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:
"use strict";

// readline().split(' ').map(value => +value);
var input = readline().split(' ').map(value => +value);
var n = input[0];
var m = input[1];

var M = [];
for (var i = 0; i < m; ++i) {
    M.push(readline().split(' ').map(value => +value));
}

M.sort(function(a, b) {
    if (a[1] !== b[1])
        return a[1] - b[1];
    return a[2] - b[2];
});

var R = new Array(n + 10);
R[1] = 9999;
for (var i = 1, j = 2; i < n; ++i, ++j) {
    R[j] = R[i] - 1;
}

for (var i = 0; i < m; ++i) {
    var t = M[i][0];
    var l = M[i][1];
    var r = M[i][2];
    
    if (t === 1) {
        for (var j = l; j <= r; ++j) {
            R[j] = R[l];
        }
    }
}

var f = true;
for (var i = 0; i < m; ++i) {
    var t = M[i][0];
    var l = M[i][1];
    var r = M[i][2];
    
    if (t === 1) {
        for (var j = l, k = l+1; k <= r; ++j, ++k) {
            if (R[j] > R[k]) {
                f = false;
            }
        }
    } else {
        var b = false;
        for (var j = l, k = l+1; k <= r; ++j, ++k) {
            if (R[j] > R[k]) {
                b = true;
            }
        }
        f = f && b;
    }
}

if (f) {
    write('YES\n');
    write(R.slice(1, n+1).join(' '));
} else {
    write('NO\n');
}