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.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.Random;

public class Main {
    private static FastScanner sc = new FastScanner();
    private static boolean DEBUG_FLG = false;

    public static void main(String[] args) {
    	int n = sc.nextInt();
    	int m = sc.nextInt();
    	boolean[] nextDec = new boolean[n-1];
    	for(int i=0; i<n-1; i++) {
    		nextDec[i] = true;
    	}
    	Fact[] f = new Fact[m];
    	for(int i=0; i<m; i++) {
    		f[i] = new Fact(sc.nextInt(), sc.nextInt()-1, sc.nextInt()-1);
    	}
    	shuffleArray(f);
    	Arrays.sort(f, (a,b) -> b.t - a.t);
    	a:
    	for(int i=0; i<m; i++) {
    		if(f[i].t == 1) {
    			for(int j=f[i].l; j<f[i].r; j++) {
    				nextDec[j] = false;
    			}
    		} else {
    			for(int j=f[i].l; j<f[i].r; j++) {
    				if(nextDec[j]) {
    					continue a;
    				}
    			}
    			System.out.println("NO");
    			return;
    		}
    	}
    	int[] ans = new int[n];
    	ans[0] = 1000;
    	for(int i=0; i<n-1; i++) {
    		if(nextDec[i]) {
    			ans[i+1] = ans[i] - 1;
    		} else {
    			ans[i+1] = ans[i];
    		}
    	}
    	System.out.println("YES");
    	for(int i=0; i<n; i++) {
    		if(i != 0) System.out.print(" ");
    		System.out.print(ans[i]);
    	}
    	System.out.println();

    }

    static class Fact {
    	int t;
    	int l;
    	int r;
		public Fact(int t, int l, int r) {
			this.t = t;
			this.l = l;
			this.r = r;
		}

    }

    static void debug(long... args) {
    	if(!DEBUG_FLG) return;
    	boolean flg = false;
    	for(long s : args) {
    		if(flg) System.out.print(" ");
    		flg = true;
    		System.out.print(s);
    	}
    	System.out.println();
    }

    static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;
        private boolean hasNextByte() {
            if(ptr < buflen) {
                return true;
            } else {
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch(IOException e) {
                    e.printStackTrace();
                }
                if(buflen <= 0) {
                    return false;
                }
            }
            return true;
        }
        private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
        private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
        private void skipUnprintable() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}
        public boolean hasNext() { skipUnprintable(); return hasNextByte();}
        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while(isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public int nextInt(){
            return Integer.parseInt(next());
        }
        public double nextDouble(){
            return Double.parseDouble(next());
        }
    }

    static void shuffleArray(Fact[] arr){
        int n = arr.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
        	Fact tmp = arr[i];
            int randomPos = i + rnd.nextInt(n-i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }
    }
}