From e1c70e78272c3fd0f750cea6d247917add54d0ed Mon Sep 17 00:00:00 2001
From: Grimmauld <Grimmauld@grimmauld.de>
Date: Thu, 5 Dec 2024 11:21:11 +0100
Subject: [PATCH] day 5

---
 day5/default.nix |   23 +
 day5/input       | 1367 ++++++++++++++++++++++++++++++++++++++++++++++
 utils.nix        |    2 +
 3 files changed, 1392 insertions(+)
 create mode 100644 day5/default.nix
 create mode 100644 day5/input

diff --git a/day5/default.nix b/day5/default.nix
new file mode 100644
index 0000000..9527c62
--- /dev/null
+++ b/day5/default.nix
@@ -0,0 +1,23 @@
+{ lib, utils, ... }:
+with lib;
+with builtins;
+with utils;
+let
+  input_parts = reSplit "\n\n" (readFile ./input);
+  orders = map (reSplit "\\|") (reSplit "\n" (head input_parts));
+  records = map (reSplit ",") (init (reSplit "\n" (last input_parts)));
+
+  # defines mapping of number -> [ blocked numbers that can't come after. Sorted for readability. ]
+  blocking = mapAttrs (_: v: map head v |> naturalSort |> unique ) (groupBy last orders);
+
+  isValid = r: all (i: let p = elemAt r i; in !hasAttr p blocking || (intersectLists (drop (i + 1) r ) blocking."${p}") == [] ) (listRange r);
+
+  sortRecord = r: if r == [] then [] else (let
+    h = head r;
+    intersect = if !hasAttr h blocking then [] else intersectLists (tail r ) blocking."${h}";
+    # Idea: check first element, and pull all "bad" elements ahead. If there is no "bad" elements, take the head and go down.
+  in if intersect == [] then [h] ++ sortRecord (tail r) else sortRecord (intersect ++ [ h ] ++ (removeAll intersect (tail r))) );
+in {
+  part1 = filter isValid records |> map elemAtMid |> listSumWith toInt;
+  part2 = filter (invert isValid) records |> map sortRecord |> map elemAtMid |> listSumWith toInt;
+}
diff --git a/day5/input b/day5/input
new file mode 100644
index 0000000..9de4e14
--- /dev/null
+++ b/day5/input
@@ -0,0 +1,1367 @@
+88|12
+44|33
+44|26
+29|91
+29|23
+29|84
+19|17
+19|84
+19|53
+19|79
+23|48
+23|31
+23|12
+23|72
+23|98
+18|44
+18|88
+18|94
+18|41
+18|83
+18|31
+26|48
+26|43
+26|86
+26|87
+26|15
+26|24
+26|27
+86|55
+86|91
+86|74
+86|98
+86|13
+86|48
+86|36
+86|67
+13|43
+13|49
+13|53
+13|94
+13|88
+13|24
+13|19
+13|16
+13|72
+42|21
+42|23
+42|75
+42|67
+42|54
+42|36
+42|62
+42|58
+42|84
+42|29
+72|53
+72|16
+72|17
+72|79
+72|52
+72|38
+72|29
+72|94
+72|45
+72|83
+72|19
+94|61
+94|35
+94|12
+94|16
+94|75
+94|31
+94|17
+94|78
+94|44
