Little Santa loves to play games on the Christmas Eve. He has invited N nice children from all over the world. Each child has a unique number from 1 to N. Among these N children, he will select only those children who have a divisor of N (including 1 and N).

Now he asked all the selected children to stand in a circle. Little Santa wants to have each pair of adjacent children to be a Good Pair. A Good Pair $(a, b)$ is a pair in which either a divides b or b divides a.

All the children got confused and asked your help to place them.

Note: $N = p_1^{a_1} * p_2^{a_2} * ... * p_k^{a_k}$ where $p_1, p_2, ... , p_k$ are the prime factors of N.

Input format:
First line contains an integer, k $(1 \le k \le 15)$, number of prime factors of N $(2 \le N \le 10^{18})$. Next k lines contains two space separated integers each, $p_i$ and $a_i$.

All $p_i$ are pairwise distinct primes, $a_i$ are positive integers.

Output format:
Print T space separated integers denoting the placement of children on the circle. T is the number of divisors of N. Print No if there is no solution.