Score : 400 points
There are N people standing on the x-axis. Let the coordinate of Person i be x_i. For every i, x_i is an integer between 0 and 10^9 (inclusive). It is possible that more than one person is standing at the same coordinate.
You will given M pieces of information regarding the positions of these people. The i-th piece of information has the form (L_i, R_i, D_i). This means that Person R_i is to the right of Person L_i by D_i units of distance, that is, x_{R_i} - x_{L_i} = D_i holds.
It turns out that some of these M pieces of information may be incorrect. Determine if there exists a set of values (x_1, x_2, ..., x_N) that is consistent with the given pieces of information.
Input is given from Standard Input in the following format:
N M L_1 R_1 D_1 L_2 R_2 D_2 : L_M R_M D_M
If there exists a set of values (x_1, x_2, ..., x_N) that is consistent with all given pieces of information, print Yes
; if it does not exist, print No
.
3 3 1 2 1 2 3 1 1 3 2
Yes
Some possible sets of values (x_1, x_2, x_3) are (0, 1, 2) and (101, 102, 103).
3 3 1 2 1 2 3 1 1 3 5
No
If the first two pieces of information are correct, x_3 - x_1 = 2 holds, which is contradictory to the last piece of information.
4 3 2 1 1 2 3 5 3 4 2
Yes
10 3 8 7 100 7 9 100 9 8 100
No
100 0
Yes