Funny Graph

Bugland is a country with $N$ cities. Being a newly founded country, the $N$ cities are not connected by any roads, thus the government decided to initiate a project which will last exactly $M$ days and whose purpose is to create a network of roads between the cities.

In each day of the project, the workers build two new weighted unidirectional roads, one from city $x$ to city $y$ whose weight is $z$ and one from city $y$ to city $x$ whose weight is $-z$.

After each day the inhabitants of Bugland ask themselves a question: is there a way of to label the cities with numbers such that if there is an edge from city $x$ to city $y$, the weight of the edge is $C_x-C_y$, where $C_i$ is the label of the $i^{th}$ city?

Input data

The first line will contain the number of cities $N$ and the number of days of the project $M$. The next $M$ lines each contain three numbers $x, y, z$ describing the roads built in each day.

Output data

You will write $M$ lines, on the $i^{th}$ line YEP :) if there is a way to number the cities, or NOPE :/ if there is none.

Constraints and clarifications

• $1 \leq N \leq 5 \cdot 10^4$
• $1 \leq M \leq 10^5$
• $-10^9 \leq z_i \leq 10^9\ \forall\ 1 \leq i \leq M$
• $0 \leq x_i, y_i \leq N - 1\ \forall\ 1 \leq i \leq M$
• For tests worth $30$ points: $1 \leq N \leq 10^3$ and $1 \leq M \leq 10^4$
• Bugland can have multiple roads between two cities or roads form one city to itself.

Example 1

stdin

4 5 
0 1 1 
1 3 -1 
3 0 0 
3 2 4 
2 0 3

stdout

YEP :)
YEP :)
YEP :)
YEP :)
NOPE :/