,.....:KKEWWWWKKKKKKKWKK####WKKKKEEEGL          .,;tfLGGGGDDDDDDDDDD *
	 *jti.                                ...:.  .:,GEEKKKKKWKKKKKWWWWWWWW####WWWWWWWWWKKKWWKii;fDLGDK: EEi:E:.............EKEEKK;;..L...........KKKWWWWKKKKKKKWKK####WKKKWKEEDf          .,;tfGGGGDDDDDDDDDDD *
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	 *jti.                                ...:.    GEKKKKKWWKKKKKWWWWWWWWWW##WWWWWWWKKKKKKt;EiKKKK,   ...t................jEKKG;;..,.....,LGi....KWWWWWWKKKKKKWKKKW####WKKKKKEEL,,,:.     .,;tfGGGDDDDDDDDDDDD *
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	 *fjt:            .:::::::,,,,,,,DEEKWWWWWWKKKKKKKWWWWWWWWWWWWKKWKKKKKKWWWWK#WWKKKKWitE;........... ............................:G;;:...............KKKWWKKWWWWWWWWWGWWWKKGGGGWGGGGGGGGGGGGGGGGGGGGGGGGGGL *
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	 *fjti;;iiii;;,:::::::,,,,,,,,;EEEKWWWWWWWKKKKWWWWWWWWKKKKKKKWKKKKKKKWWWWWWW#W#KKKKWEEii;...................................f;:....,;L...................EEKWWWWWWWWDDWWKKDDDDDKEDDDDDDDDDDDDDDDDDDDDDGGGG *
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	 *fjt.    .:,,,:::::,,,,,,,;;;EEKWWWWWWWKKKKKKWKKKKKKKKKKKKKKKKKKKKKWKKKWKW##W#KKKKWEti;;G;........................tEEEL;;;;;;;;;;L..........................DKKKKKEDDWWKEDGftiLE;;;;itjLGGGGGGDDDDDDDDDDD *
	 *fjt.       .j::::,,,,,,,;;;DEEWWWWWWWWKKKKWKKKKKKKKKKKKKKKKKKKKKKKWKKWWWK##W#KKKKKEii;;;L;...................iDEEEEEEKKi;j;;;;jD.....:......................,KKKKDGGEKKE:::::;E::::::::::,tLGGDDDDDDDDDD *
	 *fjt.       .;:::,,,,,,,;;;;EEKWWWWWWWWKWKKKKKKKKKKKKKKKWKKKKKKKKKKWKKWWWW#WW#KKKKKKii;;;;f;.............:tDEEEEEKKKKKKKKEti;;;L...............................EEKf;:iKKE::::::E::::::::::::::ifDDDDDDDDD *
	 *fjt:        :::,,,,,,,,;;;DEEWWWWWWWWWEKKKKKKKKKKKKKKKKKKKKKKKKKKWWKKWWWW####KKKKKEiii;;;;f,.........iDEEEEKKKKKKKKKKKKKKKf;iG......i..........................fK::::KKE::::::E::::::::::::::::,tGGDDDDD *
	 *fjt:       t:::,,,,,,;;;;iDEKWWWWWWKEKKKKKKKKKKKKKKKKKKKKKKKKKKKKWWKKWWWW####WKKKKLiii;;;;;L,....,Li;EDEEEEKKKKKKKKKKKKKKKKiG......;:...........................:i:::KKE:::::,E,::::::::::::::::::iGDDDD *
	 *jjt.       f::,,,,,,,;;;;GEEWWWWKEEKEKKKKKKKKKKKKKKKKWKKKKKKKKKKKWWKWWWWW###WWKKKKiii;;;;;;;G,;L;;iiEEEEEEEKKKKKKKKKKKKKWWKE......;t.........:....................j::KEE:,::,,D,,::::,,,,,,:::::::::tDDD *
