fun max lst = 
	foldl (fn (e, max) => Int.max(e, max)) (hd lst) (tl lst)
 
fun count_gaps lst=
	case lst of
		[] => 0
		| [_] => 0
		| head::neck::tail => (neck-head-1) + count_gaps(neck::tail)
 
fun insert_sorted(lst, vs) = 
	let fun insert_v(lst, v) =
		case lst of 
			[] => [v]
			| head::tail => if v<=head then v::head::tail else head::insert_v(tail, v)
	in
		case vs of
			[] => lst
			| h::t => insert_v(insert_sorted(lst, t), h)
	end
 
fun filter_indexes f lst =
	let fun help f lst c = 
		case lst of
			[] => []
			| h::t => if f(h) then c::(help f t (c+1)) else help f t (c+1)
	in
		help f lst 0
	end
 
fun compute input = 
	let 
		val max = max(input)
		fun helper(n) =
			case n of
				0 => 0
				| _ => count_gaps(filter_indexes (fn e=>e>=n) input) + helper(n-1)
	in
		helper(max)
	end
 
val c1 = compute [2,5,1,2,3,4,7,7,6] = 10
val c2 = compute [0,5,0,1,0,2,1,0] = 5

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