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 Python (3.4.3) (judge verdict: Wrong Answer)

# -*- coding: utf-8 -*-
import math
from itertools import combinations_with_replacement


N = int(input())
items = {}
for n in list(range(N)):
  nth, a, b = map(int, input().split())
  items[n] = [nth, a, b]


def calcPosFromMoves(moves: list) -> list:
  points = {"x": 0, "y":0}
  for move in moves:
    points["x"] += move[0]
    points["y"] += move[1]
  return [points["x"], points["y"]]

def createMovePatterns(count: int) -> list:
  moves = [(1,0), (-1,0), (0,1), (0,-1)]
  return list(combinations_with_replacement(moves, count))
 
def observeTwoPoints(_observed: list, _expectation: list) -> bool:
  # print(observed,'?',expectation, '\n')
  result = [o == e for o, e in zip(_observed, _expectation)]
  return all(result)

def throwIfImpossible(item: list) -> bool:
  return False if item[0] < abs(item[1]) + abs(item[2]) else True
    
def readByOneLine(_items: dict) -> list:
  _judges = []
  append = _judges.append
  for _, item in _items.items():  # read one line at once
    if throwIfImpossible(item): break;
    patterns = createMovePatterns(item[0])
    expectation = [item[1], item[2]]
    for pattern in patterns:  # brute force
      observed = calcPosFromMoves(pattern) 
      if observeTwoPoints(observed, expectation): 
        append(True)
        break;
  return _judges

judges = readByOneLine(items)
print('{}'.format('Yes' if len(judges) == N and all(judges) else 'No' ))