from collections import Counter

def journeyToMoon(n, astronaut):
    # Initialize disjoint set (union-find) structures
    root = list(range(n))
    rank = [0] * n
    
    def find_root(a):
        if root[a] != a:
            root[a] = find_root(root[a])  # Path compression
        return root[a]
        
    def union(a, b):
        i, j = find_root(a), find_root(b)
        if i != j:
            if rank[i] > rank[j]:
                root[j] = i
            elif rank[i] < rank[j]:
                root[i] = j
            else:
                root[j] = i
                rank[i] += 1
    
    # Union all astronaut pairs
    for a, b in astronaut:
        union(a, b)
    
    # Count the size of each connected component
    component_sizes = list(Counter(find_root(i) for i in range(n)).values())
    
    # Calculate the number of valid pairs
    total_pairs = 0
    sum_sizes = 0
    
    for size in component_sizes:
        total_pairs += sum_sizes * size  # Pairs between current and previous components
        sum_sizes += size  # Update the cumulative size sum
    
    return total_pairs