Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

3 3
1 2 1
2 3 1
1 3 2

Sample Output 1

Yes

Some possible sets of values (x_1, x_2, x_3) are (0, 1, 2) and (101, 102, 103).

Sample Input 2

3 3
1 2 1
2 3 1
1 3 5

Sample Output 2

No

If the first two pieces of information are correct, x_3 - x_1 = 2 holds, which is contradictory to the last piece of information.

Sample Input 3

4 3
2 1 1
2 3 5
3 4 2

Sample Output 3

Yes

Sample Input 4

10 3
8 7 100
7 9 100
9 8 100

Sample Output 4

No

Sample Input 5

100 0

Sample Output 5

Yes

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

N, M = gets.chomp.split.map(&:to_i)
flag = Array.new(N,0)
pair = []
M.times do
	line = gets.chomp.split.map(&:to_i)
	flag[line[1]-1] = nil
	if flag[line[0]-1]
		flag[line[0]-1] += 1
	end
	pair.push line
end
S = []
N.times do |n|
	if flag[n] && flag[n] >= 1
		S.push n+1
	end
end
node = []
history = Array.new(N)
success = 0
raise
while !(S.empty? && node.empty?) && success
	if node.empty?
		cur = [S.shift, 0]
	else
		cur = node.shift
	end
	pair.delete_if do |p|
		if p[0] == cur[0]
			if history[p[1]-1]
				if history[p[1]-1] != cur[1]+p[2]
					success = nil
					false
					break
				end
			end
			history[p[1]-1] = cur[1]+p[2]
			node.push [p[1], cur[1] + p[2]]
			true
		else
			false
		end
	end
end
if pair.empty? && success
	print "Yes\n"
else
	print "No\n"
end