Consider an infinite triangle made up of layers. Let's number the layers, starting from one, from the top of the triangle (from top to bottom). The k-th layer of the triangle contains k points, numbered from left to right. Each point of an infinite triangle is described by a pair of numbers (r, c) (1 ≤ c ≤ r), where r is the number of the layer, and c is the number of the point in the layer. From each point (r, c) there are two directed edges to the points (r+1, c) and (r+1, c+1), but only one of the edges is activated. If r + c is even, then the edge to the point (r+1, c) is activated, otherwise the edge to the point (r+1, c+1) is activated. Look at the picture for a better understanding.

<image> Activated edges are colored in black. Non-activated edges are colored in gray.

From the point (r_1, c_1) it is possible to reach the point (r_2, c_2), if there is a path between them only from activated edges. For example, in the picture above, there is a path from (1, 1) to (3, 2), but there is no path from (2, 1) to (1, 1).

Initially, you are at the point (1, 1). For each turn, you can: 

  * Replace activated edge for point (r, c). That is if the edge to the point (r+1, c) is activated, then instead of it, the edge to the point (r+1, c+1) becomes activated, otherwise if the edge to the point (r+1, c+1), then instead if it, the edge to the point (r+1, c) becomes activated. This action increases the cost of the path by 1; 
  * Move from the current point to another by following the activated edge. This action does not increase the cost of the path. 



You are given a sequence of n points of an infinite triangle (r_1, c_1), (r_2, c_2), …, (r_n, c_n). Find the minimum cost path from (1, 1), passing through all n points in arbitrary order.

Input

The first line contains one integer t (1 ≤ t ≤ 10^4) is the number of test cases. Then t test cases follow.

Each test case begins with a line containing one integer n (1 ≤ n ≤ 2 ⋅ 10^5) is the number of points to visit.

The second line contains n numbers r_1, r_2, …, r_n (1 ≤ r_i ≤ 10^9), where r_i is the number of the layer in which i-th point is located.

The third line contains n numbers c_1, c_2, …, c_n (1 ≤ c_i ≤ r_i), where c_i is the number of the i-th point in the r_i layer.

It is guaranteed that all n points are distinct.

It is guaranteed that there is always at least one way to traverse all n points.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, output the minimum cost of a path passing through all points in the corresponding test case.

Example

Input


4
3
1 4 2
1 3 1
2
2 4
2 3
2
1 1000000000
1 1000000000
4
3 10 5 8
2 5 2 4


Output


0
1
999999999
2
# ---------------------------iye ha aam zindegi---------------------------------------------
import math
import random
import heapq, bisect
import sys
from collections import deque, defaultdict
from fractions import Fraction
import sys
#import threading
from collections import defaultdict
#threading.stack_size(10**8)
mod = 10 ** 9 + 7
mod1 = 998244353

# ------------------------------warmup----------------------------
import os
import sys
from io import BytesIO, IOBase
#sys.setrecursionlimit(300000)

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 self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")


# -------------------game starts now----------------------------------------------------import math
class TreeNode:
    def __init__(self, k, v):
        self.key = k
        self.value = v
        self.left = None
        self.right = None
        self.parent = None
        self.height = 1
        self.num_left = 1
        self.num_total = 1


class AvlTree:

    def __init__(self):
        self._tree = None

    def add(self, k, v):
        if not self._tree:
            self._tree = TreeNode(k, v)
            return
        node = self._add(k, v)
        if node:
            self._rebalance(node)

    def _add(self, k, v):
        node = self._tree
        while node:
            if k < node.key:
                if node.left:
                    node = node.left
                else:
                    node.left = TreeNode(k, v)
                    node.left.parent = node
                    return node.left
            elif node.key < k:
                if node.right:
                    node = node.right
                else:
                    node.right = TreeNode(k, v)
                    node.right.parent = node
                    return node.right
            else:
                node.value = v
                return

    @staticmethod
    def get_height(x):
        return x.height if x else 0

    @staticmethod
    def get_num_total(x):
        return x.num_total if x else 0

    def _rebalance(self, node):

        n = node
        while n:
            lh = self.get_height(n.left)
            rh = self.get_height(n.right)
            n.height = max(lh, rh) + 1
            balance_factor = lh - rh
            n.num_total = 1 + self.get_num_total(n.left) + self.get_num_total(n.right)
            n.num_left = 1 + self.get_num_total(n.left)

            if balance_factor > 1:
                if self.get_height(n.left.left) < self.get_height(n.left.right):
                    self._rotate_left(n.left)
                self._rotate_right(n)
            elif balance_factor < -1:
                if self.get_height(n.right.right) < self.get_height(n.right.left):
                    self._rotate_right(n.right)
                self._rotate_left(n)
            else:
                n = n.parent

