Andrewid the Android is a galaxy-known detective. Now he is preparing a defense against a possible attack by hackers on a major computer network.

In this network are n vertices, some pairs of vertices are connected by m undirected channels. It is planned to transfer q important messages via this network, the i-th of which must be sent from vertex si to vertex di via one or more channels, perhaps through some intermediate vertices.

To protect against attacks a special algorithm was developed. Unfortunately it can be applied only to the network containing directed channels. Therefore, as new channels can't be created, it was decided for each of the existing undirected channels to enable them to transmit data only in one of the two directions.

Your task is to determine whether it is possible so to choose the direction for each channel so that each of the q messages could be successfully transmitted.

Input

The first line contains three integers n, m and q (1 ≤ n, m, q ≤ 2·105) — the number of nodes, channels and important messages.

Next m lines contain two integers each, vi and ui (1 ≤ vi, ui ≤ n, vi ≠ ui), that means that between nodes vi and ui is a channel. Between a pair of nodes can exist more than one channel.

Next q lines contain two integers si and di (1 ≤ si, di ≤ n, si ≠ di) — the numbers of the nodes of the source and destination of the corresponding message.

It is not guaranteed that in it initially possible to transmit all the messages.

Output

If a solution exists, print on a single line "Yes" (without the quotes). Otherwise, print "No" (without the quotes).

Examples

Input

4 4 2
1 2
1 3
2 3
3 4
1 3
4 2


Output

Yes


Input

3 2 2
1 2
3 2
1 3
2 1


Output

No


Input

3 3 2
1 2
1 2
3 2
1 3
2 1


Output

Yes

Note

In the first sample test you can assign directions, for example, as follows: 1 → 2, 1 → 3, 3 → 2, 4 → 3. Then the path for for the first message will be 1 → 3, and for the second one — 4 → 3 → 2.

In the third sample test you can assign directions, for example, as follows: 1 → 2, 2 → 1, 2 → 3. Then the path for the first message will be 1 → 2 → 3, and for the second one — 2 → 1.
import java.io.*;
import java.util.*;


public class R310QgCaseOfComputerNetwork {

	static int n,m,q;
	static MyArrayList g[],g2[],roots,treeSizes;
	static boolean vis[],yes;
	static int disc[],low[],id[],root[],parent[];
	static int bridgeParent[],bridgeLevel[];
	static int P[][][];
	static int time,total,currRoot;
	static int count[][];
	
	public static void main(String args[]) {
		InputReader in = new InputReader(System.in);
		PrintWriter w = new PrintWriter(System.out);

		n = in.nextInt();
		m = in.nextInt();
		q = in.nextInt();
		
		g = new MyArrayList[n + 1];
		for(int i=1;i<=n;i++)
			g[i] = new MyArrayList();
		
		int u,v;
		for(int i=1;i<=m;i++){
			u = in.nextInt();
			v = in.nextInt();
			g[u].add(v);
			g[v].add(u);
		}
		
		vis = new boolean[n + 1];
		disc = new int[n + 1];
		low = new int[n + 1];
		parent = new int[n + 1];
		time = 0;
		
		vis[1] = true;
		dfs(1);
		
		//System.out.println(Arrays.toString(parent));
		//System.out.println(Arrays.toString(disc));
		//System.out.println(Arrays.toString(low));
		
		g2 = new MyArrayList[n + 1];
		for(int i=1;i<=n;i++)
			g2[i] = new MyArrayList();
		
		roots = new MyArrayList();
		treeSizes = new MyArrayList();
		
		Arrays.fill(vis, false);
		total = 0;
		id = new int[n + 1];
		root = new int[n + 1];
		bridgeParent = new int[n + 1];
		bridgeLevel = new int[n + 1];
		
		int start;
		for(int i=1;i<=n;i++){
			if(!vis[i]){
				vis[i] = true;
				start = total;
				id[i] = ++total;
				currRoot = roots.size();
				roots.add(i);
				dfs2(i,id[i]);
				treeSizes.add(total - start);
			}
		}
		
