A tree is a connected graph without cycles. A rooted tree has a special vertex called the root. The parent of a vertex v (different from root) is the previous to v vertex on the shortest path from the root to the vertex v. Children of the vertex v are all vertices for which v is the parent.

A vertex is a leaf if it has no children. We call a vertex a bud, if the following three conditions are satisfied: 

  * it is not a root, 
  * it has at least one child, and 
  * all its children are leaves. 



You are given a rooted tree with n vertices. The vertex 1 is the root. In one operation you can choose any bud with all its children (they are leaves) and re-hang them to any other vertex of the tree. By doing that you delete the edge connecting the bud and its parent and add an edge between the bud and the chosen vertex of the tree. The chosen vertex cannot be the bud itself or any of its children. All children of the bud stay connected to the bud.

What is the minimum number of leaves it is possible to get if you can make any number of the above-mentioned operations (possibly zero)?

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows.

The first line of each test case contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of the vertices in the given tree.

Each of the next n-1 lines contains two integers u and v (1 ≤ u, v ≤ n, u ≠ v) meaning that there is an edge between vertices u and v in the tree.

It is guaranteed that the given graph is a tree.

It is guaranteed that the sum of n over all test cases doesn't exceed 2 ⋅ 10^5.

Output

For each test case print a single integer — the minimal number of leaves that is possible to get after some operations.

Example

Input


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


Output


2
2
1
2
1

Note

In the first test case the tree looks as follows:

<image>

Firstly you can choose a bud vertex 4 and re-hang it to vertex 3. After that you can choose a bud vertex 2 and re-hang it to vertex 7. As a result, you will have the following tree with 2 leaves:

<image>

It can be proved that it is the minimal number of leaves possible to get.

In the second test case the tree looks as follows:

<image>

You can choose a bud vertex 3 and re-hang it to vertex 5. As a result, you will have the following tree with 2 leaves:

<image>

It can be proved that it is the minimal number of leaves possible to get.

def divisors(M):
    d=[]
    i=1
    while M>=i**2:
        if M%i==0:
            d.append(i)
            if i**2!=M:
                d.append(M//i)
        i=i+1
    return d

def popcount(x):
    x = x - ((x >> 1) & 0x55555555)
    x = (x & 0x33333333) + ((x >> 2) & 0x33333333)
    x = (x + (x >> 4)) & 0x0f0f0f0f
    x = x + (x >> 8)
    x = x + (x >> 16)
    return x & 0x0000007f

def eratosthenes(n):
    res=[0 for i in range(n+1)]
    prime=set([])
    for i in range(2,n+1):
        if not res[i]:
            prime.add(i)
            for j in range(1,n//i+1):
                res[i*j]=1
    return prime

def factorization(n):
    res=[]
    for p in prime:
        if n%p==0:
            while n%p==0:
                n//=p
            res.append(p)
    if n!=1:
        res.append(n)
    return res

def euler_phi(n):
    res = n
    for x in range(2,n+1):
        if x ** 2 > n:
            break
        if n%x==0:
            res = res//x * (x-1)
            while n%x==0:
                n //= x
    if n!=1:
        res = res//n * (n-1)
    return res

def ind(b,n):
    res=0
    while n%b==0:
        res+=1
        n//=b
    return res

def isPrimeMR(n):
    d = n - 1
    d = d // (d & -d)
    L = [2, 3, 5, 7, 11, 13, 17]
    for a in L:
        t = d
        y = pow(a, t, n)
        if y == 1: continue
        while y != n - 1:
            y = (y * y) % n
            if y == 1 or t == n - 1: return 0
            t <<= 1
    return 1
def findFactorRho(n):
    from math import gcd
    m = 1 << n.bit_length() // 8
    for c in range(1, 99):
        f = lambda x: (x * x + c) % n
        y, r, q, g = 2, 1, 1, 1
        while g == 1:
            x = y
            for i in range(r):
                y = f(y)
            k = 0
            while k < r and g == 1:
                ys = y
                for i in range(min(m, r - k)):
                    y = f(y)
                    q = q * abs(x - y) % n
                g = gcd(q, n)
                k += m
            r <<= 1
        if g == n:
            g = 1
            while g == 1:
                ys = f(ys)
                g = gcd(abs(x - ys), n)
        if g < n:
            if isPrimeMR(g): return g
            elif isPrimeMR(n // g): return n // g
            return findFactorRho(g)
def primeFactor(n):
    i = 2
    ret = {}
    rhoFlg = 0
    while i*i <= n:
        k = 0
        while n % i == 0:
            n //= i
            k += 1
        if k: ret[i] = k
        i += 1 + i % 2
        if i == 101 and n >= 2 ** 20:
            while n > 1:
                if isPrimeMR(n):
                    ret[n], n = 1, 1
                else:
                    rhoFlg = 1
                    j = findFactorRho(n)
                    k = 0
                    while n % j == 0:
                        n //= j
                        k += 1
                    ret[j] = k