    def _remove_one(self, node):
        """
        Side effect!!! Changes node. Node should have exactly one child
        """
        replacement = node.left or node.right
        if node.parent:
            if AvlTree._is_left(node):
                node.parent.left = replacement
            else:
                node.parent.right = replacement
            replacement.parent = node.parent
            node.parent = None
        else:
            self._tree = replacement
            replacement.parent = None
        node.left = None
        node.right = None
        node.parent = None
        self._rebalance(replacement)

    def _remove_leaf(self, node):
        if node.parent:
            if AvlTree._is_left(node):
                node.parent.left = None
            else:
                node.parent.right = None
            self._rebalance(node.parent)
        else:
            self._tree = None
        node.parent = None
        node.left = None
        node.right = None

    def remove(self, k):
        node = self._get_node(k)
        if not node:
            return
        if AvlTree._is_leaf(node):
            self._remove_leaf(node)
            return
        if node.left and node.right:
            nxt = AvlTree._get_next(node)
            node.key = nxt.key
            node.value = nxt.value
            if self._is_leaf(nxt):
                self._remove_leaf(nxt)
            else:
                self._remove_one(nxt)
            self._rebalance(node)
        else:
            self._remove_one(node)

    def get(self, k):
        node = self._get_node(k)
        return node.value if node else -1

    def _get_node(self, k):
        if not self._tree:
            return None
        node = self._tree
        while node:
            if k < node.key:
                node = node.left
            elif node.key < k:
                node = node.right
            else:
                return node
        return None

    def get_at(self, pos):
        x = pos + 1
        node = self._tree
        while node:
            if x < node.num_left:
                node = node.left
            elif node.num_left < x:
                x -= node.num_left
                node = node.right
            else:
                return (node.key, node.value)
        raise IndexError("Out of ranges")

    @staticmethod
    def _is_left(node):
        return node.parent.left and node.parent.left == node

    @staticmethod
    def _is_leaf(node):
        return node.left is None and node.right is None

    def _rotate_right(self, node):
        if not node.parent:
            self._tree = node.left
            node.left.parent = None
        elif AvlTree._is_left(node):
            node.parent.left = node.left
            node.left.parent = node.parent
        else:
            node.parent.right = node.left
            node.left.parent = node.parent
        bk = node.left.right
        node.left.right = node
        node.parent = node.left
        node.left = bk
        if bk:
            bk.parent = node
        node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1
        node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right)
        node.num_left = 1 + self.get_num_total(node.left)

    def _rotate_left(self, node):
        if not node.parent:
            self._tree = node.right
            node.right.parent = None
        elif AvlTree._is_left(node):
            node.parent.left = node.right
            node.right.parent = node.parent
        else:
            node.parent.right = node.right
            node.right.parent = node.parent
        bk = node.right.left
        node.right.left = node
        node.parent = node.right
        node.right = bk
        if bk:
            bk.parent = node
        node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1
        node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right)
        node.num_left = 1 + self.get_num_total(node.left)

    @staticmethod
    def _get_next(node):
        if not node.right:
            return node.parent
        n = node.right
        while n.left:
            n = n.left
        return n

class SegmentTree2:
    def __init__(self, data, default=3000006, func=lambda a, b: min(a,b)):
        """initialize the segment tree with data"""
        self._default = default
        self._func = func
        self._len = len(data)
        self._size = _size = 1 << (self._len - 1).bit_length()

        self.data = [default] * (2 * _size)
        self.data[_size:_size + self._len] = data
        for i in reversed(range(_size)):
            self.data[i] = func(self.data[i + i], self.data[i + i + 1])

    def __delitem__(self, idx):
        self[idx] = self._default

    def __getitem__(self, idx):
        return self.data[idx + self._size]

    def __setitem__(self, idx, value):
        idx += self._size
        self.data[idx] = value
        idx >>= 1
        while idx:
            self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
            idx >>= 1

    def __len__(self):
        return self._len

    def query(self, start, stop):
        if start == stop:
            return self.__getitem__(start)
        stop += 1
        start += self._size
        stop += self._size

        res = self._default
        while start < stop:
            if start & 1:
                res = self._func(res, self.data[start])
                start += 1
            if stop & 1:
                stop -= 1
                res = self._func(res, self.data[stop])
            start >>= 1
            stop >>= 1
        return res

    def __repr__(self):
        return "SegmentTree({0})".format(self.data)
# -----------------------------------------------binary seacrh tree---------------------------------------
class SegmentTree1:
    def __init__(self, data, default=10**10, func=lambda a, b: min(a , b)):
        """initialize the segment tree with data"""
        self._default = default
        self._func = func
        self._len = len(data)
        self._size = _size = 1 << (self._len - 1).bit_length()

