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 <cassert>
#include <cstdio>
#include <cmath>
#include <iostream>
#include <sstream>
#include <string>
#include <vector>
#include <map>
#include <queue>
#include <algorithm>

#ifdef _DEBUG
#define DMP(x) cerr << #x << ": " << x << "\n"
#else
#define DMP(x) ((void)0)
#endif

const int MOD = 1000000007, INF = 1111111111; 
using namespace std;
using lint = long long;

int main() {

	cin.tie(nullptr);
	ios::sync_with_stdio(false);

	int N;
	cin >> N;

	struct deer { 
		int t, x, y; 
		deer(int t, int x, int y) :t(t), x(x), y(y) {}
		deer() :t(0), x(0), y(0) {}
	};

	vector<deer> plan(N+1);
	for (int i = 1; i <= N; i++) cin >> plan[i].t >> plan[i].x >> plan[i].y;

	int cost, time;
	bool flag = true;
	for (int i = 1; i <= N; i++) {

		cost = abs(plan[i].x - plan[i - 1].x) + abs(plan[i].y - plan[i - 1].y);
		time = plan[i].t - plan[i - 1].t;
		if (cost > time || ((cost ^ time) & 1)) flag = false;
	}

	if (flag) cout << "Yes" << "\n";
	else cout << "No" << "\n";

	return 0;
}