407795: GYM102894 C Special Christmas Cake

The family of Diana, a nanotechnologist, is getting ready for Christmas. In order to surprise both of her best friends — Vova and Grisha — she decided to bake a pie, shaped like a $$$n$$$-sided regular polygon.

Suddenly, Diana recalled that Vova enjoys $$$a$$$-sided pies (not necessarily regular), and Grisha enjoys $$$b$$$-sided pies. Is it possible for her to split the pie with a single knife cut into two non-empty parts so that one has exactly $$$a$$$ sides, and the other has exactly $$$b$$$ sides?

The first line contains a single positive integer $$$n$$$ $$$(3 \le n \le 10^9)$$$ — the number of sides in the pie.

The second line contains a single positive integer $$$a$$$ $$$(3 \le a \le 10^9)$$$ — the number of sides that appeals to Vova.

The third line contains a single positive integer $$$b$$$ $$$(3 \le b \le 10^9)$$$ — the number of sides that appeals to Grisha.

Output YES if Diana can split the pie so that both guests will enjoy it, and NO otherwise.

4
3
3

YES

4
4
4

YES

Diana can cut a square pie into two triangular parts by splitting it along the diagonal. The resulting parts won't be regular polygons — in fact, they will be right triangles — but this is not important, according to the statement.

Also, she can cut a square pie into two rectangular ones, splitting it parallel to two of its sides.