Astralis session I

def main():
    first_line = input().split()
    n = int(first_line[0])

    if n % 2 != 0:
        print("No")
        return

    adj_list = {c: [] for c in range(1, n + 1)}
    
    for _ in range(n - 1):
        gal1, gal2 = [int(x) for x in input().split()]
        adj_list[gal1].append(gal2)
        adj_list[gal2].append(gal1)

    subtree_size = {c: 1 for c in range(1, n + 1)}
    parent = {c: 0 for c in range(1, n + 1)}
    order = []
    stack = [1]
    visited = {c: False for c in range(1, n + 1)}
    visited[1] = True
    
    while stack:
        curr = stack.pop()
        order.append(curr)
        for neighbor in adj_list[curr]:
            if not visited[neighbor]:
                visited[neighbor] = True
                parent[neighbor] = curr
                stack.append(neighbor)
#equal sizes                
    split_node = -1
    for node in reversed(order):
        p = parent[node]
        if p != 0:
            subtree_size[p] += subtree_size[node]
        if subtree_size[node] == n // 2:
            split_node = node

    if split_node == -1:
        print("No")
        return

    assignment = ['M'] * (n + 1)
    
    stack = [split_node]
    component_visited = {c: False for c in range(1, n + 1)}
    component_visited[split_node] = True
    
    while stack:
        curr = stack.pop()
        assignment[curr] = 'U'
        for neighbor in adj_list[curr]:
            if neighbor != parent[split_node] and not component_visited[neighbor]:
                component_visited[neighbor] = True
                stack.append(neighbor)

    print("Yes")
    print("".join(assignment[1:]))

main()

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED

Test 14

Verdict: ACCEPTED

Test 15

Verdict: ACCEPTED

Test 16

Verdict: ACCEPTED

Test 17

Verdict: ACCEPTED

Test 18

Verdict: ACCEPTED

Test 19

Verdict: ACCEPTED

Test 20

Verdict: ACCEPTED

Test 21

Verdict: ACCEPTED

Test 22

Verdict: ACCEPTED

Test 23

Verdict: ACCEPTED

Test 24

Verdict: ACCEPTED

Test 25

Verdict: ACCEPTED

Test 26

Verdict: ACCEPTED

Test 27

Verdict: ACCEPTED

Test 28

Verdict: ACCEPTED

Test 29

Verdict: ACCEPTED

Test 30

Verdict: ACCEPTED

Test 31

Verdict: ACCEPTED

Test 32

Verdict: ACCEPTED

Test 33

Verdict: ACCEPTED

Test 34

Verdict: ACCEPTED

Test 35

Verdict: ACCEPTED

Test 36

Verdict: ACCEPTED

Test 37

Verdict: ACCEPTED

Test 38

Verdict: ACCEPTED

Test 39

Verdict: ACCEPTED

Test 40

Verdict: ACCEPTED

Test 41

Verdict: ACCEPTED

Test 42

Verdict: ACCEPTED

Test 43

Verdict: ACCEPTED

Test 44

Verdict: ACCEPTED

Test 45

Verdict: ACCEPTED

Test 46

Verdict: ACCEPTED

Test 47

Verdict: ACCEPTED

Test 48

Verdict: ACCEPTED

Test 49

Verdict: ACCEPTED

Test 50

Verdict: ACCEPTED

Test 51

Verdict: ACCEPTED

Test 52

Verdict: ACCEPTED

Test 53

Verdict: ACCEPTED

Test 54

Verdict: ACCEPTED

Test 55

Verdict: ACCEPTED

Test 56

Verdict: ACCEPTED

Test 57

Verdict: ACCEPTED

Test 58

Verdict: ACCEPTED

Test 59

Verdict: ACCEPTED

Test 60

Verdict: ACCEPTED

Test 61

Verdict: ACCEPTED