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)

require 'pp'
# 添え字1から
x=Array.new(100001)
N,M=gets.chomp.split(' ').map{|n| n.to_i}

#xiをxj+dに置換
def refl(xi,xj,d,x)
	x.each{|el|
		if(el.nil?)
			continue
		end
		# 書き換えたい文字が同じ文字の場合（コンフリクト）
		if(el[0]==xj)
			if(el[1]!=d)
				return false
			end
		end
		if(el[0]==xi)
			el[0]=xj
			el[1]=el[1]+D
		end
	}
	return true
end

i=1
xi=1
while(i<=M)
	l,r,d = gets.chomp.split(' ').map{|n| n.to_i}
	xl = x[l]
	xr = x[r]
	if(xl.nil?&&xr.nil?)
		# puts '
		# x[L]=["x_#{xi}",0]
		# x[R]=["x_#{xi}",D]
		# '
		x[l]=["x_#{xi}",0]
		x[r]=["x_#{xi}",d]
		xi+=1
	elsif(xr.nil?)
		x[r]=[xl[0],xl[1]+d]
	elsif(xl.nil?)
		x[l]=[xr[0],xr[1]-d]
	else
		#reflection
		if(xr[0]==xl[0])
			if(xr[1]!=xl[1]+d)
				puts "No"
				return
			end
		else
			#xr[0]をxl[0]+Dに置換
			flg = relf(xr[0],xl[0],d,x)
			if(!flg)
				puts "No"
				return
			end
		end
	end
	i+=1
end
puts "Yes"

# i=1
# while(i<=M)
# 	if(!x[i].nil?)
# 		puts "i : #{x[i][0]},#{x[i][1]}"
# 	end
# 	i+=1
# end