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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
#define rep(i,n) for(int i=0; i<(n); ++i)
#define rep2(i,n) for(int i=1; i<=(n); ++i)
using namespace std;
using ll = long long;
using P = pair<int,int>;

int main()
{
  int n; cin >> n;
  vector<int> t(n+10,0);
  vector<P> xy(n+10,make_pair(0,0));
  rep2(i,n){
    int a,b;
    cin >> t[i] >> a >> b;
    xy[i] = make_pair(a,b);
  }
  bool flg = true;
  rep2(i,n){
    int t1 = t[i] - t[i-1];
    int x1 = xy[i].first - xy[i-1].first;
    int y1 = xy[i].second - xy[i-1].second;
    if(t1 < x1+y1) flg = false;
    if((t1-x1-y1)%2!=0) flg = false;    
  }
  
  puts(flg?"Yes":"No");
  return 0;
}

/*
Ctrl+@
g++ a.cpp
./a.out
*/