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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
  n,x,y,t,x1,y1,t1,i,s:longint;
begin
  readln(n);
  x:=0; y:=0;
  for i:= 1 to n do
    begin
      readln(t1,x1,y1);
      if (x=x1)and(y=y1)then begin writeln('No'); exit; end;
      if abs(x-x1)+abs(y-y1)=t1-t then begin x:=x1;y:=y1;t:=t1;end
                                  else
                                    begin
                                      if abs(x-x1)+abs(y-y1)<t1-t
                                        then
                                         begin
                                          s:=(t1-t)-(abs(x-x1)+abs(y-y1));
                                          if odd(s) then
                                                      begin
                                                        writeln('No');
                                                        exit;
                                                      end
                                                    else
                                                      begin
                                                        x:=x1;
                                                        y:=y1;
                                                        t:=t1;
                                                      end;
                                         end
                                        else
                                          begin
                                            writeln('No');
                                            exit;
                                          end

                                    end;
    end;
  writeln('Yes');
end.