Joisino is planning on touring Takahashi Town. The town is divided into square sections by north-south and east-west lines. We will refer to the section that is the from the west and the from the north as .
Joisino thinks that a touring plan is good if it satisfies the following conditions:
Let be the section where she starts the tour. Then, and hold.
Let be the section where she has lunch. Then, and hold.
Let be the section where she ends the tour. Then, and hold.
By repeatedly moving to the adjacent section (sharing a side), she travels from the starting section to the ending section in the shortest distance, passing the lunch section on the way.
Two touring plans are considered different if at least one of the following is different: the starting section, the lunch section, the ending section, and the sections that are visited on the way. Joisino would like to know how many different good touring plans there are. Find the number of the different good touring plans. Since it may be extremely large, find the count modulo .
Input is given from Standard Input in the following format:
1 1 2 2 3 4
The starting section will always be , and the lunch section will always be . There are four good touring plans where is the ending section, and six good touring plans where is the ending section. Therefore, the answer is .
1 2 3 4 5 6
77523 89555 420588 604360 845669 973451