Let $f(x)$ be the number of positive divisors of an integer $x$.
You are given $q$ queries, each of the form $(l, r)$. Calculate: $$f(l) + f(l + 1) + ... + f(r)$$
### Input
- The first line contains an integer $q$.
- The next $q$ lines, each line contains 2 integers $l, r$, a query.
### Output
- Print $q$ lines, the answers to $q$ queries.
### Constraints
- $1 \le q \le 10^5$.
- $1 \le l, r \le 10^6$.
### Example
Input:
```
1
1 4
```
Output:
```
8
```
