class node
    function __construct(public v, public fixed) end
end

local function set_boundary(m)
    m[2][2].v = 1
    m[2][2].fixed = 1
    m[7][8].v = -1
    m[7][8].fixed = -1
end

local function calc_diff(m, d, w, h)
    local total = 0
    for i = 1, h do
        for j = 1, w do
            local v = 0
            local n = 0
            if i > 1 then
                v += m[i - 1][j].v
                n += 1
            end
            if j > 1 then
                v += m[i][j - 1].v
                n += 1
            end
            if i < h then
                v +=  m[i + 1][j].v
                n += 1
            end
            if  j < w then
                v += m[i][j + 1].v
                n += 1
            end
            v = m[i][j].v - v / n
            d[i][j].v = v
            if m[i][j].fixed == 0 then total += v * v end
        end
    end
    return total
end

local function iter(m, w, h)
    local d = table.create(h)
    for i = 1, h do
        d[i] = table.create(w)
        for j = 1, w  do d[i][j] = new node(0, 0) end
    end
    local cur = {0, 0, 0}
    local diff = 1e10
    while diff > 1e-24 do
        set_boundary(m)
        diff = calc_diff(m, d, w, h)
        for i = 1, h do
            for j = 1, w do m[i][j].v -= d[i][j].v end
        end
    end
    for i = 1, h do
        for j = 1, w do
            local k = 0
            if i != 1 then k += 1 end
            if j != 1 then k += 1 end
            if i < h  then k += 1 end
            if j < w  then k += 1 end
            cur[m[i][j].fixed + 2] += d[i][j].v * k
        end
    end
    return (cur[3] - cur[1]) / 2
end

local S = 10
local mesh = table.create(S)
for i = 1, S do
    mesh[i] = table.create(S)
    for j = 1, S do mesh[i][j] = new node(0, 0) end
end
local r = 2 / iter(mesh, S, S)
print($"R = {r}")