There are N items in a market (indexed from 1 to N) each having a particular cost. The danger value of each item is given by the following pseudo code:

           Danger(cost) {
              danger_val = 0
              for ( each i from 1 to cost) {
                   if( cost modulo i is 0  ) {
                       increase danger_val by 1
                   }
              }
              return danger_val
          }

You are given Q queries which contain a range of items.

You need to find the number of pairs of items that have the same danger value.

Input format

• First line of the input contains a single integer N
• Second line of the input contains N space-separated integers denoting the prices of the items.
  
• Third line of the input contains a single integer Q denoting the number of queries
  
• Each of the next Q lines contain two space-separated integers L and R denoting the range of the items.

Output format

For each query, print the number of pairs of items that have the same danger value.

Constraints

• $1 ≤ N,Q ≤ 10^{5}$
• $1 ≤ L ≤ R ≤ N$
• $1 ≤ cost\ of\ item ≤ 10^{6}$