+94|29
+94|33
+94|52
+58|67
+58|37
+58|18
+58|49
+58|72
+58|23
+58|13
+58|74
+58|43
+58|95
+58|91
+58|48
+58|55
+67|52
+67|55
+67|27
+67|33
+67|94
+67|43
+67|23
+67|31
+67|41
+67|19
+67|72
+67|45
+67|18
+67|21
+35|55
+35|37
+35|95
+35|74
+35|87
+35|21
+35|89
+35|86
+35|43
+35|26
+35|67
+35|15
+35|13
+35|58
+35|18
+98|78
+98|75
+98|17
+98|94
+98|44
+98|62
+98|12
+98|33
+98|61
+98|29
+98|79
+98|42
+98|38
+98|53
+98|31
+98|45
+84|49
+84|13
+84|72
+84|67
+84|48
+84|23
+84|89
+84|94
+84|24
+84|15
+84|95
+84|91
+84|74
+84|86
+84|55
+84|27
+84|21
+53|58
+53|86
+53|35
+53|91
+53|17
+53|79
+53|16
+53|87
+53|37
+53|62
+53|36
+53|15
+53|12
+53|78
+53|26
+53|67
+53|75
+53|89
+79|95
+79|86
+79|89
+79|58
+79|27
+79|67
+79|18
+79|36
+79|87
+79|26
+79|84
+79|43
+79|35
+79|21
+79|23
+79|13
+79|48
+79|74
+79|49
+55|31
+55|18
+55|42
+55|45
+55|49
+55|72
+55|24
+55|12
+55|98
+55|41
+55|13
+55|44
+55|94
+55|52
+55|43
+55|17
+55|38
+55|61
+55|19
+55|88
+38|26
+38|29
+38|84
+38|42
+38|54
+38|79
+38|53
+38|52
+38|75
+38|33
+38|17
+38|45
+38|41
+38|88
+38|19
+38|58
+38|61
+38|83
+38|78
+38|62
+38|16
+24|38
+24|16
+24|78
+24|83
+24|98
+24|88
+24|19
+24|12
+24|53
+24|44
+24|94
+24|62
+24|35
+24|41
+24|52
+24|79
+24|54
+24|33
+24|29
+24|31
+24|45
+24|17
+21|13
+21|18
+21|41
+21|45
+21|53
+21|38
+21|55
+21|94
+21|24
+21|48
+21|98
+21|43
+21|49
+21|19
+21|52
+21|61
+21|23
+21|88
+21|44
+21|31
+21|83
+21|33
+21|72
+15|88
+15|41
+15|55
+15|18
+15|89
+15|23
+15|48
+15|31
+15|72
+15|43
+15|44
+15|27
+15|21
+15|38
+15|19
+15|98
+15|13
+15|74
+15|94
+15|52
+15|49
+15|83
+15|24
+15|67
+33|16
+33|89
+33|54
+33|84
+33|91
+33|53
+33|86
+33|26
+33|75
+33|37
+33|12
+33|74
+33|58
+33|87
+33|35
+33|36
+33|15
+33|95
+33|17
+33|29
+33|78
+33|79
+33|62
+33|42
+74|49
+74|83
+74|31
+74|72
+74|98
+74|67
+74|52
+74|61
+74|43
+74|94
+74|24
+74|18
+74|19
+74|23
+74|55
+74|13
+74|27
+74|44
+74|88
+74|21
+74|45
+74|38
+74|48
+74|41
+36|15
+36|94
+36|44
+36|24
+36|48
+36|21
+36|18
+36|13
+36|55
+36|49
+36|98
+36|27
+36|41
+36|38
+36|23
+36|67
+36|95
+36|89
+36|88
+36|43
+36|31
+36|72
+36|52
+36|74
+27|52
+27|94
+27|61
+27|38
+27|41
+27|24
+27|18
+27|19
+27|44
+27|49
+27|43
+27|33
+27|83
+27|45
+27|12
+27|16
+27|48
+27|13
+27|72
+27|98
+27|53
+27|55
+27|88
+27|31
+87|21
+87|27
+87|94
+87|48
+87|43
+87|49
+87|58
+87|67
+87|13
+87|72
+87|15
+87|36
+87|91
+87|24
+87|86
+87|18
+87|95
+87|37
+87|55
+87|89
+87|44
+87|98
+87|74
+87|23
