Mahmoud wants to write a new dictionary that contains n words and relations between them. There are two types of relations: synonymy (i. e. the two words mean the same) and antonymy (i. e. the two words mean the opposite). From time to time he discovers a new relation between two words.

He know that if two words have a relation between them, then each of them has relations with the words that has relations with the other. For example, if like means love and love is the opposite of hate, then like is also the opposite of hate. One more example: if love is the opposite of hate and hate is the opposite of like, then love means like, and so on.

Sometimes Mahmoud discovers a wrong relation. A wrong relation is a relation that makes two words equal and opposite at the same time. For example if he knows that love means like and like is the opposite of hate, and then he figures out that hate means like, the last relation is absolutely wrong because it makes hate and like opposite and have the same meaning at the same time.

After Mahmoud figured out many relations, he was worried that some of them were wrong so that they will make other relations also wrong, so he decided to tell every relation he figured out to his coder friend Ehab and for every relation he wanted to know is it correct or wrong, basing on the previously discovered relations. If it is wrong he ignores it, and doesn't check with following relations.

After adding all relations, Mahmoud asked Ehab about relations between some words based on the information he had given to him. Ehab is busy making a Codeforces round so he asked you for help.

Input

The first line of input contains three integers n, m and q (2 ≤ n ≤ 105, 1 ≤ m, q ≤ 105) where n is the number of words in the dictionary, m is the number of relations Mahmoud figured out and q is the number of questions Mahmoud asked after telling all relations.

The second line contains n distinct words a1, a2, ..., an consisting of small English letters with length not exceeding 20, which are the words in the dictionary.

Then m lines follow, each of them contains an integer t (1 ≤ t ≤ 2) followed by two different words xi and yi which has appeared in the dictionary words. If t = 1, that means xi has a synonymy relation with yi, otherwise xi has an antonymy relation with yi.

Then q lines follow, each of them contains two different words which has appeared in the dictionary. That are the pairs of words Mahmoud wants to know the relation between basing on the relations he had discovered.

All words in input contain only lowercase English letters and their lengths don't exceed 20 characters. In all relations and in all questions the two words are different.

Output

First, print m lines, one per each relation. If some relation is wrong (makes two words opposite and have the same meaning at the same time) you should print "NO" (without quotes) and ignore it, otherwise print "YES" (without quotes).

After that print q lines, one per each question. If the two words have the same meaning, output 1. If they are opposites, output 2. If there is no relation between them, output 3.

See the samples for better understanding.

Examples

Input

3 3 4
hate love like
1 love like
2 love hate
1 hate like
love like
love hate
like hate
hate like


Output

YES
YES
NO
1
2
2
2


Input

8 6 5
hi welcome hello ihateyou goaway dog cat rat
1 hi welcome
1 ihateyou goaway
2 hello ihateyou
2 hi goaway
2 hi hello
1 hi hello
dog cat
dog hi
hi hello
ihateyou goaway
welcome ihateyou


Output

YES
YES
YES
YES
NO
YES
3
3
1
1
2
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.io.ObjectInputStream.GetField;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Stack;
import java.util.TreeMap;
import java.util.TreeSet;
public class Q1 {
	
