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 <cmath>
#include <iostream>
#include <vector>
#include <queue>
#include <deque>
#include <map>
#include <set>
#include <stack>
#include <tuple>
#include <bitset>
#include <algorithm>
#include <functional>
#include <utility>
#include <iomanip>
#define int long long int
#define mod(x) ((x % MOD) + MOD) % MOD
#define rep(i,a,b) for(int i=(a);i<(b);++i)
#define rrep(i,a,b) for(int i=(b)-1;i>=(a);--i)

#define ALL(a) (a).begin(),(a).end()
#define SIZE(a) (int)((a).size())
#define EACH(i,c) for(typeof((c).begin()) i=(c).begin(); i!=(c).end(); ++i)
#define EXIST(s,e) ((s).find(e)!=(s).end())
#define SORT(c) sort((c).begin(),(c).end())

#define dump(x)  cerr << #x << " = " << (x) << endl;
#define debug(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl;

using namespace std;

typedef pair<int,int> P;
struct edge {
  int to, cost;
};

const int INF = 1e18;
const int MOD = 2;

template<typename T> ostream& operator<<(ostream& s, const vector<T>& v) {
  int len = v.size();
  for (int i = 0; i < len; ++i) {
    s << v[i]; if (i < len - 1) s << " ";
  }
  return s;
}


signed main()
{
  int N;
  cin >> N;
  vector<int> t(N+1);
  vector<int> x(N+1);
  vector<int> y(N+1);
  t[0] = 0; x[0] = 0; y[0] = 0;
  rep(i, 1, N+1) {
    cin >> t[i] >> x[i] >> y[i];
  }

  rep(i, 1, N+1) {
    int dist = x[i]-x[i-1] + y[i]-y[i-1];
    int time = t[i]-t[i-1];
    if (time < dist || (time - dist)%2 == 1) {
      cout << "No" << endl;
      return 0;
    }
  }

  cout << "Yes" << endl;

  return 0;
}