Petya and Divisors

Time Limit: 5 seconds

Memory Limit: 256 megabytes

Description

Little Petya loves looking for numbers' divisors. One day Petya came across the following problem:

You are given n queries in the form "xi yi". For each query Petya should count how many divisors of number xi divide none of the numbers xi - yi, xi - yi + 1, ..., xi - 1. Help him.

Input

The first line contains an integer n (1 ≤ n ≤ 105). Each of the following n lines contain two space-separated integers xi and yi (1 ≤ xi ≤ 105, 0 ≤ yi ≤ i - 1, where i is the query's ordinal number; the numeration starts with 1).

If yi = 0 for the query, then the answer to the query will be the number of divisors of the number xi. In this case you do not need to take the previous numbers x into consideration.

Output

For each query print the answer on a single line: the number of positive integers k such that

Sample Input

Input
6
4 0
3 1
5 2
6 2
18 4
10000 3
Output
3
1
1
2
2
22

Sample Output

None

Hint

Let's write out the divisors that give answers for the first 5 queries:

1) 1, 2, 4

2) 3

3) 5

4) 2, 6

5) 9, 18

Source

None

提交代码