-- The Computer Language Benchmarks Game
-- http://shootout.alioth.debian.org/
-- contributed by Mike Pall

local function A(i, j)
  local ij = i+j-1
  return 1.0 / (ij * (ij-1) * 0.5 + i)
end

local function Av(x, y, N)
  for i=1,N do
    local a = 0
    for j=1,N do a = a + x[j] * A(i, j) end
    y[i] = a
  end
end

local function Atv(x, y, N)
  for i=1,N do
    local a = 0
    for j=1,N do a = a + x[j] * A(j, i) end
    y[i] = a
  end
end

local function AtAv(x, y, t, N)
  Av(x, t, N)
  Atv(t, y, N)
end

local N = tonumber(arg and arg[1]) or 100
local u, v, t = {}, {}, {}
for i=1,N do u[i] = 1 end

for i=1,10 do AtAv(u, v, t, N) AtAv(v, u, t, N) end

local vBv, vv = 0, 0
for i=1,N do
  local ui, vi = u[i], v[i]
  vBv = vBv + ui*vi
  vv = vv + vi*vi
end
io.write(string.format("%0.9f\n", math.sqrt(vBv / vv)))