Problem:
Score : 300 points

Problem Statement

AtCoDeer the deer is going on a trip in a two-dimensional plane.
In his plan, he will depart from point (0, 0) at time 0, then for each i between 1 and N (inclusive), he will visit point (x_i,y_i) at time t_i.

If AtCoDeer is at point (x, y) at time t, he can be at one of the following points at time t+1: (x+1,y), (x-1,y), (x,y+1) and (x,y-1).
Note that he cannot stay at his place.
Determine whether he can carry out his plan.

Constraints

1 ≤ N ≤ 10^5

0 ≤ x_i ≤ 10^5

0 ≤ y_i ≤ 10^5

1 ≤ t_i ≤ 10^5

t_i < t_{i+1} (1 ≤ i ≤ N-1)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
t_1 x_1 y_1
t_2 x_2 y_2
:
t_N x_N y_N

Output

If AtCoDeer can carry out his plan, print Yes; if he cannot, print No.

Sample Input 1

2
3 1 2
6 1 1

Sample Output 1

Yes

For example, he can travel as follows: (0,0), (0,1), (1,1), (1,2), (1,1), (1,0), then (1,1).

Sample Input 2

1
2 100 100

Sample Output 2

No

It is impossible to be at (100,100) two seconds after being at (0,0).

Sample Input 3

2
5 1 1
100 1 1

Sample Output 3

No

Solution in Ruby (2.7.1) (judge verdict: Accepted)

# ans=true
# start_p=[0,0,0]

# n=gets.strip.to_i
# ps=[]
# (1..n).each do 
#     ps.push(gets.strip)
# end

# (0..n-1).each do |i|
#     t,x_end,y_end=ps[i].split.map(&:to_i)
#     t_diff=t-start_p[0]
#     puts "t_diff:#{t_diff}"
#     (0..t_diff).each do |x|
#         x_current=start_p[1]+x
#         y_current=start_p[2]+(t_diff-x)
#         if x_current==x_end&&y_current==y_end
#             ans=true
#             start_p[0]=t
#             start_p[1]=x_end
#             start_p[2]=y_end
#             puts "true:#{i+1}回目:x:#{x_current}y:#{y_current}"
#             break
#         else
#             ans=false
#             puts "false:#{i+1}回目:x:#{x_current}y:#{y_current}"
#         end
#     end
#     break if !ans
# end

# puts ans ? 'Yes' : 'No'

def is_reachable(current,next_data)
    tc,xc,yc=current
    tn,xn,yn=next_data

    dist=(xn-xc).abs+(yn-yc).abs
    
    return false if dist>tn-tc

    (dist-(tn-tc)).even?
end

n=gets.strip.to_i
data=n.times.map {gets.strip.split.map(&:to_i)}
current=[0,0,0]

data.each do |d|
    unless is_reachable(current,d)
        puts "No"
        exit 0
    end
    current=d
end

puts "Yes"