You are given an undirected tree consisting of $n$ vertices. An undirected tree is a connected undirected graph with $n - 1$ edges.

Your task is to add the minimum number of edges in such a way that the length of the shortest path from the vertex $1$ to any other vertex is at most $2$. Note that you are not allowed to add loops and multiple edges.


-----Input-----

The first line contains one integer $n$ ($2 \le n \le 2 \cdot 10^5$) — the number of vertices in the tree.

The following $n - 1$ lines contain edges: edge $i$ is given as a pair of vertices $u_i, v_i$ ($1 \le u_i, v_i \le n$). It is guaranteed that the given edges form a tree. It is guaranteed that there are no loops and multiple edges in the given edges.


-----Output-----

Print a single integer — the minimum number of edges you have to add in order to make the shortest distance from the vertex $1$ to any other vertex at most $2$. Note that you are not allowed to add loops and multiple edges.


-----Examples-----
Input
7
1 2
2 3
2 4
4 5
4 6
5 7

Output
2

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

Output
0

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

Output
1



-----Note-----

The tree corresponding to the first example: [Image] The answer is $2$, some of the possible answers are the following: $[(1, 5), (1, 6)]$, $[(1, 4), (1, 7)]$, $[(1, 6), (1, 7)]$.

The tree corresponding to the second example: [Image] The answer is $0$.

The tree corresponding to the third example: [Image] The answer is $1$, only one possible way to reach it is to add the edge $(1, 3)$.

Difficulty: introductory

Starter code:

Solutions:
from sys import stdin
n = int(stdin.readline())
g = dict()
for i in range(n-1):
    u,v = map(int,stdin.readline().split())
    g.setdefault(u-1,[]).append(v-1)
    g.setdefault(v-1, []).append(u-1)
st = [0]
rank = [0]*n
tree = [0]*n
msk = [0]*n
rd = dict()
while len(st)>0:
    top = st.pop()
    msk[top] = 1
    for c in g[top]:
        if msk[c] == 0:
            st.append(c)
            tree[c] = top
            rank[c] = rank[top]+1
            rd.setdefault(rank[c], []).append(c)
max_rank = max(rank)
reach = [0]*n
build = [0]*n
ans = 0
for r in range(max_rank, 2, -1):
    for node in rd[r]:
        if reach[node] == 0:
            reach[node] = 1
            reach[tree[node]] = 1
            reach[tree[tree[node]]] = 1
            build[tree[node]] = 1
print(sum(build))

import sys
from collections import deque
import heapq
input = sys.stdin.readline

N=int(input())
EDGE=[list(map(int,input().split())) for i in range(N-1)]

EDGELIST=[[] for i in range(N+1)]

for i,j in EDGE:
    EDGELIST[i].append(j)
    EDGELIST[j].append(i)

#EDGES=[[] for i in range(N+1)]
REDG=[None for i in range(N+1)]
QUE=deque([1])
check=[0]*(N+1)
DEPTH=[None]*(N+1)
i=0
while QUE:
    NQUE=deque()
    i+=1
    
    while QUE:
        x=QUE.pop()
        DEPTH[x]=i
        check[x]=1
        for to in EDGELIST[x]:
            if check[to]==1:
                continue
            else:
                #EDGES[x].append(to)
                REDG[to]=x
                NQUE.append(to)
    QUE=NQUE


check=[0]*(N+1)
check[1]=1
#NEXT=[]

#for i in EDGES[1]:
#    check[i]=1
#    NEXT.append(i)

#for j in NEXT:
#    for k in EDGES[j]:
#        check[k]=1


LEAF=[]
for i in range(2,N+1):
    if len(EDGELIST[i])==1:
        LEAF.append((-DEPTH[i],i))

QUE=LEAF
heapq.heapify(QUE)
ANS=0

#print(check,QUE)

while QUE:
    dep,x=heapq.heappop(QUE)
    if check[x]!=0 or dep>=-3:
        continue

    if check[REDG[x]]==2:
        continue

    if check[x]==0:
        check[x]=1
    if check[REDG[REDG[x]]]==0:
        check[REDG[REDG[x]]]=1
    check[REDG[x]]=2   
    heapq.heappush(QUE,(-DEPTH[REDG[REDG[REDG[x]]]],REDG[REDG[REDG[x]]]))
    ANS+=1

    #print(x,QUE,check)

print(ANS)





import sys
from collections import deque
mod = 10**9+7
INF = float('inf')
def inp(): return int(sys.stdin.readline())
def inpl(): return list(map(int, sys.stdin.readline().split()))

n = inp()
edges = [[] for _ in range(n)]
for _ in range(n-1):
    a,b = inpl()
    a,b = a-1,b-1
    edges[a].append(b)
    edges[b].append(a)
dist = [-1] * n
dist[0] = 0
pa = [-1] * n
se = set()
pq = []
q = deque()
q.append(0)
while q:
    now = q.popleft()
    for nx in edges[now]:
        if dist[nx] != -1:
            continue
        pa[nx] = now
        dist[nx] = dist[now] + 1
        if dist[nx] > 2:
            se.add(nx)
            pq.append((dist[nx], nx))
        q.append(nx)
pq = pq[::-1]
res = 0
ind = 0
while se:
    d,v = pq[ind]
    ind += 1
    if not v in se: 
        continue
    res += 1
    pv = pa[v]
    se.discard(pv)
    for nv in edges[pv]:
        se.discard(nv)
print(res)


import sys

def get_new_edges(graph):
    n = len(graph)
    far_vertex = []
    pi = [None]*n
    visit = [False]*n
    visit[0]
    queue = [[0,0]]
    i = 0    
    while True:
        if i >= len(queue): break
        current, d = queue[i]
        i += 1
        visit[current] = True
        for v in graph[current]:
            if not visit[v]:
                u = [v, d+1]
                pi[v] = current
                queue.append(u)
                if d+1 > 2:
                    far_vertex.append(u)
    
    far_vertex.sort(key=lambda x: -x[1])

    pos = [None]*n
    for i, e in enumerate(far_vertex):
        pos[e[0]] = i

    count = 0
    for i in range(len(far_vertex)):
        if not far_vertex[i]: continue
        vertex, depth = far_vertex[i]
        father = pi[vertex]
        count += 1
        if pos[father]:
            far_vertex[pos[father]] = None
        for u in graph[father]:
            if pos[u]:
                far_vertex[pos[u]] = None

    return count
    
def read_int_line():
    return list(map(int, sys.stdin.readline().split()))

vertex_count = int(input())
graph = [[] for _ in range(vertex_count)]

for i in range(vertex_count - 1):
    v1, v2 = read_int_line()
    v1 -= 1
    v2 -= 1
    graph[v1].append(v2)
    graph[v2].append(v1)

print(get_new_edges(graph))