Problem: You have a string S of length N. Initially, all characters in S are `1`s.

You will perform queries Q times. In the i-th query, you are given two integers L_i, R_i and a character D_i (which is a digit). Then, you must replace all characters from the L_i-th to the R_i-th (inclusive) with D_i.

After each query, read the string S as a decimal integer, and print its value modulo 998,244,353.

Constraints

* 1 \leq N, Q \leq 200,000
* 1 \leq L_i \leq R_i \leq N
* 1 \leq D_i \leq 9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N Q
L_1 R_1 D_1
:
L_Q R_Q D_Q


Output

Print Q lines. In the i-th line print the value of S after the i-th query, modulo 998,244,353.

Examples

Input

8 5
3 6 2
1 4 7
3 8 3
2 2 2
4 5 1


Output

11222211
77772211
77333333
72333333
72311333


Input

200000 1
123 456 7


Output

641437905

Solution (in JAVA):

Solution:
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";

	static void solve()
	{
		int n = ni(), Q = ni();
		SegmentTreeRUpdateRSQ st = new SegmentTreeRUpdateRSQ(n);
		st.update(0, n, 1);
		for(int i = 0;i < Q;i++){
			int l = ni()-1, r = ni()-1, d = ni();
			st.update(l, r+1, d);
			out.println(st.sum(0, n));
		}
	}

	public static class SegmentTreeRUpdateRSQ {
		public int M, H, N, LH;
		public long[] sums;
		public long[] cover;
		private final long I = Long.MAX_VALUE;
		private final int mod = 998244353;

		long[] ps, sps;

		public SegmentTreeRUpdateRSQ(int n)
		{
			N = n;
			M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
			H = M>>>1;
			LH = Integer.numberOfTrailingZeros(H);
			ps = new long[H+1];
			sps = new long[H+1];
			ps[0] = sps[0] = 1;
			for(int i = 1;i <= H;i++){
				ps[i] = ps[i-1] * 10 % mod;
				sps[i] = (sps[i-1] + ps[i]) % mod;
			}

			cover = new long[H];
			Arrays.fill(cover, I);
			sums = new long[M];
			Arrays.fill(sums, 0);
//			for(int i = H-1;i >= 1;i--)propagate(i);
		}

		public SegmentTreeRUpdateRSQ(long[] a)
		{
			this(a.length);
			for(int i = 0;i < N;i++){
				sums[H+i] = a[i];
			}
			for(int i = H-1;i >= 1;i--){
				propagate(i, H/Integer.highestOneBit(i));
			}
		}

		private void push1(int cur, int len)
		{
			if(cover[cur] == I)return;
			int L = cur*2, R = L + 1;
			sums[L] = sums[R] = cover[cur] * sps[len/2-1] % mod;
			if(L < H){
				cover[L] = cover[R] = cover[cur];
			}
			cover[cur] = I;
		}

		private void propagate(int i, int len)
		{
			sums[i] = (sums[2*i] * ps[len/2] + sums[2*i+1]) % mod;
		}

		private void update1(int cur, long v, int len)
		{
			sums[cur] = v*sps[len-1] % mod;
			if(cur < H){
				cover[cur] = v;
			}
		}

		private void push(int l, int r)
		{
			for(int i = LH;i >= 1;i--) {
				if (l >>> i << i != l) push1(l >>> i, 1<<i);
				if (r >>> i << i != r) push1(r >>> i, 1<<i);
			}
		}

		private void update(int l, int r, long v)
		{
			if(l >= r)return;
			l += H; r += H;
			push(l, r);
			for(int ll = l, rr = r, len = 1;ll < rr;ll>>>=1,rr>>>=1, len<<=1){
				if((ll&1) == 1)update1(ll++, v, len);
				if((rr&1) == 1)update1(--rr, v, len);
			}
			for(int i = 1, len = 2;i <= LH;i++, len<<=1){
				if(l>>>i<<i != l)propagate(l>>>i, len);
				if(r>>>i<<i != r)propagate(r>>>i, len);
			}
		}

		public long sum(int l, int r)
		{
			if(l >= r)return 0;
			l += H; r += H;
			push(l, r);
			long retl = 0, retr = 0;
			int llen = 0, rlen = 0;
			for(int ll = l, rr = r;ll < rr;ll>>>=1,rr>>>=1){
				if((ll&1) == 1){
					int v = ll++;
					retl = (retl * ps[H/Integer.highestOneBit(v)] + sums[v]) % mod;
					llen += H/Integer.highestOneBit(v);
				}
				if((rr&1) == 1){
					int v = --rr;
					retr = (sums[v] * ps[rlen] + retr) % mod;
					rlen += H/Integer.highestOneBit(v);
				}
			}
			return (retl * ps[rlen] + retr) % mod;
		}

		private String tos(long[] a, int ind){ return ind < a.length ? "" + a[ind] : "_";}
		private static String j(Object... o){ return Arrays.deepToString(o);}

		public String nodeToString(int cur)
		{
			return j(cur, sums[cur], tos(cover, cur));
		}

		public String toString() {  return toString(1, ""); }

		private String toString(int cur, String indent)
		{
			return cur >= M ? "" :
					toString(2*cur, indent + "  ")
							+ indent + nodeToString(cur) + "\n"
							+ toString(2*cur+1, indent + "  ");
		}
	}

	public static void main(String[] args) throws Exception
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
	}
	
	private static boolean eof()
	{
		if(lenbuf == -1)return true;
		int lptr = ptrbuf;
		while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
		
		try {
			is.mark(1000);
			while(true){
				int b = is.read();
				if(b == -1){
					is.reset();
					return true;
				}else if(!isSpaceChar(b)){
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}
	
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	
	private static 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 static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
//	private static boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
	private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private static double nd() { return Double.parseDouble(ns()); }
	private static char nc() { return (char)skip(); }
	
	private static String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private static 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 static 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 static int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private static 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 static 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 static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}