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 <iostream>
#include <algorithm>
#include <climits>
#include <vector>
#include <stack>
#include <cmath>
#include <queue>
#include <set>
#include <map>
using namespace std;

int main() {
    int N;
    cin >> N;
    int px, py,pt;
    px = py = pt = 0;
    bool flag = true;
    for (int i = 0; i < N; ++i) {
        int t, x,y;
        cin >> t >> x >> y;
        int d = abs(px-x) + abs(py-y);
        if(d > t - pt || (t - pt - d) % 2  == 1) {
            flag = false;
        }
        pt = t;
        px = x; py = y;
    }
    if(flag) {
        cout << "Yes";
    } else {
        cout << "No";
    }
    cout << endl;

    return 0;
}