多校 GCD

Give you a sequence of  N(N≤100,000)  integers :  a1,...,an(0<ai≤1000,000,000) . There are  Q(Q≤100,000)  queries. For each query  l,r  you have to calculate  gcd(al,,al+1,...,ar)  and count the number of pairs (l′,r′)(1≤l<r≤N) such that  gcd(al′,al′+1,...,ar′)  equal  gcd(al,al+1,...,ar) .

Input

The first line of input contains a number  T , which stands for the number of test cases you need to solve.

The first line of each case contains a number  N , denoting the number of integers.

The second line contains  N  integers,  a1,...,an(0<ai≤1000,000,000) .

The third line contains a number  Q , denoting the number of queries.

For the next  Q  lines, i-th line contains two number , stand for the  li,ri , stand for the i-th queries.  

Output

For each case, you need to output “Case #:t” at the beginning.(with quotes,  t  means the number of the test case, begin from 1).

For each query, you need to output the two numbers in a line. The first number stands for  gcd(al,al+1,...,ar)  and the second number stands for the number of pairs (l′,r′)  such that  gcd(al′,al′+1,...,ar′)  equal  gcd(al,al+1,...,ar) .  

Sample Input

    
    
    
    

     
     
     
     1
5
1 2 4 6 7
4
1 5
2 4
3 4
4 4
    
    
    
    

 

Sample Output

    
    
    
    

     
     
     
     Case #1:
1 8
2 4
2 4
6 1
    
    
    
    
    
    
    
    


    
    
    
    

我们注意观察

gcd(a_{l},a_{l+1},...,a_{r})gcd(a​l​​,a​l+1​​,...,a​r​​) ，当l固定不动的时候， $r=l...n$ 时，我们可以容易的发现,随着 $r$ 的増大， gcd(a_{l},a_{l+1},...,a_{r})gcd(a​l​​,a​l+1​​,...,a​r​​) 是递减的，同时 gcd(a_{l},a_{l+1},...,a_{r})gcd(a​l​​,a​l+1​​,...,a​r​​) 最多 有 $log1000,000,000$ 个不同的值，为什么呢？因为 a_{l}a​l​​ 最多也就有 $log1000,000,000$ 个质因数

所以我们可以在log级别的时间处理出所有的以L开头的左区间的gcd(a_{l},a_{l+1},...,a_{r})gcd(a​l​​,a​l+1​​,...,a​r​​) 那么我们就可以在$nlog1000,000,000$的时间内预处理出所有的gcd(a_{l},a_{l+1},...,a_{r})gcd(a​l​​,a​l+1​​,...,a​r​​)然后我们可以用一个map来记录，gcd值为key的有多少个 然后我们就可以对于每个询问只需要查询对应gcd(a_{l},a_{l+1},...,a_{r})gcd(a​l​​,a​l+1​​,...,a​r​​)为多少，然后再在map 里面查找对应答案即可.

#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include