+45|16
+45|36
+45|75
+45|62
+45|95
+45|54
+45|35
+45|84
+45|87
+45|86
+45|58
+45|79
+45|17
+45|12
+45|29
+45|15
+45|33
+45|26
+45|53
+45|37
+45|61
+45|78
+45|91
+45|42
+43|62
+43|16
+43|45
+43|94
+43|41
+43|98
+43|53
+43|61
+43|52
+43|24
+43|54
+43|19
+43|17
+43|78
+43|33
+43|42
+43|29
+43|88
+43|12
+43|38
+43|72
+43|83
+43|44
+43|31
+37|95
+37|48
+37|43
+37|41
+37|23
+37|67
+37|31
+37|55
+37|13
+37|74
+37|98
+37|18
+37|36
+37|44
+37|38
+37|89
+37|15
+37|49
+37|21
+37|24
+37|27
+37|72
+37|94
+37|91
+49|94
+49|83
+49|24
+49|16
+49|72
+49|61
+49|44
+49|17
+49|41
+49|54
+49|78
+49|98
+49|62
+49|42
+49|19
+49|33
+49|12
+49|38
+49|53
+49|45
+49|31
+49|88
+49|43
+49|52
+52|88
+52|16
+52|33
+52|26
+52|42
+52|17
+52|35
+52|62
+52|84
+52|54
+52|87
+52|37
+52|19
+52|75
+52|83
+52|53
+52|12
+52|78
+52|86
+52|45
+52|61
+52|58
+52|79
+52|29
+16|67
+16|23
+16|42
+16|91
+16|17
+16|79
+16|37
+16|95
+16|29
+16|89
+16|36
+16|62
+16|26
+16|87
+16|78
+16|75
+16|21
+16|15
+16|35
+16|86
+16|54
+16|84
+16|74
+16|58
+83|17
+83|45
+83|79
+83|37
+83|35
+83|16
+83|91
+83|36
+83|19
+83|78
+83|54
+83|84
+83|42
+83|75
+83|29
+83|26
+83|87
+83|33
+83|61
+83|62
+83|86
+83|53
+83|58
+83|12
+62|29
+62|58
+62|21
+62|74
+62|35
+62|55
+62|79
+62|23
+62|27
+62|86
+62|95
+62|36
+62|26
+62|84
+62|18
+62|75
+62|67
+62|89
+62|91
+62|87
+62|15
+62|48
+62|13
+62|37
+61|87
+61|79
+61|86
+61|26
+61|29
+61|12
+61|53
+61|75
+61|36
+61|84
+61|62
+61|35
+61|16
+61|37
+61|17
+61|54
+61|15
+61|58
+61|42
+61|95
+61|78
+61|91
+61|33
+61|89
+75|95
+75|74
+75|67
+75|13
+75|37
+75|49
+75|58
+75|87
+75|23
+75|89
+75|26
+75|27
+75|15
+75|21
+75|72
+75|55
+75|48
+75|84
+75|91
+75|18
+75|43
+75|24
+75|36
+75|86
+48|52
+48|83
+48|45
+48|31
+48|44
+48|53
+48|88
+48|98
+48|61
+48|55
+48|43
+48|33
+48|18
+48|72
+48|16
+48|13
+48|42
+48|24
+48|41
+48|94
+48|38
+48|19
+48|12
+48|49
+17|62
+17|91
+17|75
+17|37
+17|26
+17|35
+17|29
+17|23
+17|84
+17|36
+17|58
+17|15
+17|78
+17|67
+17|48
+17|89
+17|54
+17|95
+17|86
+17|79
+17|27
+17|74
+17|21
+17|87
+31|88
+31|29
+31|16
+31|45
+31|75
+31|79
+31|84
+31|87
+31|78
+31|38
+31|19
+31|52
+31|35
+31|26
+31|61
+31|41
+31|33
+31|53
+31|42
+31|17
+31|83
+31|62
+31|54
+31|12
+78|84
+78|74
+78|48
+78|89
+78|55
+78|29
+78|62
+78|37
+78|54
+78|87
+78|67
+78|79
+78|91
+78|35
+78|26
+78|36
+78|58
+78|15
+78|27
+78|95
+78|75
+78|21
+78|86
+78|23
+12|86
+12|15
+12|21
+12|58
+12|67
+12|89
+12|95
+12|26
+12|75
