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<cstdlib>
#include<vector>
using namespace std;

int main()
{
	long n;
	vector<long int> t(100002), x(100002), y(100002);

	cin >> n;

	for (int i = 1; i <= n; i++)
	{
		cin >> t[i] >> x[i] >> y[i];
	}

	x[0] = 0;
	y[0] = 0;
	t[0] = 0;

	for (int i = 1; i <= n; i++)
	{
		if (abs(x[i] - x[i - 1]) + abs(y[i] - y[i - 1]) <= (t[i] - t[i - 1]))
		{
			if ((abs(x[i] - x[i - 1]) + abs(y[i] - y[i - 1]) % 2 == 1) && (t[i] - t[i - 1]) % 2 == 1 || ((abs(x[i] - x[i - 1]) + abs(y[i] - y[i - 1]) % 2 == 0) && (t[i] - t[i - 1]) % 2 == 0));
			else break;
		}
		else break;

		if (i == n)
		{
			cout << "Yes" << endl;
			return 0;
		}
	}
	cout << "No" << endl;
}