How do I get a histogram-like summary of interval data in R?

My MWE data has four intervals.

```
interval range
Int1 2-7
Int2 10-14
Int3 12-18
Int4 25-28
```

I want a histogram-like function which counts how the intervals Int1-Int4 span a range split across fixed-size bins. The function output should look like this:

```
bin count which
[0-4] 1 Int1
[5-9] 1 Int1
[10-14] 2 Int2 and Int3
[15-19] 1 Int3
[20-24] 0 None
[25-29] 1 Int4
```

Here the range is [minfloor(Int1, Int2, Int3, Int40), maxceil(Int1, Int2, Int3, Int4)) = [0,30) and there are six bins of size = 5.

I would greatly appreciate any pointers to R packages or functions that implement the functionality I want.

**Update:**

So far, I have a solution from the IRanges package which uses a fast data structure called NCList, which is faster than Interval Search Trees according to users.

```
> library(IRanges)
> subject <- IRanges(c(2,10,12,25), c(7,14,18,28))
> query <- IRanges(c(0,5,10,15,20,25), c(4,9,14,19,24,29))
> countOverlaps(query, subject)
[1] 1 1 2 1 0 1
```

But I am still unable to get which are the ranges that overlap. Will update if I get through.