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binary search

data structures

number theory

*1900

No tag edit access

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B. Petya and Divisors

time limit per test

5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

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

You are given *n* queries in the form "*x*_{i} *y*_{i}". For each query Petya should count how many divisors of number *x*_{i} divide none of the numbers *x*_{i - yi}, *x*_{i - yi + 1}, ..., *x*_{i - 1}. Help him.

Input

The first line contains an integer *n* (1 ≤ *n* ≤ 10^{5}). Each of the following *n* lines contain two space-separated integers *x*_{i} and *y*_{i} (1 ≤ *x*_{i} ≤ 10^{5}, 0 ≤ *y*_{i} ≤ *i* - 1, where *i* is the query's ordinal number; the numeration starts with 1).

If *y*_{i} = 0 for the query, then the answer to the query will be the number of divisors of the number *x*_{i}. 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

Examples

Input

6

4 0

3 1

5 2

6 2

18 4

10000 3

Output

3

1

1

2

2

22

Note

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

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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