| The far-off land of Tamriel is brimming with opportunity! Opportunity for | |
| adventure, politics, romance... and, perhaps most importantly of all, | |
| commerce. | |
| A group of Khajiit merchants, traditionally known for roaming the countryside | |
| selling their wares, have recently set up permanent bazaars in a number of | |
| towns. Having gotten their cat-like paws on a large supply of raw amber and | |
| bronze, they're prepared to strategically work together to maximize their | |
| profits selling it! | |
| One bazaar has been set up in each of **N*****M**+1 towns. The towns are | |
| numbered from 0 to **N*****M**, inclusive, and are connected by roads in a | |
| hub-and-spokes arrangement, with town 0 in the center and **N** lines of **M** | |
| towns each arranged around it. The _i_th such line consists of towns | |
| **M***(_i_-1)+1 to **M***_i_, inclusive, connected together in order by | |
| **M**-1 roads (with one between towns **M***(_i_-1)+1 and **M***(_i_-1)+2, | |
| another between towns **M***(_i_-1)+2 and **M***(_i_-1)+3, and so on). For | |
| each line _i_, there is furthermore a road connecting its first town | |
| (**M***(_i_-1)+1) to town 0. Note that each of the **N*****M** roads may be | |
| travelled in either direction, and that each town may be reached from each | |
| other town by following a sequence of roads. | |
| For example, if **N**=4 and **M**=2, the arrangement of towns and roads would | |
| look as follows: | |
|  | |
| Initially, the bazaar in each town _i_ is stocked with either amber (if **Xi** | |
| = "A") or bronze (if **Xi** = "B"). However, in order to satisfy demand, it | |
| should end up stocked with a potentially different ware, either amber (if | |
| **Yi** = "A") or bronze (if **Yi** = "B"). It's guaranteed that the number of | |
| bazaars initially stocked with amber is equal to the number of bazaars which | |
| should end up stocked with amber (consequently, the same holds true for | |
| bronze). | |
| In order to accomplish their goal, the Khajiit merchants may repeatedly select | |
| a pair of towns which are directly connected by a road, and swap their | |
| bazaars' wares. Please help them determine the minimum number of such swaps | |
| required for all **N*****M**+1 bazaars to end up stocked with the required | |
| wares! This is guaranteed to be possible for every possible valid input. | |
| ### Input | |
| Input begins with an integer **T**, the number of Khajiit groups. | |
| For each group, there is first a line containing the space-separated integers | |
| **N** and **M**. | |
| Then follows a line with the length-(**N** * **M** \+ 1) string **X**, the | |
| characters **X0** through **XN*M**. | |
| Then follows a line with the length-(**N** * **M** \+ 1) string **Y**, the | |
| characters **Y0** through **YN*M**. | |
| ### Output | |
| For the _i_th group, print a line containing "Case #_i_: " followed by one | |
| integer, the minimum number of swaps required to stock all of the bazaars with | |
| the required wares. | |
| ### Constraints | |
| 1 ≤ **T** ≤ 80 | |
| 1 ≤ **N**, **M** ≤ 1,000,000 | |
| 1 ≤ **N** * **M** ≤ 1,000,000 | |
| The sum of **N** * **M** across all **T** test cases is no greater than | |
| 10,000,000. | |
| ### Explanation of Sample | |
| In the first case, no swaps are required. | |
| In the second case, bazaars 1 and 2 should swap their goods. | |
| In the third case, the bazaars are initially set up as follows (with ones | |
| carrying amber marked in yellow, and ones carrying bronze marked in orange): | |
|  | |
| The following sequence of 3 swaps could then be performed to arrive at the | |
| required configuration: | |
|  | |
|  | |
|  | |