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)

using namespace std;
#include<bits/stdc++.h>
#define BEGIN ios_base::sync_with_stdio(0);cin.tie(0)
#define END return EXIT_SUCCESS
#define FOR(I,A,B) for((I)=(A);(I)<(B);(I)++)
#define REP(I,N) FOR(I,0,N)
#define UP(I,A,B) for((I)=(A);(I)<=(B);(I)++)
#define DW(I,A,B) for((I)=(A);(I)>=(B);(I)--)
#define IN(P) cin>>(P)
#define IN2(P1,P2) cin>>(P1)>>(P2)
#define IN3(P1,P2,P3) cin>>(P1)>>(P2)>>(P3)
#define INS(I,N,V) REP(I,N) cin>>V[I]
#define INS2(I,N,V1,V2) REP(I,N) cin>>V1[I]>>V2[I];
#define INS3(I,N,V1,V2,V3) REP(I,N) cin>>V1[I]>>V2[I]>>V3[I];
#define OUT(P) cout<<P<<endl
#define OUT2(P1,P2) cout<<P1<<" "<<P2<<endl
#define OUT3(P1,P2,P3) cout<<P1<<" "<<P2<<" "<<P3<<endl
#define OUTS(I,N,V) REP(I,N) cout<<V[i]<<endl
#define ALL(C) (C).begin(),(C).end()
#define RALL(C) (C).rbegin(),(C).rend()
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
typedef unsigned long ul;
const ul INF=1LL<<60;
const ul NN=1e5;
long N,t[NN],x[NN],y[NN],i,T,D;
inline void solve(){
  IN(N);
  INS3(i,N,t,x,y);
  if(t[0]<x[0]+y[0]){
    OUT("No");
    return;
  }
  FOR(i,1,N){
    T=t[i]-t[i-1];
    D=abs(x[i]-x[i-1])+abs(y[i]-y[i-1]);
    if(T<D){
      OUT("No");
      return;
    }
    if((T-D)%2){
      OUT("No");
      return;
    }
    if(x[i]==x[i-1]&&y[i]==y[i-1]){
      OUT("No");
      return;
    }
  }
  OUT("Yes");
}

int main(int argc,char**argv){
  BEGIN;
  solve();
  END;
}