Title
Problem Statement
There are N people standing on the x-axis.
Let the coordinate of Person i be xi.
For every i, xi is an integer between 0 and 109 (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 (Li, Ri, Di).
This means that Person Ri is to the right of Person Li by Di units of distance, that is, xRi - xLi = Di holds.
It turns out that some of these M pieces of information may be incorrect.
Determine if there exists a set of values (x1, x2, ..., xN) that is consistent with the given pieces of information.
Constraints
- 1 ≤ N ≤ 100 000
- 0 ≤ M ≤ 200 000
- 1 ≤ Li, Ri ≤ N (1 ≤ i ≤ M)
- 0 ≤ Di ≤ 10 000 (1 ≤ i ≤ M)
- Li ≠ Ri (1 ≤ i ≤ M)
- If i ≠ j, then (Li, Ri) ≠ (Lj, Rj) and (Li, Ri) ≠ (Rj, Lj).
- Di are integers.
Input
Input is given from Standard Input in the following format:
N M
L1 R1 D1
L2 R2 D2
:
LM RM DM
Output
If there exists a set of values (x1, x2, ..., xN) that is consistent with all given pieces of information, print Yes; if it does not exist, print No.
Sample Input 1
3 3
1 2 1
2 3 1
1 3 2
Sample Output 1
Yes
Some possible sets of values (x1, x2, x3) are (0, 1, 2) and (101, 102, 103).
Sample Input 2
3 3
1 2 1
2 3 1
1 3 5
Sample Output 2
No
If the first two pieces of information are correct, x3 - x1 = 2 holds, which is contradictory to the last piece of information.
Sample Input 3
4 3
2 1 1
2 3 5
3 4 2
Sample Output 3
Yes
Sample Input 4
10 3
8 7 100
7 9 100
9 8 100
Sample Output 4
No
Sample Input 5
100 0
Sample Output 5
Yes