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 x,y:array[1..100000]of longint;
    i,j,n,tmp,lastt,lastx,lasty:longint;
begin
  readln(n);
  for i:=1 to 100000 do
  begin
    x[i]:=10000000;
    y[i]:=10000000;
  end;
  for i:=1 to n do
  begin
    read(tmp);
    readln(x[tmp],y[tmp]);
  end;
  for i:=1 to 100000 do
  begin
    if x[i]=10000000 then continue;
    if abs(lastx-x[i])+abs(lasty-y[i])>i-lastt then
    begin
      writeln('No'); exit;
    end;
    if ((i-lastt)-(abs(lastx-x[i])+abs(lasty-y[i]))) mod 2<>0 then
    begin
      writeln('No'); exit;
    end;
    lastt:=i;
    lastx:=x[i];
    lasty:=y[i];
  end;
  writeln('Yes');
end.