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 <bits/stdc++.h>
#define rep(i,a,b) for (int64_t i = (a); i < (b); i++)
#define REP(i,n) rep(i,0,n)
using namespace std;
typedef long long ll;
int dx[]={1,-1,0,0,1,-1,1,-1};
int dy[]={0,0,1,-1,1,-1,-1,1};

int main()
{
    int n,nowt=0,nowx=0,nowy=0;cin>>n;
    REP(i,n)
    {
        int x,y,t;cin>>t>>x>>y;
        int tt=abs(x+y-nowx-nowy);
        if((t-nowt)<tt){cout<<"No"<<endl;return 0;}
        if((t-nowt)%2!=tt%2){cout<<"No"<<endl;return 0;}
        nowt+=tt;nowx=x;nowy=y;
    }
    cout<<"Yes"<<endl;
}