Background

When the two elves were grinding the old-age room, they found that it was not easy. They had to make many prime number judgments. Please help them finish grinding the old-age room quickly.

两个小精灵在磨养老房的时候，发现并不是很容易，要进行多次的质数判断，请你帮他们竟快磨完养老房

Description

There are 2~n integers. within this range, if it is a prime number, yes is output, and if it is a non-prime number, no (one row in total) is output. next, the number of prime numbers (a) and the number of non-prime numbers (b) between these 2~n are counted and not output. Then one operation is carried out to judge whether b*a is a prime number, if so, the values of yes and b*a are output, if not, the penultimate digits of no and b*a are output.

有2~n个整数，在这个范围内，是质数则输出yes，是非质数则输出no（共占一行），接下来统计这2~n之间质数的个数（a）和非质数的个数（b），不输出。然后一次操作，判断b*a是否为质数，是质数则输出yes和b*a的值，如果不是则输出no和b*a的倒数第二位数字。

Input

A total of one line, an integer n, representing 2~n integers.

共一行，一个整数n，表示2~n个整数。

Output

In the first row, n-1 combinations of yes and no, the first value in the second row is yes or no, and the second number is the penultimate digit of b*a or b * a.

第一行n-1个yes和no的组合，第二行第一个值为yes或者no，第二个数为b*a或b*a倒数第二位的数字。

Sample 1

Input

5

Output

yes yes no yes
yes 3

Sample 2

Input

6

Output

yes yes no yes no
no 0

Limitation

对于10%的数据n<=100;
对于40%的数据100<n<=1000;
对于50%的数据1000<n<10000;

Source

Amorphophallus Orz Group