from collections import deque

START = 'svr'
END = 'out'

def dfs_sort(graph): 
    visited = set()
    order = deque()

    def dfs_helper(node):
        visited.add(node)
        for v in graph.get(node, []):
            if v not in visited:
                dfs_helper(v)
        
        order.appendleft(node)
    
    dfs_helper(START)
    return order

def dp(graph, order, start_i, end_is):
    dp = {node: 0 for node in graph}
    dp[start_i] = 1

    for node in order:
        for neighbor in graph[node]:
            dp[neighbor] += dp[node]
    
    return [dp[end_i] for end_i in end_is]

with open('input.txt', 'r') as file:
    lines = file.readlines()

graph = {}
for line in lines:
    line = line.strip()
    nodes = line.split()
    node = nodes[0].rstrip(':')
    edges = nodes[1:]
    graph[node] = edges

graph[END] = []

topological_order = dfs_sort(graph)

print(topological_order)

pruned_graph = {node: graph[node] for node in topological_order if node in graph}

# Path combinations: svr->fft->dac->out and svr->dac->fft->out

svr_fft, svr_dac = dp(pruned_graph, topological_order, START, ['fft', 'dac'])
fft_out, fft_dac = dp(pruned_graph, topological_order, 'fft', [END, 'dac'])
dac_fft, dac_out = dp(pruned_graph, topological_order, 'dac', ['fft', END])

result = (svr_fft * fft_dac * dac_out) + (svr_dac * dac_fft * fft_out)

print(result)