        self.data = [default] * (2 * _size)
        self.data[_size:_size + self._len] = data
        for i in reversed(range(_size)):
            self.data[i] = func(self.data[i + i], self.data[i + i + 1])

    def __delitem__(self, idx):
        self[idx] = self._default

    def __getitem__(self, idx):
        return self.data[idx + self._size]

    def __setitem__(self, idx, value):
        idx += self._size
        self.data[idx] = value
        idx >>= 1
        while idx:
            self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
            idx >>= 1

    def __len__(self):
        return self._len

    def query(self, start, stop):
        if start == stop:
            return self.__getitem__(start)
        stop += 1
        start += self._size
        stop += self._size

        res = self._default
        while start < stop:
            if start & 1:
                res = self._func(res, self.data[start])
                start += 1
            if stop & 1:
                stop -= 1
                res = self._func(res, self.data[stop])
            start >>= 1
            stop >>= 1
        return res

    def __repr__(self):
        return "SegmentTree({0})".format(self.data)


# -------------------game starts now----------------------------------------------------import math
class SegmentTree:
    def __init__(self, data, default=0, func=lambda a, b:a + b):
        """initialize the segment tree with data"""
        self._default = default
        self._func = func
        self._len = len(data)
        self._size = _size = 1 << (self._len - 1).bit_length()

        self.data = [default] * (2 * _size)
        self.data[_size:_size + self._len] = data
        for i in reversed(range(_size)):
            self.data[i] = func(self.data[i + i], self.data[i + i + 1])

    def __delitem__(self, idx):
        self[idx] = self._default

    def __getitem__(self, idx):
        return self.data[idx + self._size]

    def __setitem__(self, idx, value):
        idx += self._size
        self.data[idx] = value
        idx >>= 1
        while idx:
            self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
            idx >>= 1

    def __len__(self):
        return self._len

    def query(self, start, stop):
        if start == stop:
            return self.__getitem__(start)
        stop += 1
        start += self._size
        stop += self._size

        res = self._default
        while start < stop:
            if start & 1:
                res = self._func(res, self.data[start])
                start += 1
            if stop & 1:
                stop -= 1
                res = self._func(res, self.data[stop])
            start >>= 1
            stop >>= 1
        return res

    def __repr__(self):
        return "SegmentTree({0})".format(self.data)


# -------------------------------iye ha chutiya zindegi-------------------------------------
class Factorial:
    def __init__(self, MOD):
        self.MOD = MOD
        self.factorials = [1, 1]
        self.invModulos = [0, 1]
        self.invFactorial_ = [1, 1]

    def calc(self, n):
        if n <= -1:
            print("Invalid argument to calculate n!")
            print("n must be non-negative value. But the argument was " + str(n))
            exit()
        if n < len(self.factorials):
            return self.factorials[n]
        nextArr = [0] * (n + 1 - len(self.factorials))
        initialI = len(self.factorials)
        prev = self.factorials[-1]
        m = self.MOD
        for i in range(initialI, n + 1):
            prev = nextArr[i - initialI] = prev * i % m
        self.factorials += nextArr
        return self.factorials[n]

    def inv(self, n):
        if n <= -1:
            print("Invalid argument to calculate n^(-1)")
            print("n must be non-negative value. But the argument was " + str(n))
            exit()
        p = self.MOD
        pi = n % p
        if pi < len(self.invModulos):
            return self.invModulos[pi]
        nextArr = [0] * (n + 1 - len(self.invModulos))
        initialI = len(self.invModulos)
        for i in range(initialI, min(p, n + 1)):
            next = -self.invModulos[p % i] * (p // i) % p
            self.invModulos.append(next)
        return self.invModulos[pi]

    def invFactorial(self, n):
        if n <= -1:
            print("Invalid argument to calculate (n^(-1))!")
            print("n must be non-negative value. But the argument was " + str(n))
            exit()
        if n < len(self.invFactorial_):
            return self.invFactorial_[n]
        self.inv(n)  # To make sure already calculated n^-1
        nextArr = [0] * (n + 1 - len(self.invFactorial_))
        initialI = len(self.invFactorial_)
        prev = self.invFactorial_[-1]
        p = self.MOD
        for i in range(initialI, n + 1):
            prev = nextArr[i - initialI] = (prev * self.invModulos[i % p]) % p
        self.invFactorial_ += nextArr
        return self.invFactorial_[n]


class Combination:
    def __init__(self, MOD):
        self.MOD = MOD
        self.factorial = Factorial(MOD)

    def ncr(self, n, k):
        if k < 0 or n < k:
            return 0
        k = min(k, n - k)
        f = self.factorial
        return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD


# --------------------------------------iye ha combinations ka zindegi---------------------------------
def powm(a, n, m):
    if a == 1 or n == 0:
        return 1
    if n % 2 == 0:
        s = powm(a, n // 2, m)
        return s * s % m
    else:
        return a * powm(a, n - 1, m) % m