	static long MOD = 1000000007;
	static boolean b[];
	static ArrayList<Integer>[] amp;
	static ArrayList<Graph>[] amp1;
	static int sum[],dist[],cnt[],arr[],start[],color[],parent[];
	static long ans = 0;
	static int p = 0;
	static FasterScanner sc = new FasterScanner();
	static Queue<Integer> q = new LinkedList<>();
	static PriorityQueue<Integer> pq;
	static BufferedWriter log;
	static HashSet<Integer> hs;
	static HashMap<String,Integer> hm;
	static Pair prr[];
	static long parent1[],parent2[],size[][],size1[],size2[];
	public static void main(String[] args) throws Exception {
    	new Thread(null, new Runnable() {
			public void run() {
				try {
					soln();
				} catch (Exception e) {
					e.printStackTrace();
				}
			}
		}, "1", 1 << 26).start();
	}
	public static class ExampleComparator  implements Comparator<String> {
		  public int compare(String obj1, String obj2) {
			StringBuilder sb = new StringBuilder();
			sb.append(obj1);sb.append(obj2);
			StringBuilder sb2 = new StringBuilder();
			sb2.append(obj2);sb2.append(obj1);
		    if (sb.toString() == sb2.toString()) {
		        return 0;
		    }
		    return sb.toString().compareTo(sb2.toString());
		  }
		}
	public static void soln() throws IOException {
		log = new BufferedWriter(new OutputStreamWriter(System.out));
		int n = sc.nextInt(), m = sc.nextInt(), q = sc.nextInt();
		hm = new HashMap<>();
		for(int i = 0; i<n;i++){
			hm.put(sc.nextString(), i);
		}
		String map[] = new String[m];
		for(int i =0 ; i< m ;i++){
			map[i] = sc.nextLine();
		}
		amp1 =(ArrayList<Graph>[]) new ArrayList[n];
		for(int i =0 ;i < n; i++){
			amp1[i] = new ArrayList<>();
		}
		parent = new int[n];
		for(int i =0 ; i< n; i++) parent[i] = i;
		HashSet<Integer> left = new HashSet<>();
		String ans[] = new String[m];
		for(int i = 0;i<m;i++){
			String s[] = map[i].split(" ");
			int val = Integer.parseInt(s[0])/2,x1 =hm.get(s[1]), y1 = hm.get(s[2]);
			int x = getParent(x1), y = getParent(y1);
			if(x!=y){
				ans[i] = "YES";
				amp1[x1].add(new Graph(y1,val));
				amp1[y1].add(new Graph(x1,val));
				parent[x] = y;
			}
			else left.add(i);
		}
		b = new boolean[n];
		dist = new int[n];
		for(int i = 0; i< n; i++){
			if(!b[i]){
				dfs(i);
			}
		}
		//for(int i =0 ;i<n;i++){
		//	System.out.println(parent[i]+" "+dist[i]);
		//}
		for(int i:left){
			String s[] = map[i].split(" ");
			int val = Integer.parseInt(s[0]),x1 =hm.get(s[1]), y1 = hm.get(s[2]);
			if(val==((dist[x1]^dist[y1])+1)) ans[i] = "YES";
			else ans[i] = "NO";
		}
		for(String i:ans) log.write(i+"\n");
		for(int i =0 ;i < q;i++){
			int x = hm.get(sc.nextString()), y = hm.get(sc.nextString());
			//System.out.println(dist[x]+" "+dist[y]);
			if(getParent(x)!=getParent(y)) log.write(3+"\n");
			else log.write(((dist[y]^dist[x])+1)+"\n");
		}
		log.close();
	}
	static class Graph{
		int vertex;
		int weight;
		Graph(int v, int w){
			vertex = v;
			weight = w;
		}
	}
	static void dfs(int x){
		b[x] = true;
		for(Graph e:amp1[x]){
			int v = e.vertex, w = e.weight;
			if(!b[v]){
				dist[v] = dist[x]^w;
				dfs(v);
			}
		}
	}
	public static void bfs(int x,int arr[]){
	b = new boolean[arr.length];
	b[x] = true;
	q = new LinkedList<>();
	q.add(x);
	while(!q.isEmpty()){
		int y = q.poll();
		for(int i = 0;i<amp[y].size();i++) {
			if(!b[amp[y].get(i)]){
				q.add(amp[y].get(i));
				b[amp[y].get(i)] = true;
				arr[amp[y].get(i)] = (arr[y]+1);
			}
		}
	}
	}
	
	static long get(long x){
		if((x%10)<5) return x-(x%10);
		else return x+(10-x%10);
	}
	static long func(long n, long d, long t){
		return (t*(2*(n-1)+(t-1)*(d)))/2;
	}
	static class Pair implements Comparable<Pair> {
		long u;
		long v;
		public Pair(long u, long v) {
			this.u = u;
			this.v = v;
		}
		
		public int hashCode() {
			int hu = (int) (u ^ (u >>> 32));
			int hv = (int) (v ^ (v >>> 32));
			return 31*hu + hv;
		}
 