    if n > 1: ret[n] = 1
    if rhoFlg: ret = {x: ret[x] for x in sorted(ret)}
    return ret

def divisors(n):
    res = [1]
    prime = primeFactor(n)
    for p in prime:
        newres = []
        for d in res:
            for j in range(prime[p]+1):
                newres.append(d*p**j)
        res = newres
    res.sort()
    return res

def xorfactorial(num):
    if num==0:
        return 0
    elif num==1:
        return 1
    elif num==2:
        return 3
    elif num==3:
        return 0
    else:
        x=baseorder(num)
        return (2**x)*((num-2**x+1)%2)+function(num-2**x)

def xorconv(n,X,Y):
    if n==0:
        res=[(X[0]*Y[0])%mod]
        return res
    x=[X[i]+X[i+2**(n-1)] for i in range(2**(n-1))]
    y=[Y[i]+Y[i+2**(n-1)] for i in range(2**(n-1))]
    z=[X[i]-X[i+2**(n-1)] for i in range(2**(n-1))]
    w=[Y[i]-Y[i+2**(n-1)] for i in range(2**(n-1))]
    res1=xorconv(n-1,x,y)
    res2=xorconv(n-1,z,w)
    former=[(res1[i]+res2[i])*inv for i in range(2**(n-1))]
    latter=[(res1[i]-res2[i])*inv for i in range(2**(n-1))]
    former=list(map(lambda x:x%mod,former))
    latter=list(map(lambda x:x%mod,latter))
    return former+latter

def merge_sort(A,B):
    pos_A,pos_B = 0,0
    n,m = len(A),len(B)
    res = []
    while pos_A < n and pos_B < m:
        a,b = A[pos_A],B[pos_B]
        if a < b:
            res.append(a)
            pos_A += 1
        else:
            res.append(b)
            pos_B += 1
    res += A[pos_A:]
    res += B[pos_B:]
    return res

class UnionFindVerSize():
    def __init__(self, N):
        self._parent = [n for n in range(0, N)]
        self._size = [1] * N
        self.group = N

    def find_root(self, x):
        if self._parent[x] == x: return x
        self._parent[x] = self.find_root(self._parent[x])
        stack = [x]
        while self._parent[stack[-1]]!=stack[-1]:
            stack.append(self._parent[stack[-1]])
        for v in stack:
            self._parent[v] = stack[-1]
        return self._parent[x]

    def unite(self, x, y):
        gx = self.find_root(x)
        gy = self.find_root(y)
        if gx == gy: return

        self.group -= 1

        if self._size[gx] < self._size[gy]:
            self._parent[gx] = gy
            self._size[gy] += self._size[gx]
        else:
            self._parent[gy] = gx
            self._size[gx] += self._size[gy]

    def get_size(self, x):
        return self._size[self.find_root(x)]

    def is_same_group(self, x, y):
        return self.find_root(x) == self.find_root(y)

class WeightedUnionFind():
    def __init__(self,N):
        self.parent = [i for i in range(N)]
        self.size = [1 for i in range(N)]
        self.val = [0 for i in range(N)]
        self.flag = True
        self.edge = [[] for i in range(N)]

    def dfs(self,v,pv):
        stack = [(v,pv)]
        new_parent = self.parent[pv]
        while stack:
            v,pv = stack.pop()
            self.parent[v] = new_parent
            for nv,w in self.edge[v]:
                if nv!=pv:
                    self.val[nv] = self.val[v] + w
                    stack.append((nv,v))

    def unite(self,x,y,w):
        if not self.flag:
            return
        if self.parent[x]==self.parent[y]:
            self.flag = (self.val[x] - self.val[y] == w)
            return

        if self.size[self.parent[x]]>self.size[self.parent[y]]:
            self.edge[x].append((y,-w))
            self.edge[y].append((x,w))
            self.size[x] += self.size[y]
            self.val[y] = self.val[x] - w
            self.dfs(y,x)
        else:
            self.edge[x].append((y,-w))
            self.edge[y].append((x,w))
            self.size[y] += self.size[x]
            self.val[x] = self.val[y] + w
            self.dfs(x,y)

class Dijkstra():
    class Edge():
        def __init__(self, _to, _cost):
            self.to = _to
            self.cost = _cost

    def __init__(self, V):
        self.G = [[] for i in range(V)]
        self._E = 0
        self._V = V

