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

5 6 3

150 180 165 184 156

152 168 175 159 168 190

Sample Output

3

Sample Input

5 5 5

150 180 165 184 156

152 168 175 159 168

Sample Output

12