Problem: Polycarp plays a (yet another!) strategic computer game. In this game, he leads an army of mercenaries.

Polycarp wants to gather his army for a quest. There are n mercenaries for hire, and the army should consist of some subset of them.

The i-th mercenary can be chosen if the resulting number of chosen mercenaries is not less than l_i (otherwise he deems the quest to be doomed) and not greater than r_i (he doesn't want to share the trophies with too many other mercenaries). Furthermore, m pairs of mercenaries hate each other and cannot be chosen for the same quest. 

How many non-empty subsets does Polycarp need to consider? In other words, calculate the number of non-empty subsets of mercenaries such that the size of this subset belongs to [l_i, r_i] for each chosen mercenary, and there are no two mercenaries in the subset that hate each other.

The answer may be large, so calculate it modulo 998244353.

Input

The first line contains two integers n and m (1 ≤ n ≤ 3 ⋅ 10^5, 0 ≤ m ≤ min(20, (n(n-1))/(2))) — the number of mercenaries and the number of pairs of mercenaries that hate each other.

Then n lines follow, the i-th of them contains two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ n).

Then m lines follow, the i-th of them contains two integers a_i and b_i (1 ≤ a_i < b_i ≤ n) denoting that the mercenaries a_i and b_i hate each other. There are no two equal pairs in this list.

Output

Print one integer — the number of non-empty subsets meeting the constraints, taken modulo 998244353.

Examples

Input


3 0
1 1
2 3
1 3


Output


3


Input


3 1
1 1
2 3
1 3
2 3


Output


2

Solution (in JAVA):

Solution:
//package ecr94;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;

public class G {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni(), m = ni();
		int[][] lr = new int[n][];
		for(int i = 0;i < n;i++){
			lr[i] = new int[]{ni(), ni()};
		}
		
		boolean[] touch = new boolean[n];
		int[][] ng = new int[m][];
		for(int i = 0;i < m;i++){
			ng[i] = new int[]{ni()-1, ni()-1};
			touch[ng[i][0]] = true;
			touch[ng[i][1]] = true;
		}
		
		int[] f = new int[n];
		int[] nfs = new int[1<<m];
		for(int i = 0;i < 1<<m;i++){
			for(int j = 0;j < m;j++){
				if(i<<~j<0){
					if(++f[ng[j][0]] == 1)nfs[i]++;
					if(++f[ng[j][1]] == 1)nfs[i]++;
				}
			}
			for(int j = 0;j < m;j++){
				if(i<<~j<0){
					f[ng[j][0]] = f[ng[j][1]] = 0;
				}
			}
		}
		
		int[][] es = new int[2*n][];
		for(int i = 0;i < n;i++){
			es[i] = new int[]{lr[i][0], i};
			es[i+n] = new int[]{lr[i][1]+1, i};
		}
		Arrays.sort(es, new Comparator<int[]>() {
			public int compare(int[] a, int[] b) {
				return a[0] - b[0];
			}
		});
		
		boolean[] isin = new boolean[n];
		int p = 0;
		int nin = 0;
		long ans = 0;
		int mod = 998244353;
		int[][] fif = enumFIF(350000, mod);
		int[] co = new int[2*m+1];
		co[0] = 1;
		for(int K = 1;K <= n;K++){
			boolean recon = false;
			while(p < 2*n && es[p][0] <= K){
				if(isin[es[p][1]]){
					nin--;
				}else{
					nin++;
				}
				isin[es[p][1]] ^= true;
				if(touch[es[p][1]]){
					recon = true;
				}
				p++;
			}
			if(recon){
				co = reconstruct(ng, isin, nfs);
			}
			
			long lans = 0;
			for(int i = 0;i <= 2*m;i++){
				lans += C(nin-i, K-i, mod, fif) * co[i];
			}
			lans %= mod;
			
			ans += lans;
		}
		ans %= mod;
		if(ans < 0)ans += mod;
		
		out.println(ans);
	}
	
	int[] reconstruct(int[][] ng, boolean[] isin, int[] nfs)
	{
		int m = ng.length;
		int[] ret = new int[2*m+1];
		
		int ptn = 0;
		for(int j = 0;j < m;j++){
			if(isin[ng[j][0]] && isin[ng[j][1]]){
				ptn |= 1<<j;
			}
		}
		
		for(int i = ptn;i >= 0;i--){ i &= ptn; 
			ret[nfs[i]] += (Integer.bitCount(i) & 1) == 0 ? 1 : -1;
		} // include i=0
		return ret;
	}
	
	
	
	public static long C(int n, int r, int mod, int[][] fif) {
		if (n < 0 || r < 0 || r > n)
			return 0;
		return (long) fif[0][n] * fif[1][r] % mod * fif[1][n - r] % mod;
	}

	
	public static int[][] enumFIF(int n, int mod) {
		int[] f = new int[n + 1];
		int[] invf = new int[n + 1];
		f[0] = 1;
		for (int i = 1; i <= n; i++) {
			f[i] = (int) ((long) f[i - 1] * i % mod);
		}
		long a = f[n];
		long b = mod;
		long p = 1, q = 0;
		while (b > 0) {
			long c = a / b;
			long d;
			d = a;
			a = b;
			b = d % b;
			d = p;
			p = q;
			q = d - c * q;
		}
		invf[n] = (int) (p < 0 ? p + mod : p);
		for (int i = n - 1; i >= 0; i--) {
			invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod);
		}
		return new int[][] { f, invf };
	}

	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new G().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}