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())
par=[i for i in range(n)]
ws =[0 for _ in range(n)]

def root(x):
    if par[x]==x:
        return x
    else:
        r =root(par[x])
        ws[x] +=ws[par[x]]
        par[x]=r
        return par[x]

def weight(x):
    root(x)
    return ws[x]
def diff(x,y):
    return weight(x) -weight(y)

def merge(x,y,w):
    if root(x)==root(y):
        if diff(x,y)!=w:
            print('No')
            exit()
        else:
            return
    else:
        wy=weight(y)
        wx=weight(x)
        x=root(x)
        y=root(y)
        if w+wy>=wx:
            
            par[x]=y
            ws[x]=w+wy-wx
        else:
            par[y]=x
            ws[y]=wx-w-wy

for _ in range(m):
    x,y,z= map(int,input().split())
    x -=1
    y -=1
    merge(x,y,z)

print('Yes')