# --------------------------------------iye ha power ka zindegi---------------------------------
def sort_list(list1, list2):
    zipped_pairs = zip(list2, list1)

    z = [x for _, x in sorted(zipped_pairs)]

    return z


# --------------------------------------------------product----------------------------------------
def product(l):
    por = 1
    for i in range(len(l)):
        por *= l[i]
    return por


# --------------------------------------------------binary----------------------------------------
def binarySearchCount(arr, n, key):
    left = 0
    right = n - 1

    count = 0

    while (left <= right):
        mid = int((right + left) / 2)

        # Check if middle element is
        # less than or equal to key
        if (arr[mid] <=key):
            count = mid + 1
            left = mid + 1

        # If key is smaller, ignore right half
        else:
            right = mid - 1

    return count


# --------------------------------------------------binary----------------------------------------
def countdig(n):
    c = 0
    while (n > 0):
        n //= 10
        c += 1
    return c
def binary(x, length):
    y = bin(x)[2:]
    return y if len(y) >= length else "0" * (length - len(y)) + y

def countGreater(arr, n, k):
    l = 0
    r = n - 1

    # Stores the index of the left most element
    # from the array which is greater than k
    leftGreater = n

    # Finds number of elements greater than k
    while (l <= r):
        m = int(l + (r - l) / 2)
        if (arr[m] > k):
            leftGreater = m
            r = m - 1

        # If mid element is less than
        # or equal to k update l
        else:
            l = m + 1

    # Return the count of elements
    # greater than k
    return (n - leftGreater)


# --------------------------------------------------binary------------------------------------
class TrieNode:
    def __init__(self):
        self.children = [None] * 26
        self.isEndOfWord = False
class Trie:
    def __init__(self):
        self.root = self.getNode()
    def getNode(self):
        return TrieNode()
    def _charToIndex(self, ch):
        return ord(ch) - ord('a')
    def insert(self, key):
        pCrawl = self.root
        length = len(key)
        for level in range(length):
            index = self._charToIndex(key[level])
            if not pCrawl.children[index]:
                pCrawl.children[index] = self.getNode()
            pCrawl = pCrawl.children[index]
        pCrawl.isEndOfWord = True
    def search(self, key):
        pCrawl = self.root
        length = len(key)
        for level in range(length):
            index = self._charToIndex(key[level])
            if not pCrawl.children[index]:
                return False
            pCrawl = pCrawl.children[index]
        return pCrawl != None and pCrawl.isEndOfWord
#-----------------------------------------trie---------------------------------
class Node:
    def __init__(self, data):
        self.data = data
        self.count=0
        self.left = None  # left node for 0
        self.right = None  # right node for 1
class BinaryTrie:
    def __init__(self):
        self.root = Node(0)
    def insert(self, pre_xor,t):
        self.temp = self.root
        for i in range(31, -1, -1):
            val = pre_xor & (1 << i)
            if val:
                if not self.temp.right:
                    self.temp.right = Node(0)
                self.temp = self.temp.right
                self.temp.count+=t
            if not val:
                if not self.temp.left:
                    self.temp.left = Node(0)
                self.temp = self.temp.left
                self.temp.count += t
        self.temp.data = pre_xor
    def query(self, p,l):
        ans=0
        self.temp = self.root
        for i in range(31, -1, -1):
            val = p & (1 << i)
            val1= l & (1<<i)
            if val1==0:
                if val==0:
                    if self.temp.left and self.temp.left.count>0:
                        self.temp = self.temp.left
                    else:
                        return ans
                else:
                    if self.temp.right and self.temp.right.count>0:
                        self.temp = self.temp.right
                    else:
                        return ans
            else:
                if val !=0 :
                    if self.temp.right:
                        ans+=self.temp.right.count
                    if self.temp.left and self.temp.left.count > 0:
                        self.temp = self.temp.left
                    else:
                        return ans
                else:
                    if self.temp.left:
                        ans += self.temp.left.count
                    if self.temp.right and self.temp.right.count > 0:
                        self.temp = self.temp.right
                    else:
                        return ans
        return ans
#-------------------------bin trie-------------------------------------------
for ik in range(int(input())):
    n=int(input())
    a=list(map(int,input().split()))
    b=list(map(int,input().split()))
    b=sort_list(b,a)
    a.sort()
    last=1
    last1=1
    ans=0
    for i in range(n):
        r1,c1=a[i],b[i]
        if r1-last==c1-last1:
            ans+=r1-last
        else:
            if (last+last1)%2==0:
                last+=1
            last+=c1-last1
            ans+=int(math.ceil((r1-last)/2))
        last=r1
        last1=c1
    print(ans)