	 *fjt:.      ,::,,,,,,,;;;;EEWWKEEEEEEKKKKKKKKKKKKKKKKWKKKKKKKKKKKWWKKWWWWW#W#KKKKKKiiiiii;;;;;i;;iiiEEKEEKKWKKKKKKKWKKKKKWWWGi;...;t......,;;;;,....................:,EEE,,,,,,D,,,,,,,,,,,,,,,,::,::::tG *
	 *fjt:.     ,::,,,,,,,;;;;DEKEEEEEEEEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKWWWWWWWWW#W#KKKKKKiiiii;;i;;;;;iiiKKKEKKKKWWKWWWWWWKKKKWWWWW;;;:;L.....;;;;;;;;;....................,KEE,,,,,,E,,,,,,,,,,,,,,,,,,,,,,,,; *
	 *fjt:.     f:,,,,,,,;;;;jEDEEEEEEEEEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKWWWWWWWW#W##KKKKKKiiiiiiii;i;;iiiEKKKKKKKKWKWWWWWWWWKKKWWWWWKi;;i.....,jEEfGi;;;;;...................EED,,,,,,E,,,,,,,,,,,,,,,,,,,,,,,,, *
	 *fjt:.    .f::,,,,,,;;jEEDEEEEEEEEEEKKKKKKKKKKKKKKKWKKKKKKKKKKKKKWWWKWWWWW###KKKKKLiiiiiiiiiiiiiiEEKKKKKKKKWWWWWWWWWWWWKWWWWWWGi;i;,..;jDDDKEGi;;;;;;:................EED,,,,,,D,,,,,,,,,,,,,,,,,,,,,,,,, *
	 *fjt:.  .. ;::,,,,,;;EDDEEEEEEEEEEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKWWKKW#WW####KWKKKiiiiiiiiiiiiijKKKKKKKKKKWWWWWWWWWWWWWWWWWWWWWt;i;;;;i;DDDDDDGi;;;;;;;;:.............EDf;,,,;,G;;;;;;;;;;;;;;;,,,,,,,,,, *
	 *fjt:......:,,,,,,;LDDDEEEEEEEEEEEKKKKKKKKKKKKKKKKWKKKKKKKKKKKKKWWWWKWWWW####KKKKKiiiiiiiiiiijKEKKWKKKKKKKWWWWWWWWWWWWWWWWWWWWWWiLiii;i;DEEEEDDE;i;;;;;;;;;:..........EDi,;;;;;L;;;;;;;;;;;;;;;;;;,,,,,,, *
	 *fjt:......:,,,,,;EDDDEEKEEEEEEEEEKKKKKKKKKKKKKKKWKKKKKKKKKKKKKKWWWWKKWWW##W#KWKKWEiiiiiijGKKKKKWWKKKKKKKKWWWWWWWWWWWWWWWWWWWWWWKi;iiiiDDEEEEEEDEi;;;;;;;;;;;;;,:.....ED;;;;;;;j;;;;;;;;;;;;;;;;;;;;;;;,, *
	 *fjt:.....t,,,,,;DDDDEEEKEEEEEEEEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKWWWKKKWWWW##WKWKKWKiiiKKKKKKKKKWWKKKKKKKKWWWWWWWWWWWWWWW#WWWWWWWWWiiiiifLEEEEEEEEDi;i;;;;;;;;;;;;.....DD;;;;;;;i;;;;;;;;;;;;;;;;;;;;;;;;; *
	 *fjt:.....G,,,,,GDDDEEEEEEEEEEEEKKKKKKKKKKKKKKKKWKKKKKKKKKKKKKKKWWWKKKWWW###WKWKKWKitKKKKKKKKKWKKKKKKKKKKWWWWWWWWWWWWWW###WWWWWWWWEiiiiiiiEEEEEEEEDGiiii;;;;;;;;;.....GD;;;;;;;i;;;;;;;;;;;;;;;;;;;;;;;;; *
	 *fjt:.....L,,,,;GDDDEEEEEEEEEEKEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKWWWWWDGWWW###KKWWKWKKKKKKKKKKKKKKKKKKKKKKKWWWWWWWWWWWWW####WWWWWWWWWiiiiiiiiEEEEEEEEEEDi;i;;;;;;;;.....Lj;;;;;;i;iiiiii;;;;;;ii;;;;;;;;;;; *
	 ***********************************************************************************************************************************************************************************************************/

