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 Ishu
{
    static class Fact
    {
    int t;
    int l;
    int r;
    Fact() {}
    Fact(int t, int l, int r)
        {
        this.t = t;
        this.l = l;
        this.r = r;
        }
    }
    static Scanner scan = new Scanner(System.in);
    static BufferedWriter output = new BufferedWriter(new OutputStreamWriter(System.out)); 
    static void tc() throws Exception
    {
    int n = scan.nextInt();
    int m = scan.nextInt();
    Fact[] facts = new Fact[m];
    int i;
    
    int[] cnt = new int[n + 1];
    for(i=0;i<m;++i)
        {
        int t = scan.nextInt();
        int l = scan.nextInt();
        int r = scan.nextInt();
        facts[i] = new Fact(t, l, r);
        if(t == 1)
            {
            cnt[l]++;
            cnt[r]--;
            }
        }
    
    int[] b = new int[n + 1];
    boolean flag = false;    
    int sum = 0;
    int pre = -1;
    for(i=1;i<=n;++i)    
        {
        sum += cnt[i];
        if(!flag && sum > 0)
            {
            flag = true;
            pre = i;
            }
        else if(flag && sum == 0)
            {
            sum = 0;
            flag = false;
            b[pre] = 1;
            b[i] = -1;
            pre = -1;
            }
        }
          
    int[] zero = new int[n + 1];
    int[] tot = new int[n + 1];
    tot[0] = b[0];
    for(i=1;i<=n;++i)
        {
        tot[i] = tot[i-1] + b[i];
        zero[i] = zero[i-1];
        if(b[i] == 0)
            ++zero[i];
        }
//    for(i=1;i<=n;++i)
//        System.out.print(b[i] + " ");      
//            System.out.println();      
        
    boolean ans = true;
    int[] A = new int[n + 1];   
    Arrays.fill(A, 1);
    
    int st = 1000000;
    flag = false;
    for(i=1;i<=n;++i)
        {
        if(b[i] == 1)
            flag = true;
            
        if(flag)
            A[i] = st;
            
        if(b[i] == -1)
            {
            --st;
            flag = false;
            }        
        }
        
    for(i=0;i<m;++i)
        {
        int t = facts[i].t;
        if(t == 1)
            continue;
        int l = facts[i].l;
        int r = facts[i].r;
        
        int S = zero[r] - zero[l-1];
        if((S == r - l + 1 && tot[l-1] - tot[0] > 0) || (S == r - l && b[l] == 1) || (S == r - l && b[r] == -1) || (S == r - l - 1 && b[l] == 1 && b[r] == -1))
            {
            ans = false;
            break;
            }    
        }    
    if(!ans)
        output.write("NO\n");
    else
        {
        st = n;
        sum = 0;
        for(i=1;i<=n;++i)
            {
            sum += b[i];
            A[i] = st;
            if(sum == 0)
                --st;
            }
        output.write("YES\n");
        for(i=1;i<=n;++i)
            output.write(A[i] + " ");
        output.write("\n");
        }
    output.flush();
    }
    public static void main(String[] args) throws Exception
    {
    int t = 1;
    //t = scan.nextInt();
    while(t-- > 0)
        tc();
    }
}