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 PYTHON3):

Solution:
# python template for atcoder1
import sys
sys.setrecursionlimit(10**9)
input = sys.stdin.readline


class UnionFind:

    def __init__(self, N):
        self.parent = [i for i in range(N)]
        self.size = [1 for _ in range(N)]

    def find(self, x):
        if self.parent[x] == x:
            return x
        else:
            return self.find(self.parent[x])

    def union(self, x, y):
        px = self.find(x)
        py = self.find(y)
        if px == py:
            return
        if self.size[px] < self.size[py]:
            self.parent[px] = py
            self.size[py] += self.size[px]
        else:
            self.parent[py] = px
            self.size[px] += self.size[py]

    def same(self, x, y):
        return self.find(x) == self.find(y)


def solve():
    N, M = map(int, input().split())
    inc_query = []
    non_inc_query = []

    for _ in range(M):
        t, l, r = map(lambda x: int(x)-1, input().split())
        if t == 0:
            inc_query.append([l, r])
        else:
            non_inc_query.append([l, r])

    Un = UnionFind(N)
    for l, r in inc_query:
        for i in range(l, r):
            Un.union(i, i+1)

    for l, r in non_inc_query:
        for i in range(l, r):
            if Un.same(l, r):
                print("NO")
                return

    s = 10**4
    ans = [s]
    for i in range(1, N):
        if Un.same(i, i-1):
            ans.append(s)
        else:
            ans.append(s-1)
            s -= 1
    print("YES")
    print(*ans)


solve()