def run(n)
    result = findRuns(getMarchingWidthValues(n).reverse)
    puts "#{result.inspect}"
end


def getMarchingWidthValues(n)
    Array.new(n) {|i| [i + 2, biggestFactorSmallerThanSquareRoot(i + 2)]}
end


def biggestFactorSmallerThanSquareRoot(n)

    arr = divisors(n).select{|x| x <= squareRootFloor(n)}

    val = arr.pop

    if val ** 2 == n
        val = arr.pop
    end

    return val
end

def findRuns(arr)
    runs = Hash.new

    target = 1

    currentRun = []
    arr.each_index do |i|
        if target == arr[i][1]
            currentRun.push(arr[i])
            target = target + 1
        else
            runs[currentRun.length] = currentRun
            currentRun = []
            target = 1
        end
    end

    return runs
end













def squareRootFloor(n)
    min = 1
    max = n / 2

    while (max - min > 1)
        g = (max + min) / 2

        if g ** 2 == n
            return g
        end

        if g ** 2 > n
            max = g
        else
            min = g
        end

    end

    return min
end

def divisors(n)
    result = []

    max = squareRootFloor(n) + 1
    k = 1

    while k <= max
        if n % k == 0
            result.push(k)
            result.push(n / k)
        end
        k = k + 1
    end


    return result.uniq.sort
end




run 1000