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;

const int MOD=1000000007;
typedef long long int ll;

int gcd(int a,int b)
{
	if (b==0) return a;
	return gcd(b,a%b);
}

template<class T,class K>
pair<T,K> mp(T a,K b)
{
	return make_pair(a,b);
}

ll mult(ll a,ll b)
{
	return (a*b)%MOD;
}

ll pot(ll n,ll k)
{
	if (k==0) return 1;
	ll a=pot(n,k/2);
	a=mult(a,a);
	if (k%2) return mult(a,n);
	else return a;
}

ll divide(ll a,ll b)
{
	return mult(a,pot(b,MOD-2));
}

ll sub(ll a,ll b)
{
	return (a-b+MOD)%MOD;
}

ll add(ll a,ll b)
{
	return (a+b)%MOD;
}

int n,x,y,t,a,b,w;

int main()
{
	std::ios_base::sync_with_stdio(false);
	cin>>n;
	for (int i=0;i<n;++i)
	{
		cin>>a>>b>>w;
		int k=abs(x-a)+abs(y-b);
		if (k>w-t)
		{
			cout<<"No"<<endl;
			return 0;
		}
		if ((k-(w-t))%2==1)
		{
			cout<<"No"<<endl;
			return 0;
		}
		t=w;
		x=a;
		y=b;
	}
	cout<<"Yes"<<endl;
}