Find the Length of the Longest Common Prefix

Choose one positive integer from each of the two arrays and compare the common prefix of their usual decimal representations; return the maximum prefix length over all cross-array pairs, or 0 if no pair shares a first digit.

输入格式

The first line contains n m, the second line contains n numbers, and the third line contains m numbers. Original bounds: 1≤n,m≤50000, 1≤value≤100000000; the largest value has 9 digits.

输出格式

Output a single integer, the answer.

样例 1

输入：

3 1
1 10 100
1000

输出：

3

样例 2

输入：

3 3
1 2 3
4 4 4

输出：

0

样例 3

输入：

1 1
100000000
100000000

输出：

9

样例说明

The outputs of the three public examples are, in order: 3; 0; 9. Verified by independent enumeration or direct simulation.