Spiral Permutation Sequence We can roll up the natural numbers in a rectangular spiral:

 17--16--15--14--13
  |               |
 18   5---4---3  12
  |   |       |   |
 19   6   1---2  11
  |   |           |
 20   7---8---9--10
  |
 21--22--23--24--25


But now that we have them on a rectangular grid we can unwind the spiral in a different order, e.g. going clockwise, starting north:

 17  16--15--14--13
  |   |           |
 18   5   4---3  12
  |   |   |   |   |
 19   6   1   2  11
  |   |       |   |
 20   7---8---9  10
  |               |
 21--22--23--24--25


The resulting sequence is clearly a permutation of the natural numbers:

1, 4, 3, 2, 9, 8, 7, 6, 5, 16, 15, 14, 13, 12, 11, 10, 25, 24, 23, 22, 21, 20, 19, 18, 17, ...


Your task is to compute this sequence. (OEIS A020703, but spoiler warning: it contains another interesting definition and several formulae that you might want to figure out yourself.)

Fun fact: all 8 possible unwinding orders have their own OEIS entry.

The Challenge

Given a positive integer n, return the nth element of the above sequence.

You may write a program or function, taking input via STDIN (or closest alternative), command-line argument or function argument and outputting the result via STDOUT (or closest alternative), function return value or function (out) parameter.

Standard code-golf rules apply.

Test Cases

1       1
2       4
3       3
4       2
5       9
6       8
7       7
8       6
9       5
100     82
111     111
633     669
1000    986
5000    4942
9802    10000
10000   9802


For a complete list up to and including n = 11131 see the b-file on OEIS.
Japt, 20 19 16 bytes
V=U¬c)²-V *2-U+2

Test it online!
Based on the observation that

 F(N) = ceil(N^.5) * (ceil(N^.5)-1) - N + 2

Or, rather, that

 F(N) = the first square greater than or equal to N, minus its square root, minus N, plus 2.

I don't know if this explanation is on the OEIS page, as I haven't looked at it yet.