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:
arr = input()

N,M = [int(x) for x in arr.split(' ')]

clue = [[0]*3 for _ in range(M)]

for i in range(M):
    
    arr = input()

    T,L,R = [int(x) for x in arr.split(' ')]
    
    clue[i][0] = L
    clue[i][1] = R
    clue[i][2] = T
    

clue.sort()
#print(clue)
ans = [-1]*N

number = 10000000

possible = 0

for i in range(M):
    if clue[i][2]==1:
        left = clue[i][0] - 1
        right = clue[i][1] - 1
        # if all -1, number-2000
        flag = -1
        for j in range(left,right+1):
            if ans[j]!=-1:
                flag = ans[j] 
                break
            
        if flag == -1:
            number -= 2000
            for j in range(left,right+1):
                ans[j] = number
        else:
            for j in range(left,right+1):
                ans[j] = flag


for i in range(M):
    if clue[i][2]==0:
        left = clue[i][0] - 1
        right = clue[i][1] - 1
        
        
        # if ordered, but required unordered, fail
        last = ans[left]
        unorder = 0
        idx = left+1
        while idx<=right:
            if ans[idx]<last or ans[idx]==-1 or last==-1:
                unorder = 1
                break
            last = ans[idx]
            idx += 1
            
        
        
        if unorder==0:
            
            possible = 1
            break
                    

            
if possible==1:
    print('NO')
else:
    for i in range(N-1):
        if ans[i]!=-1 and ans[i+1]==-1:
            ans[i+1] = ans[i] - 1
    
    k = 100010000
    for i in range(N):
        if ans[i]==-1:
            ans[i] = k 
            k -= 1   
        else:
            break
    
    print('YES')
    for x in ans:
        print(x,end=' ')