Fraud

Time limit1sMemory limit1024 MB

Summary

Decide whether positive integers X and Y exist so that the weighted score Ai*X + Bi*Y strictly decreases along the given contestant order.

Level: Medium7 of 10
Topics: Geometry, Sorting, Greedy, Math
Solved: No attempts yet

Problem

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?

Input

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.

Output

Your program must print to standard output.

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

Constraints

2 ≤ N ≤ 3 × 105
0 ≤ Ai, Bi ≤ 106

Examples3

Example 1
Input
```
2
1 2
2 1
```
Expected output
```
YES
```
Example 2
Input
```
3
2 4 3
4 2 3
```
Expected output
```
NO
```
Example 3
Input
```
2
5 1
0 0
```
Expected output
```
YES
```