Task

Some robot components are stacked in the warehouse, such as heads, arms, bodies and legs. Your task is to determine AT LEAST how many robots these components belong to.

Preload

There are five kinds of robots in all. An object array ROBOTS was preloaded, like this:

[
{type:"A",head:5,arm:20,body:10,leg:20},
{type:"B",head:8,arm:15,body:20,leg:20},
{type:"C",head:5,arm:10,body:15,leg:15},
{type:"D",head:6,arm:20,body:15,leg:10},
{type:"E",head:8,arm:15,body:15,leg:10}
]

You can use it directly without redefining it in your code.

Input

• heads, an integer array, each element represents the size of a robot's head.

• arms, an integer array, each element represents the length of a robot's arm.

• bodies, an integer array, each element represents the size of a robot's body.

• legs, an integer array, each element represents the length of a robot's leg.

Output

An integer, the minimum possible number of robots.

Examples

For heads = [], arms = [], bodies = [] and legs = []

The output should be 0.

There is no robot component in the warehouse.

For heads = [5], arms = [20,20], bodies = [10] and legs = [20,20]

The output should be 1.

All of these component can belong to one robot(type A).

For heads = [5,8], arms = [20,15,20], bodies = [10,20] and legs = [20,20,20]

The output should be 2.

these components can belong to a robot(type A):

heads [5], arms [20,20], bodies [10] legs [20,20]`

these components can belong to a robot(type B):

heads [8], arms [15], bodies [20] legs [20]`

See more examples in testcases.

Note

• Each robot has 1 head, 2 arms, 1 body and 2 legs.

• All inputs are valid.

• Testcases or reference solution may contains bug, please test and feedback ;-)

• Happy Coding ^_^