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,n) for(int i=0; i<(n); i++)
#define pb push_back
#define all(v) v.begin(),v.end()
#define fi first
#define se second
#define bigger (char)toupper
#define smaller (char)tolower
using namespace std;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<vi> vii;
typedef vector<string> vs;
typedef vector<char> vc;
typedef long long ll;
typedef unsigned long long ull;

int main() {
    int N;
    cin>>N;
    vii txy(N,vi(3));
    rep(i,N) {
        rep(j,3) {
            cin>>txy[i][j];
        }
    }
    bool ok=true;
    rep(i,N) {
        if((txy[i][1]+txy[i][2])%2!=txy[i][0]%2) ok=false;
    }
    int d=txy[0][1]+txy[0][2];
    if(d>txy[0][0]) ok=false;
    for(int i=1; i<N-1; i++) {
        int diff=abs(txy[i][0]-txy[i+1][0]);
        int a=abs(txy[i][1]-txy[i+1][1]);
        int b=abs(txy[i][2]-txy[i+1][2]);
        int distance=a+b;
        if(distance>diff) ok=false;
    }
    rep(i,N-1) {
        if(txy[i][2]==txy[i+1][2]&&txy[i][1]==txy[i+1][1]) ok=false;
    }
    if(ok) cout<<"Yes"<<endl;
    else cout<<"No"<<endl;
}