Given the height of ~N~ men and ~M~ women. We need to form ~X~ pairs of one man and one woman. ~H~ is the maximum height difference of a pair, ~H~ = max({|pair.manHeight – pair.womanHeight| for ~X~ pairs}). What is the minimum possible value of ~H~?

Input

• The first line contains three integers ~N~, ~M~, ~X~ ~(1 ≤ N ≤ 10^{5}~).

• The second line contains ~N~ integers indicating the height of ~N~ men.

• The third line contains ~M~ integers indicating the height of ~M~ women.

Output

The minimum possible value of ~H~.

Note:

• 50% test case: ~X~ = ~N~ = ~M~

Sample Input 1

5 6 3
150 180 165 184 156
152 168 175 159 168 190

Sample Output 1

3

Sample Input 2

5 5 5
150 180 165 184 156
152 168 175 159 168

Sample Output 2

12