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;
typedef long long ll;

#define REP(i, n) for (ll i = 0; i < n; i++)
#define FOR(i, m, n) for (ll i = m; i < n; i++)

int main(int argc, char const *argv[])
{
    ll n;
    cin >> n;
    vector<ll> t(n + 1, 0), x(n + 1, 0), y(n + 1, 0);
    FOR(i, 1, n + 1)
    cin >> t[i] >> x[i] >> y[i];
    bool res = true;
    REP(i, n)
    {
        ll dt = t[i + 1] + t[i];
        ll dx = abs(x[i + 1] - x[i]);
        ll dy = abs(y[i + 1] - y[i]);
        if (dt < dx + dy)
        {
            // 制限時間内に到達不可能
            res = false;
            break;
        }
        if (dt % 2 != (dx + dy) % 2)
        {
            // 余った時間で(x, y)と(x + 1, y)の間を往復不可
            res = false;
            break;
        }
    }
    cout << (res ? "Yes" : "No") << endl;
    return 0;
}