+12|36
+12|37
+12|29
+12|84
+12|91
+12|74
+12|35
+12|42
+12|62
+12|79
+12|54
+12|17
+12|78
+12|87
+12|16
+41|45
+41|52
+41|78
+41|42
+41|88
+41|87
+41|26
+41|35
+41|58
+41|29
+41|75
+41|84
+41|17
+41|86
+41|54
+41|33
+41|53
+41|79
+41|61
+41|16
+41|19
+41|83
+41|12
+41|62
+54|67
+54|26
+54|27
+54|86
+54|75
+54|89
+54|79
+54|23
+54|48
+54|29
+54|37
+54|18
+54|62
+54|95
+54|58
+54|36
+54|21
+54|87
+54|84
+54|35
+54|74
+54|15
+54|91
+54|55
+91|41
+91|23
+91|67
+91|36
+91|24
+91|27
+91|38
+91|55
+91|98
+91|49
+91|18
+91|13
+91|72
+91|43
+91|44
+91|31
+91|48
+91|21
+91|15
+91|95
+91|74
+91|52
+91|94
+91|89
+89|98
+89|23
+89|49
+89|38
+89|31
+89|72
+89|74
+89|55
+89|43
+89|67
+89|45
+89|88
+89|83
+89|41
+89|48
+89|27
+89|52
+89|13
+89|24
+89|44
+89|94
+89|18
+89|19
+89|21
+95|67
+95|94
+95|44
+95|83
+95|88
+95|27
+95|23
+95|43
+95|89
+95|48
+95|72
+95|24
+95|55
+95|18
+95|74
+95|13
+95|21
+95|38
+95|41
+95|52
+95|15
+95|98
+95|31
+95|49
+88|84
+88|29
+88|33
+88|35
+88|78
+88|19
+88|86
+88|16
+88|37
+88|53
+88|83
+88|75
+88|45
+88|91
+88|42
+88|79
+88|54
+88|62
+88|26
+88|87
+88|17
+88|61
+88|58
+44|35
+44|42
+44|17
+44|16
+44|29
+44|83
+44|41
+44|54
+44|88
+44|62
+44|31
+44|84
+44|19
+44|75
+44|78
+44|45
+44|38
+44|12
+44|52
+44|61
+44|53
+44|79
+29|75
+29|58
+29|89
+29|13
+29|35
+29|15
+29|26
+29|95
+29|86
+29|74
+29|21
+29|55
+29|67
+29|37
+29|79
+29|87
+29|49
+29|48
+29|36
+29|27
+29|18
+19|61
+19|35
+19|33
+19|12
+19|45
+19|42
+19|95
+19|86
+19|16
+19|37
+19|26
+19|36
+19|91
+19|58
+19|54
+19|87
+19|78
+19|62
+19|29
+19|75
+23|44
+23|19
+23|43
+23|38
+23|83
+23|13
+23|61
+23|18
+23|24
+23|27
+23|49
+23|55
+23|45
+23|52
+23|53
+23|88
+23|94
+23|33
+23|41
+18|24
+18|33
+18|53
+18|19
+18|13
+18|43
+18|12
+18|78
+18|72
+18|52
+18|61
+18|45
+18|42
+18|98
+18|17
+18|49
+18|38
+18|16
+26|89
+26|49
+26|98
+26|55
+26|74
+26|13
+26|21
+26|91
+26|67
+26|36
+26|84
+26|23
+26|37
+26|58
+26|72
+26|18
+26|95
+86|94
+86|18
+86|43
+86|89
+86|37
+86|49
+86|23
+86|21
+86|72
+86|38
+86|31
+86|27
+86|15
+86|24
+86|44
+86|95
+13|83
+13|41
+13|52
+13|61
+13|44
+13|98
+13|78
+13|33
+13|17
+13|12
+13|31
+13|38
+13|42
+13|45
+13|54
+42|27
+42|35
+42|17
+42|37
+42|15
+42|91
+42|78
+42|89
+42|87
+42|86
+42|95
+42|26
+42|74
+42|79
+72|62
+72|98
+72|33
+72|24
+72|12
+72|31
+72|78
+72|44
+72|54
+72|41
+72|88
+72|42
+72|61
+94|42
+94|79
+94|26
+94|54
+94|62
+94|38
+94|83
+94|19
+94|45
+94|53
+94|41
