human
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:


Firstly you can choose...
The above is tricky. Write me a correct solution in PYTHON3.
 ... Give me a Python program to print a single integer — the minimal number of leaves that is possible to get after some operations?
assistant
#Here is Python program to print a single integer — the minimal number of leaves that is possible to get after some operations.

#!/usr/bin/env python
from __future__ import division, print_function

import os
import sys
from io import BytesIO, IOBase

if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from future_builtins import ascii, filter, hex, map, oct, zip

def dfs(graph, start=0):
    n = len(graph)

    dp = [0] * n
    visited, finished = [False] * n, [False] * n

    stack = [start]
    while stack:
        start = stack[-1]

        # push unvisited children into stack
        if not visited[start]:
            visited[start] = True
            for child in graph[start]:
                if not visited[child]:
                    stack.append(child)

        else:
            stack.pop()

            # base case
            dp[start] += 1

            # update with finished children
            for child in graph[start]:
                if finished[child]:
                    dp[start] += dp[child]

            if dp[start] > 1:
                dp[start] = 0

            finished[start] = True

    return dp

def main():
    t = int(input())

    for _ in range(t):
        n = int(input())

        tree = [[] for _ in range(n)]
        for _ in range(n - 1):
            u, v = map(int, input().split())
            tree[u - 1].append(v - 1)
            tree[v - 1].append(u - 1)

        dp = dfs(tree)

        print(sum([1 if i == 1 else -1 for i in dfs(tree)]) + (dp[0] == 0))

# region fastio

BUFSIZE = 8192

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return...