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: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
typedef pair<LL,LL> P;
const LL mod=1000000007;

int main(){
    int N;
    cin >> N;
    int t[N+1],x[N+1],y[N+1];
    t[0]=0;
    x[0]=0;
    y[0]=0;
    for(int i=1;i<=N;i++){
        cin >> t[i] >> x[i] >> y[i];
    }
    for(int i=0;i<N;i++){
        int check,T;
        check=abs(x[i+1]-x[i])+abs(y[i+1]-y[i]);
        T=t[i+1]-t[i];
        if(check>T){
            puts("No");
            return 0;
        }
        else if((T-check)%2==1){
            puts("No");
            return 0;
        }
    }
    puts("Yes");
    return 0;
}