You are given a sequence of integers A1,A2,…,AN. You may change any number of its elements (possibly zero), obtaining a new sequence of positive integers B1,B2,…,BN. Each element of B must be an integer between 2 and 50 (both inclusive).
Let's define an undirected graph G with N vertices (numbered 1 through N). For each pair of different vertices i and j, there is an edge between i and j if and only if Bi and Bj are coprime.
You should choose the sequence B in such a way that G is a connected graph. The number of elements which need to be changed to obtain B from A should be minimum possible. Find one such sequence B and the minimum required number of changes.
It can be proven that a solution always exists — it is always possible to modify sequence A in such a way that G is connected.
Example 1: There is an edge in G between vertices 1 and 2. This graph is connected, so there is no need to change any elements.
Example 2: There is no edge between vertices 1 and 2 since gcd(2,4)≠1. This graph is not connected. We can change element A2=4 to 3 and make this graph connected.