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 the next N lines there are three numbers, ai, bi, ci (0 <= ai < bi <= 10^9, (bi-ai)/2 < ci <= bi-ai), time when round i starts, time when round i ends, 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

Added by:Krzysztof Lewko
Date:2011-06-04
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

hide comments
2016-10-16 13:45:36 enigmus
Watch for the boundaries of the input data, they hold the key to the solution!
2015-11-02 07:38:31 rahul_verma
give me more test cases
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