		public boolean equals(Object o) {
			Pair other = (Pair) o;
			return (u == other.u && v == other.v);
		}
 
		public int compareTo(Pair other) {
			return Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)) : (Long.compare(v, other.v));
		}
		
		public String toString() {
			return "[u=" + u + ", v=" + v + "]";
		}
	}
	public static void buildGraph(int n){
		for(int i =0;i<n;i++){
			int x = sc.nextInt(), y = sc.nextInt();
			amp[--x].add(--y);
			amp[y].add(x);
		}
	}
	
	
	public static int getParent(int x){
		while(parent[x]!=x){
			parent[ x] = parent[(int) parent[ x]];
			x = parent[ x];
		}
		return x;
	}
	static long min(long a, long b, long c){
		if(a<b && a<c) return a;
		if(b<c) return b;
		return c;
	}
	/*
	
	static class Pair3{
		int x, y ,z;
		Pair3(int x, int y, int z){
			this.x = x;
			this.y = y;
			this.z = z;
		}
	}*/
	static int sum(int n){
		String str = Integer.toString(n);
		int cnt = 0;
		for(int i = 0; i< str.length();i++){
			cnt+=(str.charAt(i)-'0');
		}
		return cnt;
	}
	 static void KMPSearch(String pat, String txt)
	    {
	        int M = pat.length();
	        int N = txt.length();
	 
	        // create lps[] that will hold the longest
	        // prefix suffix values for pattern
	        int lps[] = new int[M];
	        int j = 0;  // index for pat[]
	 
	        // Preprocess the pattern (calculate lps[]
	        // array)
	        computeLPSArray(pat,M,lps);
	 
	        int i = 0;  // index for txt[]
	        while (i < N)
	        {
	            if (pat.charAt(j) == txt.charAt(i))
	            {
	                j++;
	                i++;
	            }
	            if (j == M)
	            {
	               // parent.add((i-j));
	                j = lps[j-1];
	            }
	 
	            // mismatch after j matches
	            else if (i < N && pat.charAt(j) != txt.charAt(i))
	            {
	                // Do not match lps[0..lps[j-1]] characters,
	                // they will match anyway
	                if (j != 0)
	                    j = lps[j-1];
	                else
	                    i = i+1;
	            }
	        }
	    }
	 static void computeLPSArray(String pat, int M, int lps[])
	    {
	        // length of the previous longest prefix suffix
	        int len = 0;
	        int i = 1;
	        lps[0] = 0;  // lps[0] is always 0
	 
	        // the loop calculates lps[i] for i = 1 to M-1
	        while (i < M)
	        {
	            if (pat.charAt(i) == pat.charAt(len))
	            {
	                len++;
	                lps[i] = len;
	                i++;
	            }
	            else  // (pat[i] != pat[len])
	            {
	                // This is tricky. Consider the example.
	                // AAACAAAA and i = 7. The idea is similar 
	                // to search step.
	                if (len != 0)
	                {
	                    len = lps[len-1];
	 
	                    // Also, note that we do not increment
	                    // i here
	                }
	                else  // if (len == 0)
	                {
	                    lps[i] = len;
	                    i++;
	                }
	            }
	        }
	    }
	private static void permutation(String prefix, String str) {
	    int n = str.length();
	    if (n == 0); //hs.add(prefix);
	    else {
	        for (int i = 0; i < n; i++)
	            permutation(prefix + str.charAt(i), str.substring(0, i) + str.substring(i+1, n));
	    }
	}
	public static char give(char c1,char c2){
		if(c1!='a' && c2!='a') return 'a';
		if(c1!='b' && c2!='b') return 'b';
		return 'c';
	}
	
	public static void buildTree(int n){
		int arr[] = sc.nextIntArray(n);
		for(int i = 0;i<n;i++){
			int x = arr[i]-1;
			amp[i+1].add(x);
			amp[x].add(i+1);
		}
	}
	
	
	static class SegmentTree{
		int pre[], suf[], max[], val[];
		SegmentTree( int n){
			int size = 4*n;
			pre = new int[size];
			suf = new int[size];
			max = new int[size];
			val = new int[size];
			build(0,n-1,1);
		}
		void build(int ss, int se, int si){
			if(ss==se){
				pre[si] = 1;
				suf[si] = 1;
				max[si] = 1;
				val[si] = arr[ss];
			}
			else{
			int mid = (ss+se)>>2;
			si*=2;
			build(ss,mid,si);build(mid+1,se,si+1);
			}
		}
		
