Given an infinite array of integers 2,3,.... Now do some operations on it.
The operation is to choose a minimum number from the array which is never been chosen, then change the status of its multiples excluding itself, i.e remove the multiples of the chosen number if they are in the array , otherwise add it to the array.keep the order after change.
For instance, the first step, choose number 2, change the status of 4, 6, 8, 10... They are all removed from the array. The second step, choose 3, change the status of 6, 9, 12, 15...
Pay attention: 9 and 15 are removed from the array while 6 and 12 are added to the array.
Every line contains an integer n. The zero value for n indicates the end of input.
Print "yes" or "no" according whether n is in the array.
The number n never has a prime factor greater than 13000000, but n may be extremely large.