It precomputes sums of all rows and columns in a 2d array for fast `O(1)` querying of sums of areas within it.
It does this:
```rust,ignore
let mut sum = 0;
for row in y1..y2 {
}
```
but faster:
```rust,ignore
// precompute
let s = SummedArea::new(input, width);
// now it's fast:
let sum = s.sum_range(x1..x2, y1..y2);
```