How to get overlap count (in basepair) of two IRange objects?

Question

[Tori]

I have following two IRanges objects query and ref. I would like to get overlap in number of basepairs.

> ref
  chr start  end
1   1   120  190
2   1   910 1050
3   1  1100 1140
4   1  2550 2650
5   2    50  100
> query
  chr start  end
1   1   101  173
2   1   918 1000
3   1  1060 1115
4   1  2468 2508

I got only this far.

library(GenomicRanges)
query = structure(list(chr = c("1", "1", "1", "1"), 
    start = c(101L, 918L, 1060L, 2468L),
    end = c(173L, 1000L, 1115L, 2508L)
), .Names = c("chr", "start", "end"), 
row.names = c(1L, 2L, 3L, 4L), class = "data.frame")


ref = structure(list(chr = c("1", "1", "1", "1","2"), 
    start = c(120L, 910L, 1100L, 2550L, 50L),
    end = c(190L, 1050L, 1140L, 2650L, 100L)
), .Names = c("chr", "start", "end"), 
row.names = c(1L, 2L, 3L, 4L, 5L), class = "data.frame")


refIR <- IRanges(start= ref$start, end =ref$end, name=ref$chr)
testIR <- IRanges(start = query$start, end =query$end, name=query$chr)

result <- findOverlaps(refIR, testIR, type="any")

data.frame(refIR[queryHits(result),], testIR[subjectHits(result),])