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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

long long n,m,c,x,y,a,b,t, hasil=0, tag, dist;
int arr[200001];
bool mulai[200001];
bool sel[200001];
bool valid = true;

int main() {
    cin >> m;
    a = 0;
    b = 0;
    for (int i = 1; i <= m; i++){
        cin >> t >> x >> y;
        t = t-hasil;
        dist = (abs(x-a) + abs(y-b));
        if ( (t-dist)% 2 == 0 && t >= dist){
            a = x;
            b = y;
            hasil = t;
        }
        else {
            valid = false;
            break;
        }
        
    }
    if(valid == true){
        cout << "Yes" << endl;
    }
    else cout << "No" <<  endl;
   
}