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;
#define double long double
#define rep(i,n) for(int i=0;i<(int)n;i++)
#define sp(p) cout<<setprecision(16)<<fixed<<p<<endl;
#define debug(x) cerr<<#x<<": "<<x<<endl;
#define all(a) a.begin(),a.end()
#define SORT(a) sort(all(a))
#define rsort(a) sort(all(a),greater<>())
#define judge(f,y,n) cout<<(f?y:n)<<"\n";
#define debg(a) cout<<#a<<" "<<a<<endl;
#define show(a) for(cont &y:a){for(cont &x:y){cout<<x<<" ";}cout<<endl;}
template<class T>inline int out(const T &t){ print(t); putchar('\n'); return 0; }
template<class T>inline T gcd(T a,T b){if(b==0)return a; return(gcd(b,a%b));}
template<class T>inline T lcm(T a,T b){return a/gcd(a,b)*b;}
typedef long long ll;
typedef pair<ll,ll> P;
typedef vector<ll> V;
const long long MOD=1000000007;
const long long INF = 1e18;
clock_t time_ini = clock();
double time_diff(){
  ll time_tmp = clock();
  const double time = static_cast<double>(time_tmp - time_ini) / CLOCKS_PER_SEC * 1000.0;
  return time;
}
#define saiaku if(time_diff() > 1990)
vector <ll> dp;

const string YES = "Yes";
const string NO = "No";

void solve_old(long long N, std::vector<long long> t, std::vector<long long> x, std::vector<long long> y){
    bool flg = false;
    for (ll i = 0; i < N; i++) {
        ll dt = (i ? t[i] - t[i-1] : t[i]);
        ll d = (i ? abs(x[i] - x[i-1]) + abs(y[i] - y[i-1]) : abs(x[i]) + abs(y[i]));
        if (d <= dt && ((dt%2) == (d%2)) ) {
            flg = true;
        } else {
            flg = false;
            break;
        }
    }
    cout << (flg ? YES : NO) << "\n";
}

void solve(long long N, std::vector<long long> t, std::vector<long long> x, std::vector<long long> y){
    bool flg = true;
    for (ll i = 0; i < N; i++) {
        ll dt = (i ? t[i] - t[i-1] : t[i]);
        ll d = (i ? abs(x[i] - x[i-1]) + abs(y[i] - y[i-1]) : abs(x[i]) + abs(y[i]));
        if (!(d <= dt && ((dt%2) == (d%2))) ) {
            flg = false;
            break;
        }
    }
    judge(flg, YES, NO);
}

int main(){
    long long N;
    scanf("%lld",&N);
    std::vector<long long> t(N);
    std::vector<long long> x(N);
    std::vector<long long> y(N);
    for(int i = 0 ; i < N ; i++){
        scanf("%lld",&t[i]);
        scanf("%lld",&x[i]);
        scanf("%lld",&y[i]);
    }
    solve(N, std::move(t), std::move(x), std::move(y));
    return 0;
}