Score : 700 points
There are N towns numbered 1, 2, \cdots, N.
Some roads are planned to be built so that each of them connects two distinct towns bidirectionally. Currently, there are no roads connecting towns.
In the planning of construction, each town chooses one town different from itself and requests the following: roads are built so that the chosen town is reachable from itself using one or more roads.
These requests from the towns are represented by an array P_1, P_2, \cdots, P_N. If P_i = -1, it means that Town i has not chosen the request; if 1 \leq P_i \leq N, it means that Town i has chosen Town P_i.
Let K be the number of towns i such that P_i = -1. There are (N-1)^K ways in which the towns can make the requests. For each way to make requests, find the minimum number of roads needed to meet all the requests, and print the sum of those (N-1)^K numbers, modulo (10^9+7).
Input is given from Standard Input in the following format:
N P_1 P_2 \cdots P_N
For each way to make requests, find the minimum number of roads needed to meet all the requests, and print the sum of those (N-1)^K numbers, modulo (10^9+7).
4 2 1 -1 3
8
There are three ways to make requests, as follows:
Note that it is not mandatory to connect Town i and Town P_i directly.
The sum of the above numbers is 8.
2 2 1
1
There may be just one fixed way to make requests.
10 2 6 9 -1 6 9 -1 -1 -1 -1
527841