		//System.out.println(Arrays.toString(id));
		//System.out.println(Arrays.toString(bridgeLevel));
		//System.out.println(Arrays.toString(bridgeParent));
		//System.out.println(roots);
		//System.out.println(Arrays.toString(root));
		
		int ss = roots.size();
		P = new int[ss][][];
		for(int i=0;i<ss;i++)
			buildLCA(roots.get(i),i);
		
		count = new int[total + 1][2];
		
		yes = true;
		int s,d,lca;
		while(q-- > 0 && yes){
			s = in.nextInt();
			d = in.nextInt();
			if(root[s] != root[d])
				yes = false;
			else{
				count[id[s]][0]++;
				count[id[d]][1]++;
				//System.out.println(id[s] + " " + id[d] + " " + root[s]);
				lca = getLCA(id[s],id[d],root[s]);
				count[lca][0]--;
				count[lca][1]--;
			}
		}
		
		vis = new boolean[total + 1];
		
		s = roots.size();
		for(int i=0;i<s && yes;i++){
			vis[roots.get(i)] = true;
			dfs3(roots.get(i));
		}
		
		w.println(yes ? "Yes" : "No");
		w.close();
	}
	
	public static void dfs3(int curr){
		if(!yes)	return;
		int s = g2[curr].size(),x;
		for(int i=0;i<s;i++){
			x = g2[curr].get(i);
			if(!vis[x]){
				dfs3(x);
				count[curr][0] += count[x][0];
				count[curr][1] += count[x][1];
			}
		}
		if(count[curr][0] > 0 && count[curr][1] > 0)
			yes = false;
	}
	
	
	public static void buildLCA(int root,int rootId){
		bridgeParent[root] = root;
		
		int N = treeSizes.get(rootId);
		P[rootId] = new int[20][N + 1];
	
		for(int j=0;1<<j<N;j++)
			for(int i=1;i<=N;i++)
				P[rootId][j][i] = -1;
		
		for(int i=1;i<=N;i++)
			P[rootId][0][i] = bridgeParent[i];
		
		for(int j=1;(1<<j) < N;++j)
			for(int i=1;i<=N;++i)
				if(P[rootId][j-1][i] != -1)
					P[rootId][j][i] = P[rootId][j-1][P[rootId][j-1][i]];
		
	}
	
	public static int getLCA(int p,int q,int rootId){
		int tmp,log,i;
		if(bridgeLevel[p] < bridgeLevel[q]){
			tmp = p;
			p = q;
			q = tmp;
		}
		
		for(log=1;1<<log <= bridgeLevel[p];log++);
		log--;
		
		for(i = log; i >= 0; i--)
			if(bridgeLevel[p] - (1<<i) >= bridgeLevel[q])
				p = P[rootId][i][p];
		
		if(p == q)	return p;
		
		for(i = log; i >= 0; i--)
			if(P[rootId][i][p] != -1 && P[rootId][i][p] != P[rootId][i][q]){
				p = P[rootId][i][p];
				q = P[rootId][i][q];
			}
		
		return bridgeParent[p];
	}
	
	
	static public void dfs(int curr){
		disc[curr] = low[curr] = time++;
		boolean notParent = false;
		int s = g[curr].size(),x;
		for(int i=0;i<s;i++){
			x = g[curr].get(i);
			if(vis[x]){
				if(x != parent[curr])
					low[curr] = Math.min(low[curr], disc[x]);
				else{
					if(notParent)
						low[curr] = Math.min(low[curr],disc[x]);
					else
						notParent = true;
				}
			}
			else{
				vis[x] = true;
				parent[x] = curr;
				dfs(x);
				low[curr] = Math.min(low[x], low[curr]);
			}
		}
	}

	static public void dfs2(int curr,int type){
		id[curr] = type;
		root[curr] = currRoot;
		int s = g[curr].size(),x;
		for(int i=0;i<s;++i){
			x = g[curr].get(i);
			if(!vis[x]){
				vis[x] = true;
				if(low[x] > disc[curr]){
					total++;
					bridgeLevel[total] = bridgeLevel[type] + 1;
					bridgeParent[total] = type;
					g2[type].add(total);
					dfs2(x,total);
				}
				else
					dfs2(x,type);
			}
		}
	}
	
	static public class MyArrayList {
		 
	    private int[] myStore;
	    private int actSize = 0;
	     
	    public MyArrayList(){
	        myStore = new int[5];
	    }
	     
	    public int get(int index){
	        if(index < actSize)
	            return myStore[index];
	         else 
	            throw new ArrayIndexOutOfBoundsException();
	    }
	     
	    public void add(int obj){
	        if(myStore.length-actSize <= 1)
	            increaseListSize();
	        myStore[actSize++] = obj;
	    }
	   
	    public int size(){
	        return actSize;
	    }
	     
	    private void increaseListSize(){
	        myStore = Arrays.copyOf(myStore, myStore.length*2);
	    }
	}

	static class InputReader {

		private InputStream stream;
		private byte[] buf = new byte[8192];
		private int curChar;
		private int snumChars;
		private SpaceCharFilter filter;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		public int snext() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int nextInt() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}

			int res = 0;

			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));

			return res * sgn;
		}
		
		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}

			long res = 0;

			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));

			return res * sgn;
		}
		
		public String readString() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		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);
		}
	}
}
