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:
from sys import exit, setrecursionlimit
from functools import reduce
from itertools import *
from collections import defaultdict
from bisect import bisect
setrecursionlimit(1000000)


N,M = list(map(int,input().split()))

edges = [[] for _ in range(N)]

for i in range(M):
    L,R,D = list(map(int,input().split()))
    edges[L - 1].append((R -1,D))
    edges[R - 1].append((L-1, -D))


visited = [None] * N
place = [0] * N
inf = 10 ** 10


def walk(i):
    if visited[i]:
        return (i,i)
    visited[i] = True
    (n,m) = (inf, - inf)
    for j,d in edges[i]:
        #print(j,d)
        if visited[j] and place[j] != place[i] + d:
            print("No")
            exit()
        place[j] = place[i] + d
        (x,y) = walk(j)
        (n,m) = (min(n,x),max(m,y))
    return (n,m)

for i in range(N):
    if not visited[i]:
        place[i] = 0
    # 連結成分のminとmax
        (n,m) = walk(i)
        if m - n > 10 ** 9:
            print("No")
            exit()
print("Yes")