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:
class UnionFind():
    def __init__(self,n):
        self.n=n
        self.parents = [i for i in range(n+1)]
        self.dist = [0]*(n+1)
    def find(self,x):
        if self.parents[x]==x:
            return x
        else:
            p = self.parents[x]
            self.parents[x]=self.find(self.parents[x])
            self.dist[x] += self.dist[p]
            return self.parents[x]
    def unite(self,x,y,d):
        xRoot = self.find(x)
        yRoot = self.find(y)
        if xRoot == yRoot:
            if self.dist[x]-self.dist[y] != d:
                print("No")
                exit()
        else:
            diff = self.dist[y]+d-self.dist[x]
            if diff>=0:
                self.parents[xRoot] = yRoot
                self.dist[xRoot] += diff
                self.find(x)
            else:
                self.parents[yRoot] = xRoot
                self.dist[yRoot] += abs(diff)
                self.find(y)
N,M = map(int,input().split())
tree = UnionFind(N)
for _ in range(M):
    L,R,D = map(int,input().split())
    tree.unite(L,R,D)
print("Yes")