400785: GYM100247 G City Square

Mayor of one big city Sergey decided to pave the infinitely large central square of the city by the multicolored tiles. All tiles are squares of the same size. They should be placed next to each other, making the square grid. He has managed to get an infinite amount of tiles of n different colors at a reasonable price, and he wants to use all colors.

Sergey decided to create the paving design by himself. He is a perfectionist, so he wants the pattern to satisfy two conditions.

• For every two colors it should be possible to transmute the set of tiles of the first color to the set of tiles of the second color using only translation.
• For every color on the plane such Cartesian coordinate system should exist so that the set of centers of all tiles of this color is the same as the set of integer points in this system.

Now Sergey is lost in thought, if such a design can be realized at all.

The only line contains the only integer n (1 ≤ n ≤ 10⁹) — the number of colors of tiles.

Output «Yes» (without quotes), if Sergey is able to realize his idea, and «No» (without quotes), otherwise.

3

No

4

Yes

5

Yes

The following picture shows one of the ways to pave a plane with tiles of 5 colors.