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: Longint;
    x0,y0,t0: Longint;
    offset: Longint;
    offset_xy: Longint;
    even, even_T: Boolean;
    flag: Boolean;
begin
    flag:=true;
    x0:=0;
    y0:=0;
    t0:=0;
    even:=true;
    readln(n);
    while n>0 do
    begin
       readln(t,x,y);
       if not flag then
       begin
           dec(n);
           continue;
       end;
       if (x=x0)and(y=y0) then
       begin
           flag:=false;
           dec(n);
           continue;
       end;
       offset:=t-t0;
       if offset mod 2 = 0 then 
       begin
           even_T:=true;
       end
       else 
       begin
           even_T:=false;
       end;
       offset_xy:=abs(x-x0)+abs(y-y0);
       if offset_xy>offset then
       begin
            flag:=false;
            dec(n);
            continue;
       end;
       if (offset_xy mod 2 = 0)=(even xor even_T)  then
       begin
            flag:=false;
            dec(n);
            continue;
       end;
       x0:=x;
       y0:=y;
       t0:=t;
       dec(n);
    end;
    
    if flag then 
    begin
        writeln('Yes');
    end
    else 
    begin
        writeln('No');
    end;
end.