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>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> PA;
typedef priority_queue<int, vector<int>, greater<int> > PQG;
#define REP(i, a, n) for(ll i = (ll) a;i < (ll) n;i++)
#define fi first
#define se second
#define pb push_back
#define INF 1000000009
#define MOD 1000000007
#define MAXN 100005
#define MAXC 100000000000014
#define MAXV 1000000009
 
int n, x[MAXN], y[MAXN], t[MAXN], rec;
 
int main()
{
    cin >> n;
    REP(i, 1, n + 1){
        cin >> t[i] >> x[i] >> y[i];
        if(x[i] == x[i - 1] && y[i] == y[i - 1]){
            if((t[i] - t[i - 1]) % 4 == 0){
                rec++;
            }
        }
        else if((t[i] - t[i - 1]) % (abs(x[i] - x[i - 1]) + abs(y[i] - y[i - 1])) == 0){
            rec++;
        }
    }
    if(rec < n){
        cout << "No" << endl;
        return 0;
    }
    cout << "Yes" << endl;
 
 
 
 
    return 0;
}