+94|88
+58|21
+58|94
+58|36
+58|89
+58|31
+58|44
+58|98
+58|15
+58|27
+58|24
+58|86
+67|38
+67|48
+67|44
+67|61
+67|98
+67|13
+67|24
+67|49
+67|83
+67|88
+35|23
+35|91
+35|48
+35|49
+35|27
+35|75
+35|84
+35|72
+35|36
+98|35
+98|52
+98|88
+98|19
+98|41
+98|16
+98|83
+98|54
+84|58
+84|43
+84|36
+84|37
+84|18
+84|87
+84|98
+53|29
+53|54
+53|84
+53|42
+53|74
+53|95
+79|75
+79|37
+79|15
+79|55
+79|91
+55|16
+55|53
+55|83
+55|33
+38|87
+38|12
+38|35
+24|61
+24|42
+21|27
+
+87,86,37,91,36,95,89,67,21,23,27,48,55,18,13,49,43,72,24,98,94
+79,16,83,58,33,35,29,52,45,61,17,54,41,12,26
+74,49,31,72,95,27,44,23,91,89,98,67,94,18,48
+74,44,15,48,24,18,55,49,36,38,13,89,67,52,41,31,23,43,95,98,21
+67,94,49,55,15,98,58,95,74,87,18,21,72
+17,89,95,36,42,91,62,75,79,74,87,23,26,86,78,29,35,54,84,58,21
+53,79,37,74,62,58,95,89,42,12,16,17,75,86,26,36,35
+13,84,36,23,58,48,95,89,26,55,24,49,15,87,37,21,43
+91,74,55,18,98,94,41
+48,21,13,67,23,98,49,18,84
+87,74,48,18,13,24,94
+91,36,95,89,74,21,23,27,18,13,43,72,24,98,94,44,31,38,41
+58,43,89,95,23,49,72
+38,41,52,83,45,33,12,42,17,78,29,35,87
+44,23,49,37,98,31,38,95,89,74,13,67,27
+45,74,18,19,38,23,43,67,24,48,21,98,52,94,41,49,31,83,44,72,13
+26,87,86,91,36,95,74,21,23,27,48,18,13,49,43,72,24
+35,26,84,87,58,86,37,91,36,15,89,74,67,21,23,27,55,18,13,49,43
+55,18,13,49,43,72,24,98,94,44,38,41,52,88,83,19,45,61,33,53,12,16,42
+91,62,79,16,42,45,26,19,36,86,53,17,54,35,37
+13,52,45,19,16,12,72,24,78
+83,19,45,12,62,29,79,84,37
+44,83,33,16,42
+27,48,55,13,49,94,31,41,52,19,61,33,53
+45,17,31,84,42,78,19,52,26,61,83,29,88,12,62
+98,94,44,31,41,88,83,45,61,53,12,16,42,17,54,62,29,79,35
+13,49,43,72,94,31,41,52,88,83,19,45,61,33,12,16,78
+54,62,29,79,35,75,26,84,87,58,37,91,36,95,15,89,74,67,21,23,27,48,55
+33,87,88,75,16,58,42,37,78,79,62
+61,48,41,43,94,31,55,21,98,72,88,49,45,27,24
+74,67,21,27,48,13,43,72,24,44,41,52,88,19,45
+17,78,54,29,79,35,26,58,37,91,15,74,67,21,27
+53,12,42,17,62,35,75,58,37,15,74
+74,94,52,21,72,48,49,98,23,36,31,55,24,89,15,41,18,38,43,13,67,95,44
+33,45,24,88,13,12,18,48,94,55,49,72,53,41,83,52,38
+91,15,38,94,44,98,21,48,55,24,72,27,74,49,36,23,41
+61,33,12,17,78,62,35,75,37,36,15
+42,61,83,12,78,33,17,26,79,84,29,87,53,58,35,41,54,45,19
+75,26,84,87,58,37,36,95,15,89,74,67,21,23,27,48,55,13,49,43,72
+84,62,95,91,12,54,79,36,87
+33,79,26,19,17,45,52,75,12,53,31,88,42,78,84,62,29,16,54,61,41
