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
 
def read():
  return int(input())
 
def reads():
  return [int(x) for x in input().split()]
 
setrecursionlimit(1000000)
INF = 10**10
 
(N, M) = reads()
 
edges = [[] for _ in range(N)]
 
for _ in range(M):
    (L, R, D) = reads()
    (L, R) = (L-1, R-1)
    edges[L].append((R, D))
    edges[R].append((L, -D))
 
visited = [False] * N
place = [None] * N
 
def walk(i):
    if visited[i]:
        return (place[i], place[i])
    visited[i] = True
    (m, M) = (INF, -INF)
    for (j, d) in edges[i]:
        if visited[j] and place[j] != place[i] + d:
            # print("v = ", visited)
            # print("p = ", place)
            print("No")
            exit()
        place[j] = place[i] + d
        (x, y) = walk(j)
        (m, M) = (min(m, x), max(M, y))
    return (m, M)
 
for i in range(N):
    if not visited[i]:
        place[i] = 0
        (m, M) = walk(i)
        if M - m > 10**9:
            # print("(m, M) = ", (m, M))
            print("No")
            exit()
 
print("Yes")