A ceramics workshop stamps every unfired tile with a numeric mold ID before it goes into a kiln. The workshop owns exactly two kilns, and every firing session loads both kilns at once with the same number of tiles. To keep the mold stamps legible after firing, a kiln must never hold two tiles that share the same stamp number in the same session — duplicate stamps warp against each other under heat. Today's batch contains an even number of tiles. Determine whether the batch can be divided into two equal-sized groups, one per kiln, such that no group contains a repeated stamp number.

Input format

• Line 1: a single even integer n (2 ≤ n ≤ 100), the number of tiles in the batch.
• Line 2: n space-separated integers stamp_1 ... stamp_n (1 ≤ stamp_i ≤ 100), the mold stamp number on each tile.

Output format

Print true if the batch can be split into two equal-sized groups with no repeated stamp number inside either group, otherwise print false.

Constraints

• 2 ≤ n ≤ 100, and n is always even.
• 1 ≤ stamp_i ≤ 100 for every tile.

6
1 1 2 2 3 4

true

4
1 1 1 1

false