    @property
    def E(self):
        return self._E

    @property
    def V(self):
        return self._V

    def add_edge(self, _from, _to, _cost):
        self.G[_from].append(self.Edge(_to, _cost))
        self._E += 1

    def shortest_path(self, s):
        import heapq
        que = []
        d = [10**15] * self.V
        d[s] = 0
        heapq.heappush(que, (0, s))

        while len(que) != 0:
            cost, v = heapq.heappop(que)
            if d[v] < cost: continue

            for i in range(len(self.G[v])):
                e = self.G[v][i]
                if d[e.to] > d[v] + e.cost:
                    d[e.to] = d[v] + e.cost
                    heapq.heappush(que, (d[e.to], e.to))
        return d

#Z[i]:length of the longest list starting from S[i] which is also a prefix of S
#O(|S|)
def Z_algorithm(s):
    N = len(s)
    Z_alg = [0]*N

    Z_alg[0] = N
    i = 1
    j = 0
    while i < N:
        while i+j < N and s[j] == s[i+j]:
            j += 1
        Z_alg[i] = j
        if j == 0:
            i += 1
            continue
        k = 1
        while i+k < N and k + Z_alg[k]<j:
            Z_alg[i+k] = Z_alg[k]
            k += 1
        i += k
        j -= k
    return Z_alg

class BIT():
    def __init__(self,n,mod=0):
        self.BIT = [0]*(n+1)
        self.num = n
        self.mod = mod

    def query(self,idx):
        res_sum = 0
        mod = self.mod
        while idx > 0:
            res_sum += self.BIT[idx]
            if mod:
                res_sum %= mod
            idx -= idx&(-idx)
        return res_sum

    #Ai += x O(logN)
    def update(self,idx,x):
        mod = self.mod
        while idx <= self.num:
            self.BIT[idx] += x
            if mod:
                self.BIT[idx] %= mod
            idx += idx&(-idx)
        return

class dancinglink():
    def __init__(self,n,debug=False):
        self.n = n
        self.debug = debug
        self._left = [i-1 for i in range(n)]
        self._right = [i+1 for i in range(n)]
        self.exist = [True for i in range(n)]

    def pop(self,k):
        if self.debug:
            assert self.exist[k]
        L = self._left[k]
        R = self._right[k]
        if L!=-1:
            if R!=self.n:
                self._right[L],self._left[R] = R,L
            else:
                self._right[L] = self.n
        elif R!=self.n:
            self._left[R] = -1
        self.exist[k] = False

    def left(self,idx,k=1):
        if self.debug:
            assert self.exist[idx]
        res = idx
        while k:
            res = self._left[res]
            if res==-1:
                break
            k -= 1
        return res

    def right(self,idx,k=1):
        if self.debug:
            assert self.exist[idx]
        res = idx
        while k:
            res = self._right[res]
            if res==self.n:
                break
            k -= 1
        return res

class SparseTable():
    def __init__(self,A,merge_func,ide_ele):
        N=len(A)
        n=N.bit_length()
        self.table=[[ide_ele for i in range(n)] for i in range(N)]
        self.merge_func=merge_func

        for i in range(N):
            self.table[i][0]=A[i]

        for j in range(1,n):
            for i in range(0,N-2**j+1):
                f=self.table[i][j-1]
                s=self.table[i+2**(j-1)][j-1]
                self.table[i][j]=self.merge_func(f,s)

    def query(self,s,t):
        b=t-s+1
        m=b.bit_length()-1
        return self.merge_func(self.table[s][m],self.table[t-2**m+1][m])

class BinaryTrie:
    class node:
        def __init__(self,val):
            self.left = None
            self.right = None
            self.max = val

    def __init__(self):
        self.root = self.node(-10**15)

    def append(self,key,val):
        pos = self.root
        for i in range(29,-1,-1):
            pos.max = max(pos.max,val)
            if key>>i & 1:
                if pos.right is None:
                    pos.right = self.node(val)
                    pos = pos.right
                else:
                    pos = pos.right
            else:
                if pos.left is None:
                    pos.left = self.node(val)
                    pos = pos.left
                else:
                    pos = pos.left
        pos.max = max(pos.max,val)

    def search(self,M,xor):
        res = -10**15
        pos = self.root
        for i in range(29,-1,-1):
            if pos is None:
                break

