Find the path with the minimum number of transfers between stations?

Question

Input data format N (number of edges, 1 ≤ N ≤ 1000),

next N lines with a pair of numbers for vertices, two numbers representing the start and end stations.

Output data format Number of transfers.

If there are no paths between stations, output "No path found".

** Example 1**

Input data:

4
1 2
2 3
3 4
4 5
1 5

Output:

3

import heapq

def min_transfers(edges, start, end):
    graph = {}
    for u, v in edges:
        graph.setdefault(u, []).append(v)
        graph.setdefault(v, []).append(u)  # Make the graph undirected

    dist = {}
    pq = [(0, start)]
    while pq:
        transfers, vertex = heapq.heappop(pq)
        if vertex not in dist:
            dist[vertex] = transfers
            if vertex == end:
                return transfers
            for neighbor in graph[vertex]:
                heapq.heappush(pq, (transfers + 1, neighbor))

    return "No path found"

# Example usage
edges = [
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5)
]
start = 1
end = 5

min_transfers = min_transfers(edges, start, end)
print(min_transfers)  #

Why it turns out to be 4 and not 3. How to fix it?