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>

#ifdef DEBUG
#define PRINT(x)\
    cout<<"func "<<__func__<<": line "<<__LINE__<<": "<<#x<<" = "<<(x)<<endl;
#define PRINTA(a,first,last)\
    cout<<"func "<<__func__<<": line "<<__LINE__<<": "<<#a<<"["<<(first)<<", "<<(last)<<")"<<endl;\
    for (int i=(first);i<(last);++i){cout<<#a<<"["<<i<<"] = "<<(a)[i]<<endl;}
#else
#define PRINT(x)
#define PRINTA(a,first,last)
#endif

#define FOR(i,a,b) for (int i=(a);i<(b);i++)
#define RFOR(i,a,b) for (int i=(b)-1;i>=(a);i--)
#define REP(i,n) for (int i=0;i<(n);i++)
#define RREP(i,n) for (int i=(n)-1;i>=0;i--)
#define pb push_back
#define mp make_pair
#define all(a) (a).begin(),(a).end()
#define MOD 1000000007

using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;

template <class T, class U> void amax(T& x, U y) {if (x < y) x = y;}
template <class T, class U> void amin(T& x, U y) {if (x > y) x = y;}

int main(void)
{
    int N;
    cin >> N;
    int posX = 0;
    int posY = 0;
    int bt = 0;
    while (N--) {
        int t, x, y;
        cin >> t >> x >> y;
        PRINT(t);
        PRINT(x);
        PRINT(y);
        int d = abs(x - posX) + abs(y - posY);
        PRINT(d);
        if (d <= (t - bt) && (t - bt - d) % 2 == 0) {
            // ok
        } else {
            cout << "No" << endl;
            return 0;
        }
        posX = x;
        posY = y;
        bt = t;
    }
    cout << "Yes" << endl;
    return 0;
}