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

class WeightUnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n
        self.weight = [0] * n

    # xの根を求める
    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            px = self.find(self.parents[x])
            self.weight[x] += self.weight[self.parents[x]]
            self.parents[x] = px
            return px
    
    # xの根から距離
    def dist(self, x):
        self.find(x)
        return self.weight[x]

    # w[y] = w[x] + wとなるようにxとyを併合
    def unite(self, x, y, w):
        w += self.weight[x] - self.weight[y]
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return False
        else:
            # sizeの大きいほうがx
            if self.parents[x] > self.parents[y]:
                x, y = y, x
                w = -w
            self.parents[x] += self.parents[y]
            self.parents[y] = x
            self.weight[y] = w
            return True

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

    def size(self, x):
        return -self.parents[self.find(x)]

    def diff(self, x, y):
        return self.dist(y) - self.dist(x)


    


def main():
    N, M = map(int, input().split())
    uni = WeightUnionFind(N)
    for _ in range(M):
        L, R, D = map(int, input().split())
        L -= 1
        R -= 1
        if uni.same(L, R):
            if D != uni.diff(L, R):
                print('No')
                exit()
        else:
            uni.unite(L,R,D)

    print('Yes')
    


if __name__ == "__main__":
    main()