#10066The Twin Towers

Once upon a time, in an ancient Empire, there were two towers of dissimilar shapes in two different cities. The towers were built by putting circular tiles one upon another. Each of the tiles was of the same height and had integral radius. It is no wonder that though the two towers were of dissimilar shape, they had many tiles in common.

However, more than thousand years after they were built, the Emperor ordered his architects to remove some of the tiles from the two towers so that they have exactly the same shape and size, and at the same time remain as high as possible. The order of the tiles in the new towers must remain the same as they were in the original towers. The Emperor thought that, in this way the two towers might be able to stand as the symbol of harmony and equality between the two cities. He decided to name them the Twin Towers.

Now, about two thousand years later, you are challenged with an even simpler problem: given the descriptions of two dissimilar towers you are asked only to find out the number of tiles in the highest twin towers that can be built from them.

Input

The input file consists of several data blocks. Each data block describes a pair of towers. The first line of a data block contains two integers N and N (1 ≤ N, N ≤ 100) indicating the number of tiles respectively in the two towers. The next line contains N positive integers giving the radii of the tiles (from top to bottom) in the first tower. Then follows another line containing N integers giving the radii of the tiles (from top to bottom) in the second tower.

7 6
20 15 10 15 25 20 15
15 25 10 20 15 20
8 9
10 20 20 10 20 10 20 10
20 10 20 10 10 20 10 10 20
0 0

Twin Towers #1
Number of Tiles : 4

Twin Towers #2
Number of Tiles : 6