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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <algorithm>
#include <stdio.h>
#include <math.h>
using namespace std;

bool judge(long long x,long long y,long long t){
    if(abs(x)+abs(y)<=t){
        if(abs(x)+abs(y)==t)return true;
        else if((t-(abs(x)+abs(y)))%2==0)return true;
        else return false;
    }
    return false;
}

int main(){
    int N;
    while (scanf("%d",&N)==1&&N) {
        bool jud=true;
        long long t=0,x=0,y=0;
        long long t1,x1,y1;
        for(int i=0;i<N;i++){
            scanf("%lld%lld%lld",&t1,&x1,&y1);
            t=t1-t;x=x1-x;y=y1-y;
            if(!judge(x, y, t)){jud=false;break;}
        }
        if(jud)printf("Yes\n");
        else printf("No\n");
    }
    return 0;
}