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:
import sys
input = sys.stdin.readline
def main():
    def find(x):
        if par[x] < 0:
            return x
        else:
            px = find(par[x])
            wei[x] += wei[par[x]]
            par[x] = px
            return px

    def weight(x):
        find(x)
        return wei[x]

    def unite(x, y, w):
        w += wei[x] - wei[y]
        x = find(x)
        y = find(y)
        if x == y:
            return False
        else:
            # sizeの大きいほうがx
            if par[x] > par[y]:
                x, y = y, x
                w = -w
            par[x] += par[y]
            par[y] = x
            wei[y] = w
            return True

    def same(x, y):
        return find(x) == find(y)

    def size(x):
        return -par[find(x)]

    def diff(x, y):
        return weight(y) - weight(x)

    n, m = map(int, input().split())
    # 初期化
    par = [-1] * n
    wei = [0] * n
    for _ in range(m):
        l, r, d = map(int, input().split())
        l -= 1
        r -= 1
        if same(l, r):
            if diff(l, r) != d:
                print('No')
                sys.exit()
        else:
            unite(l, r, d)
    print('Yes')
    
if __name__ == '__main__':
    main()