Fraud

You have been put in charge of the 24th National Olympiad in Informatics!

This year, the competition consisted of N contestants and 2 rounds. The ith contestant scored Ai points in the first round and Bi points in the second round.

Furthermore, the rounds have associated positive integer weightages X and Y respectively. The ith contestant’s final score Si is given by Si = Ai × X + Bi × Y.

As the chairman, you have been given the freedom to select the values of X and Y as you wish.

Alas, Squeaky the Mouse has bribed you into committing fraud. To be exact, he has promised to reward you handsomely if you select some X and Y such that Si > Sj for all 1 ≤ i < j ≤ N.

But is it even possible to do so?

Your program must read from standard input.

The first line contains a single integer N, the number of contestants.

The second line contains N space-separated integers, A1, . . . , AN.

The third line contains N space-separated integers, B1, . . . , BN.

Your program must print to standard output.

Output YES if it is possible to commit fraud and NO otherwise.

• 2 ≤ N ≤ 3 × 105
• 0 ≤ Ai, Bi ≤ 106