As you remember, Zinium is a chessboard of size n × n cells. The cell in its bottom left corner has coordinates (1, 1), and the cell in its top right corner has coordinates (n, n). According to a legend, if n queens are placed on the board so that none of them attacks another, the released energy of Zinium will change the world beyond recognition. Rivers will turn back, the sky will fall onto the earth, people will learn to call things by their proper names…

Everybody had believed the legend about Zinium until Igor got hold of the artifact. He managed to place n queens as required but nothing happened (at least he didn't notice anything unusual). Then Igor conjectured that the chessboard in the legend was not usual but toric. A toric n × n chessboard is obtained from the usual chessboard of the same size by gluing together its upper and lower ranks as well as its leftmost and rightmost files. The figure shows the cells of a toric 8 × 8 chessboard attacked by a queen. Igor wants to check his conjecture by placing n queens on the toric board so that none of them attacks another. Help him to do this.

The only line contains the integer n (4 ≤ n ≤ 10⁵).

If the queens can be arranged as required, output “Yes” in the first line and n integers in the second line. The ith number must be the y coordinate of the queen whose x coordinate is i. If there are several possible arrangements, output any of them. If the queens can't be arranged as required, output “No” in the only line.