+88,83,19,45,61,33,16,42,17,78,62,79,35,26,87,86,37
+31,41,38,23,15,83,72,27,55,98,49,13,21,48,24,94,67,74,89
+15,74,27,18,49,72,24,31,83
+12,16,42,17,78,54,62,29,79,35,75,26,84,58,86,37,91,36,95,15,89,74,67
+26,19,37,42,78,35,45,16,87,54,84,53,86,83,29,33,88,58,62,79,75,17,61
+17,78,54,62,29,79,35,75,26,84,87,58,86,37,91,36,95,15,89,74,67,23,27
+18,13,49,72,24,98,44,31,38,41,52,83,45,61,33,53,17
+18,49,43,72,98,44,88,42,17
+83,88,53,31,18,17,41,42,49,12,98,19,44,33,94
+61,54,31,44,42
+26,84,58,86,37,91,95,15,74,13,24
+26,86,37,91,36,95,55,18,13,49,24
+86,37,91,36,23,18,13,49,43,98,31
+16,87,45,83,78,12,17,88,54,79,75,29,84,35,19
+72,24,44,31,38,41,52,19,61,12,16,17,78,54,62
+75,26,84,87,86,37,91,36,95,15,89,67,21,23,18,49,43
+48,55,43,44,88,61,16
+78,67,87,74,36,29,75,17,95,89,15,79,58
+61,35,86,12,33
+94,24,27,74,87,67,48,91,18,37,36,49,23,21,55,89,15,95,13,98,86,43,58
+26,29,95,55,48,54,74,21,86,84,62,27,67
+41,83,16,17,29
+74,67,23,27,55,18,13,43,72,24,98,31,38,41,52,88,83,19,45
+79,15,42,74,78,35,36,12,17
+27,23,15,52,49,89,38,72,48,13,44,74,18,31,24,95,88,21,55,43,98,41,94
+31,55,43,72,49,12,53,88,52,44,41,27,33
+35,75,26,84,87,58,86,37,91,36,95,15,74,67,21,23,27,48,55,18,13,49,43
+89,74,67,23,27,48,18,49,72,98,44,38,41,52,19
+23,62,54,78,74
+91,36,15,67,48,38,41
+79,35,75,26,84,87,58,86,37,91,36,95,15,74,67,21,23,27,48,55,18,13,49
+86,27,55,13,49,24,98
+38,17,41,78,19,43,12,83,54,88,49,24,98
+79,35,75,26,84,87,58,86,37,91,95,15,89,74,67,21,23,27,48,55,18,13,49
+89,74,67,21,23,27,48,55,18,13,49,43,72,24,98,94,44,31,38,41,52,88,19
+78,16,54,62,58,26,45,33,87,84,61,19,12,37,29,36,79,53,42,17,86
+54,29,79,35,26,84,87,58,37,91,36,95,15,89,74,67,21,23,27,48,55
+61,36,17,45,16,33,79,54,86,37,53,91,12,29,78
+88,19,61,12,17,78,62,29,79,35,26,58,37
+17,78,54,62,29,35,75,26,84,87,86,37,95,15,89,23,27
+52,24,98,17,83,31,78,33,62,53,44,88,43
+86,36,15,27,48,98,31
+18,55,52,24,48,13,45,38,67,61,88,41,19
+49,52,27,23,41,48,18,43,21,98,72,74,36,13,95,67,89
+42,37,62,16,26,89,54,91,21,58,78,79,74,87,35,86,75,84,15
+16,17,62,29,54,75,12,79,91,53,36,78,33,86,42,84,58
+72,24,94,44,41,52,45,61,33,16,54,62,29
+45,61,53,12,16,42,17,78,54,29,79,75,26,84,87,37,91,36,95
+67,19,38,43,49,89,31,88,21,48,24
+72,21,67,23,18,55,58,49,86,98,94,15,89,87,24
+19,79,86,83,87,12,35,52,78,62,42,88,54
+42,78,35,75,84,87,37,21,23
+23,91,84,37,74,75,86,67,13,89,15,21,26,87,36,27,18,48,58,95,55,29,79
+88,42,16,31,49,45,61,55,43