		/*int[] get(int qs, int qe, int ss, int se, int si){
			if(qe < ss || se < qs)
        		return new int[2];
			if(qs<=ss && qe>=se){
				return new int[]{max[si],val[si]};
			}
			int mid = (ss+se)/2;
			si*=2;
			if(qe<=mid) return get(qs,qe,ss,mid,si);
			else if(qs>mid) return get(qs,qe,mid+1,se,si+1);
			long a1[] = build(ss,mid,si*2), a2[] = build(mid+1,se,si*2+1);
			long ans[] = new long[4];
			if(arr[mid] == arr[mid+1]){
			    long temp = a1[2]+a2[0];
			    if(temp>=a2[1] && temp>=a1[1]){
			        ans[1] = temp;
			        ans[3] = arr[mid];
			    }
			    else if(a2[1]>=a1[1]){
			        ans[1] = a2[1];
			        ans[3] = a2[3];
			    }
			    else{
			        ans[1] = a1[1];
			        ans[3] = a1[3];
			    } 
			    if(a1[1]==(mid-ss+1)) ans[0] = ans[1];
			    else ans[0] = a1[0];
			    if(a2[2]==(se-mid)) ans[2] = ans[1];
				else ans[2] = a2[2];
			}
			else{
				if(a2[1]>=a1[1]){
			        ans[1] = a2[1];
			        ans[3] = a2[3];
			    }
			    else{
			        ans[1] = a1[1];
			        ans[3] = a1[3];
			    } 
				ans[0] = a1[0];
				ans[2] = a2[2];
			}
            return ans;
		}
		void print(){
			for(int i = 0;i<st.length;i++){
				System.out.println(st[i][0]+" "+st[i][1]+" "+st[i][2]+" "+st[i][3]);
			}
			System.out.println();
		}*/
	}
	static int convert(int x){
		int cnt = 0;
		String str = Integer.toBinaryString(x);
		//System.out.println(str);
		for(int i = 0;i<str.length();i++){
			if(str.charAt(i)=='1'){
				cnt++;
			}
		}
		int ans = (int) Math.pow(3, 6-cnt);
		return ans;
	}
	static class Node2{
		Node2 left = null;
		Node2 right = null;
		Node2 parent = null;
		int data;
	}
	static class BinarySearchTree{
		Node2 root = null;
		int height = 0;
		int max = 0;
		int cnt = 1;
		ArrayList<Integer> parent = new ArrayList<>();
		HashMap<Integer, Integer> hm = new HashMap<>();
		public void insert(int x){
			Node2 n = new Node2();
			n.data = x;
			if(root==null){
				root = n;
			}
			else{
				Node2 temp = root,temp2 = null;
				while(temp!=null){
					temp2 = temp;
					if(x>temp.data) temp = temp.right;
					else temp = temp.left;
				}
				if(x>temp2.data) temp2.right = n;
				else temp2.left = n;
				n.parent = temp2;
				parent.add(temp2.data);
			}
		}
		public Node2 getSomething(int x, int y, Node2 n){
			if(n.data==x || n.data==y) return n;
			else if(n.data>x && n.data<y) return n;
			else if(n.data<x && n.data<y) return getSomething(x,y,n.right);
			else return getSomething(x,y,n.left);
		}
		public Node2 search(int x,Node2 n){
			if(x==n.data){
				max = Math.max(max, n.data);
				return n;
			}
			if(x>n.data){
				max = Math.max(max, n.data);
				return search(x,n.right);
			}
			else{
				max = Math.max(max, n.data);
				return search(x,n.left);
			}
		}
		public int getHeight(Node2 n){
			if(n==null) return 0;
			height = 1+ Math.max(getHeight(n.left), getHeight(n.right));
			return height;
		}
	}
	static long findDiff(long[] arr, long[] brr, int m){
		int i = 0, j = 0;
		long fa = 1000000000000L;
		while(i<m && j<m){
			long x = arr[i]-brr[j];
			if(x>=0){
				if(x<fa) fa = x;
				j++;
			}
			else{
				if((-x)<fa) fa = -x;
				i++;
			}
		}
		return fa;
	}
	public static long max(long x, long y, long z){
		if(x>=y && x>=z) return x;
		if(y>=x && y>=z) return y;
		return z;
	}
	
