1073_F. Choosing Two Paths
You are given an undirected unweighted tree consisting of n vertices.

An undirected tree is a connected undirected graph with n - 1 edges.

Your task is to choose two pairs of vertices of this tree (all the chosen vertices should be distinct) (x_1, y_1) and (x_2, y_2) in such a way that neither x_1 nor y_1 belong to the simple path from x_2 to y_2 and vice versa (neither x_2 nor y_2 should not belong to the simple path from x_1 to y_1).

It is guaranteed that it is possible to choose such pairs for the given tree.

Among all possible ways to choose such pairs you have to choose one with the maximum number of common vertices between paths from x_1 to y_1 and from x_2 to y_2. And among all such pairs you have to choose one with the maximum total length of these two paths.

It is guaranteed that the answer with at least two common vertices exists for the given tree.

The length of the path is the number of edges in it.

The simple path is the path that visits each vertex at most once.

Input

The first line contains an integer n — the number of vertices in the tree (6 ≤ n ≤ 2 ⋅ 10^5).

Each of the next n - 1 lines describes the edges of the tree.

Edge i is denoted by two integers u_i and v_i, the labels of vertices it connects (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i).

It is guaranteed that the given edges form a tree.

It is guaranteed that the answer with at least two common vertices exists for the given tree.

Output

Print any two pairs of vertices satisfying the conditions described in the problem statement.

It is guaranteed that it is possible to choose such pairs for the given tree.

Examples

Input

7
1 4
1 5
1 6
2 3
2 4
4 7


Output

3 6
7 5


Input

9
9 3
3 5
1 2
4 3
4 7
1 7
4 6
3 8


Output

2 9
6 8


Input

10
6 8
10 3
3 7
5 8
1 7
7 2
2 9
2 8
1 4


Output

10 6
4 5


Input

11
1 2
2 3
3 4
1 5
1 6
6 7
5 8
5 9
4 10
4 11


Output

9 11
8 10

Note

The picture corresponding to the first example: <image>

The intersection of two paths is 2 (vertices 1 and 4) and the total length is 4 + 3 = 7.

The picture corresponding to the second example: <image>

The intersection of two paths is 2 (vertices 3 and 4) and the total length is 5 + 3 = 8.

The picture corresponding to the third example: <image>

The intersection of two paths is 3 (vertices 2, 7 and 8) and the total length is 5 + 5 = 10.

The picture corresponding to the fourth example: <image>

The intersection of two paths is 5 (vertices 1, 2, 3, 4 and 5) and the total length is 6 + 6 = 12.
```python
import sys

n = int(sys.stdin.readline())
edges = [[] for _ in range(n)]
for _ in range(n - 1):
    i, j = tuple(int(k) for k in sys.stdin.readline().split())
    i -= 1
    j -= 1
    edges[i].append(j)
    edges[j].append(i)

# Prunes the graph starting from the vertices with
# only 1 edge until we reach a vertex with 3+ edges.
# Stores the distance from each non-pruned vertex
# to each of the leaves it reaches.
def prune():
    pruned = [False for _ in range(n)]
    leaves = [[] for _ in range(n)]
    todo = []
    for i in range(n):
        if len(edges[i]) == 1:
            todo.append((0, i, i))
    while len(todo) > 0:
        d, i, j = todo.pop()
        pruned[j] = True
        for k in edges[j]:
            if not pruned[k]:
                if len(edges[k]) < 3:
                    todo.append((d + 1, i, k))
                else:
                    leaves[k].append((d + 1, i))
    return pruned, leaves

pruned, leaves = prune()

# Returns the furthest non-pruned vertices
# from another non-pruned vertex.
def furthest(i):
    assert not pruned[i]
    visited = list(pruned)
    top_distance = 0
    top_vertices = [i]
    todo = [(0, i)]
    while len(todo) > 0:
        d, i = todo.pop()
        visited[i] = True
        if d > top_distance:
            top_distance = d
            top_vertices = []
        if d == top_distance:
            top_vertices.append(i)
        for j in edges[i]:
            if not visited[j]:
                todo.append((d + 1, j))
    return top_distance, top_vertices

# Single center topology.
# Only 1 vertex with 3+ edges.
def solve_single_center(i):
    l = list(reversed(sorted(leaves[i])))[:4]
    return list(l[j][1] for j in range(4))

# Scores non-pruned vertices according to the sum
# of the distances to their two furthest leaves.
def vertices_score(v):
    scores = []
    for i in v:
        assert not pruned[i]
        l = list(reversed(sorted(leaves[i])))[:2]
        score = (l[0][0] + l[1][0]), l[0][1], l[1][1]
        scores.append(score)
    return list(reversed(sorted(scores)))

# Single cluster topology.
# 1 cluster of vertices, all equally far away from each other.
def solve_single_cluster(v):
    scores = vertices_score(v)[:2]
    return scores[0][1], scores[1][1], scores[0][2], scores[1][2]

# Double cluster topology.
# 2 clusters of vertices, pairwise equally far away from each other.
def solve_double_cluster(v1, v2):
    scores1 = vertices_score(v1)[:1]
    scores2 = vertices_score(v2)[:1]
    return scores1[0][1], scores2[0][1], scores1[0][2], scores2[0][2]

def solve():
    def start_vertex():
        for i in range(n):
            if not pruned[i]:
                return i
    i = start_vertex()
    distance, v1 = furthest(i)
    if distance == 0:
        return solve_single_center(v1[0])
    else:
        distance, v1 = furthest(v1[0])
        distance, v2 = furthest(v1[0])
        v = list(set(v1) | set(v2))
        if len(v) < len(v1) + len(v2):
            return solve_single_cluster(v)
        else:
            return solve_double_cluster(v1, v2)

a, b, c, d = solve()
print(a + 1, b + 1)
print(c + 1, d + 1)

```