Programming teacher Dmitry Olegovich is going to propose the following task for one of his tests for students:
You are given a tree
T with
n vertices, specified by its adjacency matrix
a[1... n,1... n]. What is the output of the following pseudocode?
used[1 ... n] = {0, ..., 0};
procedure dfs(v):
print v;
used[v] = 1;
for i = 1, 2, ..., n:
if (a[v][i] == 1 and used[i] == 0):
dfs(i);
dfs(1);
In order to simplify the test results checking procedure, Dmitry Olegovich decided to create a tree
T such that the result is his favorite sequence
b. On the other hand, Dmitry Olegovich doesn't want to provide students with same trees as input, otherwise they might cheat. That's why Dmitry Olegovich is trying to find out the number of different trees
T such that the result of running the above pseudocode with
T as input is exactly the sequence
b. Can you help him?
Two trees with
n vertices are called different if their adjacency matrices
a1 and
a2 are different, i. e. there exists a pair
(i,j), such that
1≤i,j≤n and
a1[i][j]≠a2[i][j].