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)

class Graph
  def initialize
    @vertices = {}
  end

  def connect( from, to, weight )
	  addVertex(from, to, weight)
	  addVertex(to, from, weight * -1)
  end

  def addVertex(from, to, weight)
	@vertices[from] = Vertex.new(from) unless @vertices[from]
	@vertices[to] = Vertex.new(to) unless @vertices[to]
	@vertices[from].connect(@vertices[to], weight)
  end
  attr :vertices
end

# 辺
class Edge
	def initialize(from, to, weight)
		@passed = false
		@from = from
		@to = to
		@weight = weight
	end
	def move
		@passed = true
	end
  attr_accessor  :from, :to, :weight, :passed
end

# 頂点
class Vertex
  def initialize( id )
    @id = id
    @edges = {}
  end
  def connect( to, weight )
	raise "vertex weight error" if @edges[to] && @edges[to] != weight
    @edges[to] = Edge.new(@id, to, weight)
  end

  def setPoint( point, fromId = nil )
	  # 自分の座標セットOR既にセットされている場合は優先
	  @point = point	  unless @point
      raise "point error id:%d before: %d  after:%d " % [@id,@point,point]  unless @point == point

	  # 繋がっている先の座標をセット
	  @edges.each{|vertex,edge|
		  if !edge.passed && edge.to.id != fromId
			  edge.passed = true
			  edge.to.setPoint( @point + edge.weight , @id )
		  end
	  }
  end

  attr :id, :edges, :point, :passed
end

n,m = gets.split.map(&:to_i)
graph = Graph.new

begin
m.times{
	l,r,d = gets.split.map(&:to_i)

	graph.connect(l, r, d)
}
# 各頂点にX軸上の位置を割り当てする
graph.vertices.each{|k,vertex|
	vertex.setPoint(vertex.point ? vertex.point : 0)
}

	puts "Yes"
rescue => e
#	puts e
	puts "No"
end