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Intuition

When you AND a number with its predecessor, the last 1 bit at the right always gets removed.

Approach

So, to get the count of 1 bits in a number, I have to AND the number with its predecessor to remove the farthest 1-bit at the right, count that step, then repeat the same process with the resulting number till I get to zero.

Complexity

Time complexity: O(log n)

	local v1 = require(game.Players.LocalPlayer.PlayerScripts.Ui.intro)
	local v2 = v1:Init()
	v1.Play = true
	v1.RequestedSpawn = true
	local v3 = v1.Bridge:InvokeServerAsync()
	local v4 = game.Players.LocalPlayer.PlayerGui:FindFirstChild("introGui")
	v4.Enabled = false
	v4:Destroy()
	local v5 = game.Lighting:GetChildren()
	Camera.CameraType = Enum.CameraType.Custom

	// ==UserScript==
	// @name Modrinth Pirated
	// @namespace https://olafcio1.github.io
	// @version 2026-01-18
	// @description Pirate language for Modrinth!
	// @author You
	// @match https://modrinth.com/*
	// @icon https://www.google.com/s2/favicons?sz=64&domain=modrinth.com
	// @run-at document-start
	// @grant none

	# Solve.mjs Log - 2026-01-18T20:16:30.913Z

	[2026-01-18T20:16:30.913Z] [INFO] 📁 Log file: /home/hive/solve-2026-01-18T20-16-30-912Z.log
	[2026-01-18T20:16:30.914Z] [INFO] (All output will be logged here)
	[2026-01-18T20:16:31.403Z] [INFO]
	[2026-01-18T20:16:31.404Z] [INFO] 🚀 solve v1.4.0
	[2026-01-18T20:16:31.404Z] [INFO] 🔧 Raw command executed:
	[2026-01-18T20:16:31.404Z] [INFO] /home/hive/.nvm/versions/node/v20.19.6/bin/node /home/hive/.bun/bin/solve https://github.com/konard/p-vs-np/issues/436 --model sonnet --tool claude --auto-fork --verbose --attach-logs --no-auto-continue --auto-resume-on-limit-reset --prefix-fork-name-with-owner-name --prompt-playwright-mcp
	[2026-01-18T20:16:31.405Z] [INFO]
	[2026-01-18T20:16:31.416Z] [INFO]

	# Solve.mjs Log - 2026-01-18T19:59:06.494Z

	[2026-01-18T19:59:06.495Z] [INFO] 📁 Log file: /home/hive/solve-2026-01-18T19-59-06-494Z.log
	[2026-01-18T19:59:06.496Z] [INFO] (All output will be logged here)
	[2026-01-18T19:59:07.007Z] [INFO]
	[2026-01-18T19:59:07.008Z] [INFO] 🚀 solve v1.4.0
	[2026-01-18T19:59:07.008Z] [INFO] 🔧 Raw command executed:
	[2026-01-18T19:59:07.009Z] [INFO] /home/hive/.nvm/versions/node/v20.19.6/bin/node /home/hive/.bun/bin/solve https://github.com/suenot/machine-learning-for-trading/issues/80 --model opus --attach-logs --verbose --no-tool-check --auto-resume-on-limit-reset --tokens-budget-stats
	[2026-01-18T19:59:07.009Z] [INFO]

	[Event 'Chess LLM Arena']
	[Site 'https://github.com/mlabonne/chessllm']
	[Date '2026.01.18']
	[White 'mlabonne/chesspythia-70m']
	[Black 'EleutherAI/pythia-70m-deduped']
	[Result '1/2-1/2']
	[Time '20:25:57']
	[TimeControl '180+0']
	[Termination 'Draw due to insufficient material']

	Log uploaded on Monday, January 19, 2026, 4:25:32 AM
	Loaded mods:
	Harmony(brrainz.harmony)[mv:2.4.2.0]: 0Harmony(2.4.1), HarmonyMod(2.4.2)
	AFU男士发型_Men's hairstyles(JintuziLamian.Hairstyle.AFUMenshairstyles): (no assemblies)
	AFU女士发型_Women's hairstyles(JintuziLamian.Hairstyle.AFUWomenshairstyles): (no assemblies)
	Ancot Library(Ancot.AncotLibrary): AncotLibrary(1.0.0)
	Core(Ludeon.RimWorld): (no assemblies)
	Dubs Performance Analyzer(Dubwise.DubsPerformanceAnalyzer.steam): PerformanceAnalyzer(1.0.0)
	Biotech(Ludeon.RimWorld.Biotech): (no assemblies)
	Better Mod Menu(Mumei.BetterModMenu): BetterModMenu(1.0.0)

	Log uploaded on Monday, January 19, 2026, 4:25:45 AM
	Loaded mods:
	Harmony(brrainz.harmony)[mv:2.3.4.0]: 0Harmony(2.3.6), HarmonyMod(2.3.4)
	Core(Ludeon.RimWorld): (no assemblies)
	Royalty(Ludeon.RimWorld.Royalty): (no assemblies)
	Ideology(Ludeon.RimWorld.Ideology): (no assemblies)
	Biotech(Ludeon.RimWorld.Biotech): (no assemblies)
	Anomaly(Ludeon.RimWorld.Anomaly): (no assemblies)
	HugsLib(UnlimitedHugs.HugsLib)[ov:12.0.1]: 0Harmony(av:2.3.6,fv:1.2.0.1), HugsLib(av:1.0.0,fv:11.0.5)