FUPRCO  Funny programming contest
Bob is trying to solve many problems.
Today he's trying to do his best at "Funny programming contest". In this contest there is N rounds.
Each round is starting in moment Ai and ends in moment Bi. Rounds can overlap on each other. For each round there is one problem to solve. He can't solve more than one problem at once.
Bob knows that problems are very difficult, so he assumed that he will do each round for more than half of time the round lasts.
He knows start and end time for each round.
Help him figuring out if he can spend as much time as he want for each round.
Input
First line contains number N(1<=N<=2*10^5)
In next N lines there are three numbers, ai,bi,ci (0<=ai<bi<=10^9 , (biai)/2 < ci <= biai ), time when round i starts, time when round i end, and time which Bob wants to spend for round i.
Output
Print "YES" if Bob can spend as much time as he wants for each round, otherwise print "NO"
Example
Input:
2
1 5 3
1 2 1
Output:
YES
Input:
2
1 5 3
2 3 1
Output:
NO
hide comments
enigmus:
20161016 13:45:36
Watch for the boundaries of the input data, they hold the key to the solution! 

rahul_verma:
20151102 07:38:31
give me more test cases 
Added by:  Krzysztof Lewko 
Date:  20110604 
Time limit:  0.100s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  http://oboz.ilo.pl/ http://main.edu.pl/pl/archive/proserwy 