Time Limit: 1000 ms Memory Limit: 32768 KiB
We have a graph with size = N like that in Figure 1. Then we are going to find a downward path from the top node to one bottom node.
First, we select the top node as the beginning. Then at any node, we can go horizontally or downward along the blue edge and reach the next node. The finding will be end when we reach one of the bottom nodes. After that we can get a downward path from the top node to one bottom node. Note that we can not pass a blue edge that we have passed ago during each finding.
Your task is to calculate there exists how many downward paths.
For each test case, there is only one integer N (1 <= N <= 10^18) indicates the size of the graph.
For each test case, you should output the correct answer of the above task in one line.Because the answer may be very large, you should just output the remainder of it divided by 1000003.
For Sample 2, the yellow paths in Figure 2 show the 8 downward paths.