+75,42,37,86,26,95,17,36,35,16,33,29,61,15,87,58,12,62,53,84,91
+37,91,86,58,75,84,89,13,55,18,48,35,67,43,27,26,74,95,15
+33,12,16,17,79,26,84,87,58,15,89
+98,44,31,38,52,19,45,61,33,53,12,16,42,17,78,62,29,79,35
+36,17,42,79,67,95,26,16,12,37,35
+38,53,12,16,62,29,35,84,87
+41,52,83,45,53,12,16,42,78,62,29,79,75,26,84,87,58
+62,29,79,35,75,26,84,87,58,37,36,95,89,74,67,21,23,27,48,55,18
+54,67,17,62,95,12,36,91,84,16,15,26,86,78,79,58,29,42,75,89,87
+94,48,24,55,15,58,23,98,91,86,72,44,36,67,95,37,43,18,13,74,27,21,89
+18,13,49,43,44,31,38,45,61,42,17
+95,78,29,86,15,58,42,87,37,79,17,67,26,54,74,75,12,89,84,16,62
+35,75,26,84,87,58,86,37,91,36,95,15,89,74,67,21,27,48,55,18,49
+37,26,58,74,48,72,75,36,84
+12,17,33,13,42,78,53
+44,52,62,31,79,53,24,88,45
+13,18,31,67,72,52,27,88,45,24,74
+86,84,17,16,29,62,87
+83,19,45,61,33,53,12,16,42,78,54,62,29,79,35,75,26,84,87,58,86,37,91
+75,13,26,43,89,67,74,18,91,49,35
+27,55,43,72,24,98,94,38,41,52,45,61,33,53,12
+17,78,29,79,35,26,58,86,91,95,15,74,21,23,27
+74,43,86,98,89,21,13,67,23,72,91,15,36
+94,54,29,88,17,12,42,41,62,33,98
+18,19,55,53,31,44,41,42,43
+94,33,62,38,12,31,83,17,53,41,42,54,88,45,16,61,29,78,79
+98,42,38,12,35,61,52,29,94,45,62,54,78,31,17
+42,17,78,54,62,29,79,84,58,86,37,91,36,15,89,74,67,21,23
+37,91,74,23,13,49,43,44,38
+61,33,42,17,78,54,62,29,26,84,87,58,91
+89,74,67,21,23,48,55,49,72,24,98,31,88,83,19
+35,26,87,58,86,37,91,36,15,89,21,27,48,55,18,13,43
+36,21,18,43,72,41,52
+37,74,21,44,18,49,27,43,89,48,23,24,15,86,31,98,13
+37,26,75,27,79,21,87,48,84,91,15,95,23,67,58,89,35,74,86,54,78
+43,72,98,44,31,41,83,61,33,12,16,17,62
+67,27,15,52,13,55,49,24,83,72,38,18,88,23,44,89,98,41,74
+83,98,12,31,41,44,33,16,53,42,78,43,52,54,38,72,17,19,45,61,94,62,24
+21,23,27,38,98,13,15,83,48,89,67
+33,44,83,35,45,78,19,75,42,61,31,88,12,52,54,79,26,17,62,41,53
+13,43,98,94,38,41,83,19,45,53,12,16,78
+98,49,94,83,61,41,48,55,19,23,31,27,88,24,44,67,45,72,52,38,21,43,13
+88,61,42,35,44,29,75
+67,49,44,43,95,48,27,36,21,55,58,89,98,24,13
+48,84,58,67,15,23,26,36,37,87,18,89,86,21,74,27,91,75,72,13,55,95,43
+24,87,55,89,72,86,91,49,95,37,13,15,18
+31,98,23,55,48,45,44,72,94,67,88,38,83,49,61,13,43
+88,31,53,38,42,52,55,19,61,43,24,49,44,45,12,72,18,41,94
+62,29,35,75,84,87,58,37,89,23,27,55,18
+98,18,38,23,31,48,55,13,19,45,61,41,83,53,27
+12,45,52,88,33,38,27,43,61,94,72,83,44,18,19,31,48,53,24,41,98
