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;

using ll = long long;
using ull = unsigned long long;
using st = string;
using db = double;
using vll = vector<long long>;
using vvll = vector<vll>;
using vst = vector<st>;
using vchar = vector<char>;
#define rep(i, m, n) for (int i = (int)(m); i < (int)(n); i++)
#define vrep(i, vec) for(auto& i : vec)
#define vin(vec) for(auto& i : vec) cin >> i
#define all(v) v.begin(), v.end()
ll mod = 1000000007;

bool travel(ll dt, ll dx, ll dy){
  if(dt >= dx + dy)if((dt - dx - dy) % 2 == 0) return true;
  return false;
}

int main(){
  ll n;
  cin >> n;
  vll t(n + 1), x(n + 1), y(n + 1);
  rep(i, 1, n + 1) cin >> t[i] >> x[i] >> y[i];
  t[0] = 0, x[0] = 0, y[0] = 0;
  bool ans = true;
  rep(i, 0, n){
    ll dt = t[i + 1] - t[i], dx = x[i + 1] - x[i], dy = y[i + 1] - y[i];
    if(!travel(dt, dx, dy)) ans = false;
  }
  cout << (ans ? "Yes" : "No") << endl;
}