Problem:
Score : 300 points

Problem Statement

The season for Snuke Festival has come again this year. First of all, Ringo will perform a ritual to summon Snuke. For the ritual, he needs an altar, which consists of three parts, one in each of the three categories: upper, middle and lower.

He has N parts for each of the three categories. The size of the i-th upper part is A_i, the size of the i-th middle part is B_i, and the size of the i-th lower part is C_i.

To build an altar, the size of the middle part must be strictly greater than that of the upper part, and the size of the lower part must be strictly greater than that of the middle part. On the other hand, any three parts that satisfy these conditions can be combined to form an altar.

How many different altars can Ringo build? Here, two altars are considered different when at least one of the three parts used is different.

Constraints

1 \leq N \leq 10^5

1 \leq A_i \leq 10^9(1\leq i\leq N)

1 \leq B_i \leq 10^9(1\leq i\leq N)

1 \leq C_i \leq 10^9(1\leq i\leq N)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 ... A_N
B_1 ... B_N
C_1 ... C_N

Output

Print the number of different altars that Ringo can build.

Sample Input 1

2
1 5
2 4
3 6

Sample Output 1

3

The following three altars can be built:

Upper: 1-st part, Middle: 1-st part, Lower: 1-st part

Upper: 1-st part, Middle: 1-st part, Lower: 2-nd part

Upper: 1-st part, Middle: 2-nd part, Lower: 2-nd part

Sample Input 2

3
1 1 1
2 2 2
3 3 3

Sample Output 2

27

Sample Input 3

6
3 14 159 2 6 53
58 9 79 323 84 6
2643 383 2 79 50 288

Sample Output 3

87

Solution in LuaJIT (2.0.4) (judge verdict: Wrong Answer)

do  --  Library
    table.map = function(t, f)
        local ret = {}
        for i = 1, #t do
            table.insert(ret, f(t[i]))
        end
        return ret
    end
    
    table.each = function(t, f)
        for i = 1, #t do
            f(t[i])
        end
    end
    
    table.sum = function(t)
        local sum = 0
        for i = 1, #t do
            sum = sum + t[i]
        end
        return sum
    end
    
    table.slice = function(t, b, e)
        local ret = {}
        for i = b, e do
            table.insert(ret, t[i])
        end
        return ret
    end
    
    string.split = function(str, sep)
        local ret = {}
        for i in string.gmatch(str, "[^"..sep.."]+") do
            table.insert(ret, i)
        end
        return ret
    end
end

calculate = nil
do
    local memo = {}
    local stages_to_str = function(stages)
        return table.concat(table.map(stages, tostring), ",")
    end
    
    function calculate(top_num, under_stages)
        local str_under_stages = stages_to_str(under_stages)
        if not memo[top_num] then
            memo[top_num] = {}
        elseif memo[top_num][str_under_stages] then
            return memo[top_num][str_under_stages]
        end
        
        if #under_stages == 0 then
            return 1
        end
        
        memo[top_num][str_under_stages] = table.sum(table.map(under_stages[1], function(size)
            if size <= top_num then
                return 0
            end
            
            return calculate(size, table.slice(under_stages, 2, #under_stages))
        end))
        return memo[top_num][str_under_stages]
    end
end

function main()
    local n = tonumber(io.read())
    local stages = {}
    for i = 1, 3 do
        table.insert(stages, table.map(string.split(io.read(), " "), tonumber))
    end
    
    table.each(stages, function(t)
        table.sort(t, function(a, b) return b < a end)
    end)
    
    print(calculate(0, stages))
end

main()