+19,41,35,84,42,54,79,52,33,62,31,88,45
+21,23,27,48,55,18,49,72,24,98,94,44,31,38,41,83,19,61,33
+79,35,75,26,84,86,37,95,15,89,74,21,23,18,49
+72,18,74,13,87,75,58
+15,89,21,27,13,72,24,41,83
+94,62,16,31,19,88,33,75,29,38,61,41,83,35,53,45,42
+87,91,21,29,23,35,78,86,48,67,84
+79,75,36,29,67,35,78,89,58,17,86,15,95,12,74
+16,86,53,62,35,36,89,95,15,87,42,75,74,58,29,17,37,91,26
+83,27,52,55,94,88,74,49,89,48,98,18,13,19,24,41,31
+38,29,26,41,17,45,62,84,87,33,61
+31,94,43,13,41,44,83,33,72,49,18,55,19
+49,43,31,52,88,19,61,33,12,42,54
+87,58,86,37,91,36,95,15,89,67,23,48,55,18,13,49,24,98,94
+54,88,17,94,33,19,38,78,42
+52,88,83,19,45,33,53,12,16,42,17,78,54,62,29,35,75,26,84,87,58
+83,19,61,53,42,17,78,54,62,29,79,35,75,84,87,58,86,37,91
+19,83,23,31,45,18,61,88,33,52,43,94,24,72,98,55,53,49,48
+61,38,12,48,44,55,18,33,19,13,98,53,43,52,31
+12,16,42,78,62,79,35,58,37,95,15,74,67
+91,24,84,74,89,37,23,86,36,21,58
+88,19,45,61,33,53,12,16,42,17,78,54,62,29,79,35,75,26,84,87,58,86,37
+23,49,43,13,24,67,74,27,89,55,98,41,94,52,72,31,48,19,21,18,44,88,38
+78,79,35,37,36
+31,88,83,19,45,61,33,53,12,16,17,78,54,62,79,35,75,26,84
+27,98,55,31,38,23,18,43,95,67,88,15,74,52,13,41,49,72,21,94,48,44,24
+58,86,37,91,95,15,89,67,21,27,43,24,98,94,44
+29,35,45,38,19,17,16,79,33,62,83,42,94,31,78,41,12,54,98,53,44
+36,89,67,18,43,44,31
+83,98,42,12,35,31,45,53,41,33,44
+24,38,21,41,45,88,49,31,67,43,61,19,52,98,44,23,83
+67,35,62,91,15,26,18,89,75
+29,79,35,84,58,86,37,91,36,95,15,89,74,67,21,23,27,48,55,18,13
+79,75,84,37,91,15,67,21,23,55,13
+83,19,53,12,42,78,54,62,29,79,35,75,26,84,58,37,91
+43,72,94,44,31,38,19,12,42,17,78,54,62
+33,53,12,42,17,62,79,35,75,26,84,87,58,86,37,91,36,95,89
+13,24,49,48,74,86,87,37,43,95,98,27,21,55,72,18,89
+58,86,37,91,36,95,15,89,74,67,21,23,27,48,55,18,13,49,43,72,98,94,44
+61,35,16,91,37,26,53,12,86,17,75,83,87,33,78,42,58
+54,62,29,79,35,75,26,58,86,91,95,89,74,21,23,27,48
+86,37,91,89,67,21,23,27,48,18,49,43,72,24,98,94,31
+18,24,31,98,27,44,52,61,19,43,72,67,41,94,55
+26,27,62,87,18,75,86
diff --git a/utils.nix b/utils.nix
index 53f1449..81b61e4 100644
--- a/utils.nix
+++ b/utils.nix
@@ -15,4 +15,6 @@ with builtins; rec {
   listRange = l: range 0 ((length l) - 1);
   transpose = l: map (i: map ((flip elemAt) i) l) (listRange (head l));
   invert = f: x: !(f x);
+  elemAtMid = l: elemAt l ((length l) / 2);
+  removeAll = rl: (flip pipe) (map remove rl);
 }