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:
n, m = map(int, input().split())
lrd = [list(map(int, input().split())) for _ in range(m)]


class WeightedUnionFind:
    def __init__(self, x):
        self.p = [e for e in range(x)]
        self.rank = [0] * x
        self.weight = [0] * x

    def same(self, u, v):
        return self.find_set(u) == self.find_set(v)

    def find_set(self, u):
        if u != self.p[u]:
            v = self.find_set(self.p[u])
            self.weight[u] += self.weight[self.p[u]]
            self.p[u] = v

        return self.p[u]

    def unite(self, u, v, w):
        w += self.weight[u]
        w -= self.weight[v]

        u = self.find_set(u)
        v = self.find_set(v)

        if self.rank[u] < self.rank[v]:
            u, v = v, u
            w = -w

        if self.rank[u] == self.rank[v]:
            self.rank[u] += 1

        self.p[v] = u

        self.weight[v] = w

    def get_weight(self, u):
        self.find_set(u)
        return self.weight[u]

    def diff(self, u, v):
        return self.get_weight(v) - self.get_weight(u)


wuf = WeightedUnionFind(n)

for l, r, d in lrd:
    l -= 1
    r -= 1

    if wuf.same(l, r):
        #print(l, r, d, wuf.diff(l, r), wuf.weight)
        if wuf.diff(l, r) != d:
            print("No")
            exit()

    else:
        wuf.unite(l, r, d)

print("Yes")