Problem: Vasya has an array a_1, a_2, ..., a_n.

You don't know this array, but he told you m facts about this array. The i-th fact is a triple of numbers t_i, l_i and r_i (0 ≤ t_i ≤ 1, 1 ≤ l_i < r_i ≤ n) and it means:

  * if t_i=1 then subbarray a_{l_i}, a_{l_i + 1}, ..., a_{r_i} is sorted in non-decreasing order; 
  * if t_i=0 then subbarray a_{l_i}, a_{l_i + 1}, ..., a_{r_i} is not sorted in non-decreasing order. A subarray is not sorted if there is at least one pair of consecutive elements in this subarray such that the former is greater than the latter. 



For example if a = [2, 1, 1, 3, 2] then he could give you three facts: t_1=1, l_1=2, r_1=4 (the subarray [a_2, a_3, a_4] = [1, 1, 3] is sorted), t_2=0, l_2=4, r_2=5 (the subarray [a_4, a_5] = [3, 2] is not sorted), and t_3=0, l_3=3, r_3=5 (the subarray [a_3, a_5] = [1, 3, 2] is not sorted).

You don't know the array a. Find any array which satisfies all the given facts.

Input

The first line contains two integers n and m (2 ≤ n ≤ 1000, 1 ≤ m ≤ 1000).

Each of the next m lines contains three integers t_i, l_i and r_i (0 ≤ t_i ≤ 1, 1 ≤ l_i < r_i ≤ n).

If t_i = 1 then subbarray a_{l_i}, a_{l_i + 1}, ... , a_{r_i} is sorted. Otherwise (if t_i = 0) subbarray a_{l_i}, a_{l_i + 1}, ... , a_{r_i} is not sorted.

Output

If there is no array that satisfies these facts in only line print NO (in any letter case).

If there is a solution, print YES (in any letter case). In second line print n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the array a, satisfying all the given facts. If there are multiple satisfying arrays you can print any of them.

Examples

Input


7 4
1 1 3
1 2 5
0 5 6
1 6 7


Output


YES
1 2 2 3 5 4 4


Input


4 2
1 1 4
0 2 3


Output


NO

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class R571C {

	public static void main(String[] args) {
		JS scan = new JS();
		int n = scan.nextInt();
		int m = scan.nextInt();
		PrintWriter out = new PrintWriter(System.out);
		boolean[] sorted = new boolean[n+1];
		boolean[] v= new boolean[n+1];
		v[0] = true;
		query[] arr =new query[m];
		for(int i = 0;i<m;i++){
			int q = scan.nextInt();
			int a = scan.nextInt();
			int b = scan.nextInt();
			arr[i] = new query(q,a,b);
			for(int j = a;j<=b;j++){
				v[j] = true;
			}
			if(q==1){
				for(int j = a+1;j<=b;j++){
					sorted[j] = true;
				}
			}else{
				for(int j = a+1;j<=b;j++){
					if(sorted[j]){
						continue;
					}
					sorted[j] = false;
				}
			}
		}
//		for(int i = 1;i<=n;i++){
//			if(!v[i]){
//				out.println("NO");
//				out.close();
//				out.flush();
//				return;
//			}
//		}
//		for(int i = 0;i<m;i++){
//			query curr = arr[i];
//			boolean good = false;
//			if(curr.q==0){
//				for(int j = curr.l;j<=curr.r;j++){
//					if(!sorted[j]){
//						good = true;
//						break;
//					}
//				}
//				if(!good){
//					out.println("NO");
//					out.close();
//					out.flush();
//				}
//			}
//			for(int j = 0;j<m;j++){
//				if(i==j)continue;
//				query now = arr[j];
//				if(curr.q!=now.q && curr.q==1){
//					if(curr.l<=now.l && curr.r>=now.r){
//						//what if we have chains of ones enclosing a zero
//						out.println("NO");
//						out.close();
//						out.flush();
//						return;
//					}
//				}
//			}
//		}
//		out.println("YES");
		Integer[] ans = new Integer[n+1];
		int start = 5_00_000_000;
		for(int i = n;i>0;i--){
			if(sorted[i]){
				ans[i] = start;
				start-=1001;
			}else{
				ans[i] = start;
				start+=1001;
			}
		}
		for(int i = 0;i<m;i++){
			query curr = arr[i];
			if(curr.q==0){
				boolean bad = true;
				for(int j = curr.l;j<curr.r;j++){
					if(ans[j]>ans[j+1])bad = false;
				}
				if(bad){
					out.println("NO");
					out.close();
					out.flush();
					return;
				}
			}else{
				boolean bad = false;
				for(int j = curr.l;j<curr.r;j++){
					if(ans[j]>ans[j+1])bad = true;
				}
				if(bad){
					out.println("NO");
					out.close();
					out.flush();
					return;
				}
			}
		}
		out.println("YES");
		for(int i = 1;i<n+1;i++){
			out.print(ans[i]+" ");
		}
		out.close();
		out.flush();
	}
	/*
15 5
1 1 4
0 4 8
1 12 15
1 8 10
0 10 12

10 4
1 1 3
0 2 4
1 5 10
0 3 7
10 3
1 1 5
1 5 10
0 9 10
	 */
	static class query{
		int q, l, r;
		public query(int q1, int l1, int r1){
			q = q1;
			l = l1;
			r = r1;
		}
	}
	static class JS {
		public int BS = 1 << 16;
		public char NC = (char) 0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;

		public JS() {
			in = new BufferedInputStream(System.in, BS);
		}

		public JS(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}

		public char nextChar() {
			while (bId == size) {
				try {
					size = in.read(buf);
				} catch (Exception e) {
					return NC;
				}
				if (size == -1)
					return NC;
				bId = 0;
			}
			return (char) buf[bId++];
		}

		public int nextInt() {
			return (int) nextLong();
		}

		public long nextLong() {
			num = 1;
			boolean neg = false;
			if (c == NC)
				c = nextChar();
			for (; (c < '0' || c > '9'); c = nextChar()) {
				if (c == '-')
					neg = true;
			}
			long res = 0;
			for (; c >= '0' && c <= '9'; c = nextChar()) {
				res = (res << 3) + (res << 1) + c - '0';
				num *= 10;
			}
			return neg ? -res : res;
		}

		public double nextDouble() {
			double cur = nextLong();
			return c != '.' ? cur : cur + nextLong() / num;
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while (c <= 32)
				c = nextChar();
			while (c > 32) {
				res.append(c);
				c = nextChar();
			}
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while (c <= 32)
				c = nextChar();
			while (c != '\n') {
				res.append(c);
				c = nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if (c > 32)
				return true;
			while (true) {
				c = nextChar();
				if (c == NC)
					return false;
				else if (c > 32)
					return true;
			}
		}
	}

}