	void sort(int a[]) {
		ArrayList<Integer> list=new ArrayList<>();
		for(int x: a) list.add(x);
		Collections.sort(list);
		for(int i=0;i<a.length;i++) a[i]=list.get(i);
	}
	void sort(long a[]) {
		ArrayList<Long> list=new ArrayList<>();
		for(long x: a) list.add(x);
		Collections.sort(list);
		for(int i=0;i<a.length;i++) a[i]=list.get(i);
	}
	void ruffleSort(int a[]) {
		Random rand=new Random();
		int n=a.length;
		for(int i=0;i<n;i++) {
			int j=rand.nextInt(n);
			int temp=a[i];
			a[i]=a[j];
			a[j]=temp;
		}
		Arrays.sort(a);
	}
	void ruffleSort(long a[]) {
		Random rand=new Random();
		int n=a.length;
		for(int i=0;i<n;i++) {
			int j=rand.nextInt(n);
			long temp=a[i];
			a[i]=a[j];
			a[j]=temp;
		}
		Arrays.sort(a);
	}
	
    static class FastReader { 
        BufferedReader br; 
        StringTokenizer st;
        public FastReader() { 
            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 s=""; 
            try { 
                s=br.readLine(); 
            } 
            catch (IOException e) { 
                e.printStackTrace(); 
            } 
            return s; 
        } 
    } 
    
	long fact[];
	long invFact[];
	void init(int n) {
		fact=new long[n+1];
		invFact=new long[n+1];
		fact[0]=1;
		for(int i=1;i<=n;i++) {
			fact[i]=mul(i,fact[i-1]);
		}
		invFact[n]=power(fact[n],mod-2);
		for(int i=n-1;i>=0;i--) {
			invFact[i]=mul(invFact[i+1],i+1);
		}
	}
	
	long nCr(int n, int r) {
		if(n<r || r<0) return 0;
		return mul(fact[n],mul(invFact[r],invFact[n-r]));
	}
	
	long mul(long a, long b) {
		return a*b%mod;
	}
	long add(long a, long b) {
		return (a+b)%mod;
	}
	
	long power(long x, long y) {
		long gg=1;
		while(y>0) {
			if(y%2==1) gg=mul(gg,x);
			x=mul(x,x);
			y/=2;
		}
		return gg;
	}
    
    // Functions
	static long gcd(long a, long b) { 
		return b==0?a:gcd(b,a%b);
	}
	static int gcd(int a, int b) { 
		return b==0?a:gcd(b,a%b);
	}
	
	void print(int a[]) {
		int n=a.length;
		for(int i=0;i<n;i++) out.print(a[i]+" ");
	}
	
	void print(long a[]) {
		int n=a.length;
		for(int i=0;i<n;i++) out.print(a[i]+" ");
	}
    
    //Input Arrays
    static void input(long a[], int n) {
		for(int i=0;i<n;i++) {
			a[i]=inp.nextLong();
		}
	}
	static void input(int a[], int n) {
		for(int i=0;i<n;i++) {
			a[i]=inp.nextInt();
		}
	}	
	static void input(String s[],int n) {
		for(int i=0;i<n;i++) {
			s[i]=inp.next();
		}
	}
	static void input(int a[][], int n, int m) {
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				a[i][j]=inp.nextInt();
			}
		}
	}
	static void input(long a[][], int n, int m) {
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				a[i][j]=inp.nextLong();
			}
		}
	}
		
}