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
sys.setrecursionlimit(100000)
class P_UnionFind:
    def __init__(self, n):
        self.p=[i for i in range(n)]
        self.r=[0 for i in range(n)]
        self.d=[0 for i in range(n)]

    def root(self,x):
        if self.p[x]==x:
            return x
        else:
            tmp = self.root(self.p[x])
            self.d[x] += self.d[self.p[x]]
            self.p[x] = tmp
            return self.p[x]
    
    def weight(self,x):
        self.root(x)
        return self.d[x]

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

    def uni(self,x,y,w):
        if self.same(x,y) and self.diff(x,y)!=w:
            return False
        w+=self.weight(x)
        w-=self.weight(y)
        x=self.root(x)
        y=self.root(y)
        if(x==y):
            return
        if self.r[x]<self.r[y]:
            self.p[x]=y
            self.d[x]=-w
        else:
            self.p[y]=x
            self.d[y]=w
            if self.r[x]==self.r[y]:
                self.r[x]+=1
    
    def same(self,x,y):
        return self.root(x)==self.root(y)


n,m=map(int,input().split())
uf=P_UnionFind(n)
d=[-1 for i in range(n)]
d[0]=0
data=[]
for i in range(m):
    a,b,c=map(int,input().split())
    if uf.uni(a-1,b-1,c) == False:
        print('No')
        exit()
print('Yes')