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>
#define M_PI           3.14159265358979323846  /* pi */
using namespace std;
using  ll = long long;

void walk(int t, int t0, int x0, int y0, int x, int y, bool& result) {
	if (t0 == t) {
		if (x0 == x && y0 == y) {
			result = true;
			return;
		}
		else {
			return;
		}
	}
	if (x0 < 0 || y0 < 0) {
		return;
	}

	t0++;
	walk(t, t0, x0 + 1, y0, x, y, result);
	walk(t, t0, x0 - 1, y0, x, y, result);
	walk(t, t0, x0, y0 + 1, x, y, result);
	walk(t, t0, x0, y0 - 1, x, y, result);
}

int main() {
	int n, x, y, t;
	int x0 = 0;
	int y0 = 0;
	int t0 = 0;
	bool result = false;

	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> t >> x >> y;

		walk(t, t0, x0, y0, x, y, result);
		x0 = x;
		y0 = y;
	}
	if (result == true) cout << "Yes" << endl;
	else cout << "No" << endl;
}