	public static void seive(long n){
		b = new boolean[(int) (n+1)];
		Arrays.fill(b, true);
		for(int i = 2;i*i<=n;i++){
			if(b[i]){
				for(int p = 2*i;p<=n;p+=i){
					b[p] = false;
				}
			}
		}
	}
	static long modInverse(long a, long mOD2){
	            return  power(a, mOD2-2, mOD2);
	}
	static long power(long x, long y, long m)
	{
	    if (y == 0)
	        return 1;
	    long p = power(x, y/2, m) % m;
	    p = (p * p) % m;
	 
	    return (y%2 == 0)? p : (x * p) % m;
	}
	static long power2(long x,BigInteger y,long m){
		long ans = 1;
		BigInteger two = new BigInteger("2");
		while(y.compareTo(BigInteger.ZERO)>0){
			if(y.getLowestSetBit()==y.bitCount()){
				x = (x*x)%MOD;
				y = y.divide(two);
			}
			else{
				ans = (ans*x)%MOD;
				y = y.subtract(BigInteger.ONE);
			}
		}
		return ans;
	}
	static BigInteger power2(BigInteger x, BigInteger y, BigInteger m){
		BigInteger ans = new BigInteger("1");
		BigInteger one  = new BigInteger("1");
		BigInteger two  = new BigInteger("2");
		BigInteger zero  = new BigInteger("0");
		while(y.compareTo(zero)>0){
			//System.out.println(y);
			if(y.mod(two).equals(one)){
				ans = ans.multiply(x).mod(m);
				y = y.subtract(one);
			}
			else{
				x = x.multiply(x).mod(m);
				y = y.divide(two);
			}
		}
		return ans;
	}
	static BigInteger power(BigInteger x, BigInteger y, BigInteger m)
	{
	    if (y.equals(0))
	        return (new BigInteger("1"));
	    BigInteger p = power(x, y.divide(new BigInteger("2")), m).mod(m);
	    p = (p.multiply(p)).mod(m);
	 
	    return (y.mod(new BigInteger("2")).equals(0))? p : (p.multiply(x)).mod(m);
	}
	static long d,x,y;
	public static void extendedEuclidian(long a, long b){
		if(b == 0) {
	        d = a;
	        x = 1;
	        y = 0;
	    }
	    else {
	        extendedEuclidian(b, a%b);
	        int temp = (int) x;
	        x = y;
	        y = temp - (a/b)*y;
	    }
	}
	
	public static long gcd(long n, long m){
		if(m!=0) return gcd(m,n%m);
		else return n;
	}
	
	
	public static class FasterScanner {
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
 
		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = System.in.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
 
		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}
 
		public String nextString() {
			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 long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public int nextInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
	        
	    public int[] nextIntArray(int n) {
	        return nextIntArray(n, 0);
	    }
	    
	    public int[] nextIntArray(int n, int off) {
	    	int[] arr = new int[n + off];
	    	for (int i = 0; i < n; i++) {
	    		arr[i + off] = nextInt();
	    	}
	    	return arr;
	    }
	    
	    public long[] nextLongArray(int n) {
	    	return nextLongArray(n, 0);
	    }
        
		public long[] nextLongArray(int n, int off) {
		    long[] arr = new long[n + off];
		    for (int i = 0; i < n; i++) {
		        arr[i + off] = nextLong();
		    }
		    return arr;
		}
 
	    private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
 
		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
	}
}   