Problem: 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.

Constraints

* 1 \leq N \leq 100 000
* 0 \leq M \leq 200 000
* 1 \leq L_i, R_i \leq N (1 \leq i \leq M)
* 0 \leq D_i \leq 10 000 (1 \leq i \leq M)
* L_i \neq R_i (1 \leq i \leq M)
* If i \neq j, then (L_i, R_i) \neq (L_j, R_j) and (L_i, R_i) \neq (R_j, L_j).
* D_i are integers.

Input

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


Output

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`.

Examples

Input

3 3
1 2 1
2 3 1
1 3 2


Output

Yes


Input

3 3
1 2 1
2 3 1
1 3 5


Output

No


Input

4 3
2 1 1
2 3 5
3 4 2


Output

Yes


Input

10 3
8 7 100
7 9 100
9 8 100


Output

No


Input

100 0


Output

Yes

Solution (in PYTHON3):

Solution:
#!python3

import sys
sys.setrecursionlimit(200000)


# input
N, M = list(map(int, input().split()))
LRD = [tuple(map(int, input().split())) for _ in range(M)]


def judge(W, D, visit, i):
    visit[i] = True
    for j, d in W[i]:
        if D[j] is None:
            D[j] = D[i] + d
        else:
            if D[i] + d != D[j]:
                return True
        if visit[j]:
            continue
        if judge(W, D, visit, j):
            return True
    
    return False


def main():
    W = [[] for _ in range(N)]
    for l, r, d in LRD:
        W[l - 1].append((r - 1, d))
        W[r - 1].append((l - 1, -d))
    
    D = [None] * N
    visit = [False] * N
    for i in range(N):
        if visit[i]:
            continue
        D[i] = 0
        if judge(W, D, visit, i):
            print("No")
            return
    
    print("Yes")


if __name__ == "__main__":
    main()