A mastering engineer is prepping the channel strip for a live remix session. The mixing console reports 2n channel gain settings, in decibels; a gain reading may be negative, representing attenuation rather than boost. Before printing the patch sheet, the engineer wants to wire every channel into a boost pair: two channels where one channel's gain is exactly double the other's, so that riding the base channel's fader predicts exactly how its boosted partner should move. Every one of the 2n channels must end up in exactly one pair, using each reported gain value exactly once (a gain value may repeat if several channels happen to share it). Determine whether the full set of channels can be organized into n such boost pairs.

Input format

• Line 1: a single integer n — the number of boost pairs to form.
• Line 2: 2n space-separated integers, the channel gain settings.

Output format

Print YES if the 2n channels can be fully organized into n boost pairs (each pair consisting of a base gain g and a boost gain exactly 2g), and NO otherwise.

Constraints

• 1 <= n <= 15000
• -100000 <= gain <= 100000
• The second line contains exactly 2n integers.

2
6 -3 -6 3

YES

2
7 2 7 5

NO