            if M>>i & 1:
                if xor>>i & 1:
                    if pos.right:
                        res = max(res,pos.right.max)
                    pos = pos.left
                else:
                    if pos.left:
                        res = max(res,pos.left.max)
                    pos = pos.right
            else:
                if xor>>i & 1:
                    pos = pos.right
                else:
                    pos = pos.left

        if pos:
            res = max(res,pos.max)
        return res

def solveequation(edge,ans,n,m):
    #edge=[[to,dire,id]...]
    x=[0]*m
    used=[False]*n
    for v in range(n):
        if used[v]:
            continue
        y = dfs(v)
        if y!=0:
            return False
    return x

    def dfs(v):
        used[v]=True
        r=ans[v]
        for to,dire,id in edge[v]:
            if used[to]:
                continue
            y=dfs(to)
            if dire==-1:
                x[id]=y
            else:
                x[id]=-y
            r+=y
        return r

class SegmentTree:
    def __init__(self, init_val, segfunc, ide_ele):
        n = len(init_val)
        self.segfunc = segfunc
        self.ide_ele = ide_ele
        self.num = 1 << (n - 1).bit_length()
        self.tree = [ide_ele] * 2 * self.num
        self.size = n
        for i in range(n):
            self.tree[self.num + i] = init_val[i]
        for i in range(self.num - 1, 0, -1):
            self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])

    def update(self, k, x):
        k += self.num
        self.tree[k] = x
        while k > 1:
            self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
            k >>= 1

    def query(self, l, r):
        if r==self.size:
            r = self.num

        res = self.ide_ele

        l += self.num
        r += self.num
        while l < r:
            if l & 1:
                res = self.segfunc(res, self.tree[l])
                l += 1
            if r & 1:
                res = self.segfunc(res, self.tree[r - 1])
            l >>= 1
            r >>= 1
        return res

    def bisect_l(self,l,r,x):
        l += self.num
        r += self.num
        Lmin = -1
        Rmin = -1
        while l<r:
            if l & 1:
                if self.tree[l] <= x and Lmin==-1:
                    Lmin = l
                l += 1
            if r & 1:
                if self.tree[r-1] <=x:
                    Rmin = r-1
            l >>= 1
            r >>= 1

        if Lmin != -1:
            pos = Lmin
            while pos<self.num:
                if self.tree[2 * pos] <=x:
                    pos = 2 * pos
                else:
                    pos = 2 * pos +1
            return pos-self.num
        elif Rmin != -1:
            pos = Rmin
            while pos<self.num:
                if self.tree[2 * pos] <=x:
                    pos = 2 * pos
                else:
                    pos = 2 * pos +1
            return pos-self.num
        else:
            return -1

import sys,random,bisect
from collections import deque,defaultdict
from heapq import heapify,heappop,heappush
from itertools import permutations
from math import gcd,log

input = lambda :sys.stdin.buffer.readline()
mi = lambda :map(int,input().split())
li = lambda :list(mi())

for _ in range(int(input())):
    N = int(input())
    edge = [[] for i in range(N)]
    for i in range(N-1):
        u,v = mi()
        edge[u-1].append(v-1)
        edge[v-1].append(u-1)

    deq = deque([0])
    parent = [-1 for v in range(N)]
    topo = []
    while deq:
        v = deq.popleft()
        topo.append(v)
        for nv in edge[v]:
            if nv!=parent[v]:
                parent[nv] = v
                deq.append(nv)
    
    leaf = [False for v in range(N)]
    bud_cnt = [0 for v in range(N)]
    
    res = 0
    for v in topo[::-1]:
        if v!=0 and len(edge[v])==1:
            res += 1
            leaf[v] = True
            continue
        for nv in edge[v]:
            if nv!=parent[v]:
                bud_cnt[v] += bud_cnt[nv]
        if any(leaf[nv] and nv!=parent[v] for nv in edge[v]):
            bud_cnt[v] += 1
        else:
            leaf[v] = True
            bud_cnt[v] -= 1
    
    #print(bud_cnt)
    minus = 0
    bud_cnt[0] = 0
    for v in topo:
        if v!=0 and len(edge[v])==1:
            minus = max(minus,bud_cnt[v])
        else:
            S = sum(bud_cnt[nv] for nv in edge[v] if nv!=parent[v])
            #print(S)
            for nv in edge[v]:
                if nv!=parent[v]:
                    bud_cnt[nv] = bud_cnt[v] + S - bud_cnt[nv]
    
    #print(bud_cnt)
    
    
    print(res-minus)

    
        

