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 <bits/stdc++.h>

using namespace std;

#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define INF (1LL << 55)
#define MOD (1000 * 1000 * 1000 + 7)
#define maxn 200111

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;

int x[maxn], y[maxn], t[maxn];

int dist(int a, int b){
	return abs(x[a] - x[b]) + abs(y[a] - y[b]);
}

int main(){
	int n;
	bool ok = 1;
	scanf("%d", &n);

	x[0] = 0; y[0] = 0; t[0] = 0;
	for(int i = 1; i <= n; i++){
		scanf("%d%d%d", t + i, x + i, y + i);
	}

	for(int i = 0; i < n; i++){
		int d = dist(i, i + 1);
		int cas = t[i + 1] - t[i];
		cas = cas - d;
		if(d >= 0 && d % 2 == 0)
			ok = 0;
	}

	if(ok)
		printf("YES\n");
	else
		printf("NO\n");

	return 0;
}