There are N numbers in an array. You will have Q queries. In each query, you can make 2 operations. These are:

1 X Y: This will print total number of prime numbers in the range X & Y (inclusive).

2 X a: This will update the value at index X with the value a. If previous value at index X is b, then it will now be updated as a.

All indexes are 1-based.

Input

In the first line take N (1 ≤ N ≤ 105) as input, then in the next line take N numbers as input in your array. The next line of input will take Q (1 ≤ Q ≤ 105). It indicates the total number of queries. Then next Q lines will contain the queries. The maximum value of prime number is 107.

Output

For each input, print the total number of primes in the range X and Y (inclusive).