B"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: 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. 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. 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. "...