local function checkCT(ct)
    local r = {}
    for i = 1, 8 do
        for j = i+1, 9 do
            if ct[i] == ct[j] and ct[i] ~= 0 then
                table.insert(r, {i, j})
            end
        end
    end
    if #r > 0 then return false, r end
    return true
end

local function findThisTable(this, that)
    for i = 1, #that do
        if #that[i] == #this then
            local flag = true
            for j = 1, #this do
                if this[j] ~= that[i][j] then flag = false; break end
            end
            if flag then return true, i end
        end
    end
    return false
end

function check(board)
    local rr = {}
    for x = 1, 9 do
        local ct = {}
        for y = 1, 9 do
            ct[y] = board[x][y]
        end
        local ok, r = checkCT(ct)
        if not ok then
            for _, p in ipairs(r) do
                local t = {x, p[1], x, p[2], board[x][p[1]]}
                if not findThisTable(t, rr) then
                    table.insert(rr, t)
                end
            end
        end
    end
    for y = 1, 9 do
        local ct = {}
        for x = 1, 9 do
            ct[x] = board[x][y]
        end
        local ok, r = checkCT(ct)
        if not ok then
            for _, p in ipairs(r) do
                local t = {p[1], y, p[2], y, board[p[1]][y]}
                if not findThisTable(t, rr) then
                    table.insert(rr, t)
                end
            end
        end
    end
    for i = 0, 2 do
        for j = 0, 2 do
            local ct = {}
            for x = 1, 3 do
                for y = 1, 3 do
                    ct[(x-1)*3+y] = board[x+i*3][y+j*3]
                end
            end
            local ok, r = checkCT(ct)
            if not ok then
                for _, p in ipairs(r) do
                    local x1 = ((p[1] - 1) // 3 + 1) + i * 3
                    local y1 = ((p[1] - 1) % 3 + 1) + j * 3
                    local x2 = ((p[2] - 1) // 3 + 1) + i * 3
                    local y2 = ((p[2] - 1) % 3 + 1) + j * 3
                    local t = {x1, y1, x2, y2, board[x1][y1]}
                    if not findThisTable(t, rr) then
                        table.insert(rr, t)
                    end
                end
            end
        end
    end
    if #rr > 0 then
        return false, rr
    end
    return true
end

function checkSolved(board)
    local r = {}
    for i = 1, 9 do
        for j = 1, 9 do
            if board[i][j] < 1 or board[i][j] > 9 then
                table.insert(r, {i, j, board[i][j]})
            end
        end
    end
    local ok, rr = check(board)
    if #r > 0 or (rr and #rr > 0) then
        return false, r, rr
    end
    return true
end

function pcheck(board)
    local ok, r, rr = checkSolved(board)
    if ok then
        print("Board is solved!")
        return 
    end
    for _, p in ipairs(r) do
        print(S("(%d, %d) = %d", unpack(p)))
    end
    for _, p in ipairs(rr) do
        print(S("(%d, %d) = (%d, %d) = %d", unpack(p)))
    end
end