Shohag has an integer sequence a_1, a_2, …, a_n. He can perform the following operation any number of times (possibly, zero):

  * Select any positive integer k (it can be different in different operations). 
  * Choose any position in the sequence (possibly the beginning or end of the sequence, or in between any two elements) and insert k into the sequence at this position. 
  * This way, the sequence a changes, and the next operation is performed on this changed sequence. 



For example, if a=[3,3,4] and he selects k = 2, then after the operation he can obtain one of the sequences [\underline{2},3,3,4], [3,\underline{2},3,4], [3,3,\underline{2},4], or [3,3,4,\underline{2}].

Shohag wants this sequence to satisfy the following condition: for each 1 ≤ i ≤ |a|, a_i ≤ i. Here, |a| denotes the size of a.

Help him to find the minimum number of operations that he has to perform to achieve this goal. We can show that under the constraints of the problem it's always possible to achieve this goal in a finite number of operations.

Input

The first line contains a single integer t (1 ≤ t ≤ 200) — the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 100) — the initial length of the sequence.

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the elements of the sequence.

Output

For each test case, print a single integer — the minimum number of operations needed to perform to achieve the goal mentioned in the statement.

Example

Input


4
3
1 3 4
5
1 2 5 7 4
1
1
3
69 6969 696969


Output


1
3
0
696966

Note

In the first test case, we have to perform at least one operation, as a_2=3>2. We can perform the operation [1, 3, 4] → [1, \underline{2}, 3, 4] (the newly inserted element is underlined), now the condition is satisfied.

In the second test case, Shohag can perform the following operations:

[1, 2, 5, 7, 4] → [1, 2, \underline{3}, 5, 7, 4] → [1, 2, 3, \underline{4}, 5, 7, 4] → [1, 2, 3, 4, 5, \underline{3}, 7, 4].

In the third test case, the sequence already satisfies the condition.
1
39
481199252 336470888 634074578 642802746 740396295 773386884 579721198 396628655 503722503 971207868 202647942 2087506 268792718 46761498 443917727 16843338 125908043 691952768 717268783 787375312 150414369 693319712 519096230 45277106 856168102 762263554 674936674 407246545 274667941 279198849 527268921 155191459 421436316 536134606 286802932 140515506 646837311 233465964 451394766

971207858

import bisect
import heapq
import math
import collections
import sys
import copy
from functools import reduce
import decimal
from io import BytesIO, IOBase
import os
import itertools
import functools
from types import GeneratorType

#
# sys.setrecursionlimit(10 ** 9)
decimal.getcontext().rounding = decimal.ROUND_HALF_UP

graphDict = collections.defaultdict

queue = collections.deque


################## pypy deep recursion handling ##############
# Author = @pajenegod
def bootstrap(f, stack=[]):
    def wrappedfunc(*args, **kwargs):
        to = f(*args, **kwargs)
        if stack:
            return to
        else:
            while True:
                if type(to) is GeneratorType:
                    stack.append(to)
                    to = next(to)
                else:
                    stack.pop()
                    if not stack:
                        return to
                    to = stack[-1].send(to)

    return wrappedfunc


################## Graphs ###################
class Graphs:
    def __init__(self):
        self.graph = graphDict(set)

    def add_edge(self, u, v):
        self.graph[u].add(v)
        self.graph[v].add(u)

    def dfs_utility(self, nodes, visited_nodes, colors, parity, level):
        global count
        if nodes == 1:
            colors[nodes] = -1
        else:
            if len(self.graph[nodes]) == 1 and parity % 2 == 0:
                if q == 1:
                    colors[nodes] = 1
                else:
                    colors[nodes] = -1
                    count += 1
            else:
                if parity % 2 == 0:
                    colors[nodes] = -1
                else:
                    colors[nodes] = 1
        visited_nodes.add(nodes)
        for neighbour in self.graph[nodes]:
            new_level = level + 1
            if neighbour not in visited_nodes:
                self.dfs_utility(neighbour, visited_nodes, colors, level - 1, new_level)

    def dfs(self, node):
        Visited = set()
        color = collections.defaultdict()
        self.dfs_utility(node, Visited, color, 0, 0)
        return color

    def bfs(self, node, f_node):
        count = float("inf")
        visited = set()
        level = 0
        if node not in visited:
            queue.append([node, level])
            visited.add(node)
        flag = 0
        while queue:
            parent = queue.popleft()
            if parent[0] == f_node:
                flag = 1
                count = min(count, parent[1])
            level = parent[1] + 1
            for item in self.graph[parent[0]]:
                if item not in visited:
                    queue.append([item, level])
                    visited.add(item)
        return count if flag else -1
        return False


################### Tree Implementaion ##############
class Tree:
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None


def inorder(node, lis):
    if node:
        inorder(node.left, lis)
        lis.append(node.data)
        inorder(node.right, lis)
    return lis


def leaf_node_sum(root):
    if root is None:
        return 0
    if root.left is None and root.right is None:
        return root.data
    return leaf_node_sum(root.left) + leaf_node_sum(root.right)


def hight(root):
    if root is None:
        return -1
    if root.left is None and root.right is None:
        return 0
    return max(hight(root.left), hight(root.right)) + 1


################## Union Find #######################
class UF:
    """An implementation of union find data structure.
    It uses weighted quick union by rank with path compression.
    """

    def __init__(self, N):
        """Initialize an empty union find object with N items.

        Args:
            N: Number of items in the union find object.
        """

        self._id = list(range(N))
        self._count = N
        self._rank = [0] * N

    def find(self, p):
        """Find the set identifier for the item p."""

        id = self._id
        while p != id[p]:
            p = id[p]  # Path compression using halving.
        return p

    def count(self):
        """Return the number of items."""

        return self._count

    def connected(self, p, q):
        """Check if the items p and q are on the same set or not."""

        return self.find(p) == self.find(q)

    def union(self, p, q):
        """Combine sets containing p and q into a single set."""

        id = self._id
        rank = self._rank

        i = self.find(p)
        j = self.find(q)
        if i == j:
            return

        self._count -= 1
        if rank[i] < rank[j]:
            id[i] = j
        elif rank[i] > rank[j]:
            id[j] = i
        else:
            id[j] = i
            rank[i] += 1

    def add_roads(self):
        return set(self._id)

    def __str__(self):
        """String representation of the union find object."""
        return " ".join([str(x) for x in self._id])

    def __repr__(self):
        """Representation of the union find object."""
        return "UF(" + str(self) + ")"


#################################################

def rounding(n):
    return int(decimal.Decimal(f'{n}').to_integral_value())


def factors(n):
    return set(reduce(list.__add__,
                      ([i, n // i] for i in range(1, int(n ** 0.5) + 1) if n % i == 0)))


def p_sum(array):
    return list(itertools.accumulate(array))


def base_change(nn, bb):
    if nn == 0:
        return [0]
    digits = []
    while nn:
        digits.append(int(nn % bb))
        nn //= bb
    return digits[::-1]


def diophantine(a: int, b: int, c: int):
    d, x, y = extended_gcd(a, b)
    r = c // d
    return r * x, r * y


@bootstrap
def extended_gcd(a: int, b: int):
    if b == 0:
        d, x, y = a, 1, 0
    else:
        (d, p, q) = yield extended_gcd(b, a % b)
        x = q
        y = p - q * (a // b)

    yield d, x, y


######################################################################################

'''
Knowledge and awareness are vague, and perhaps better called illusions.
Everyone lives within their own subjective interpretation.
                                                            ~Uchiha Itachi
'''

################################ <fast I/O> ###########################################
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, **kwargs):
        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)


#############################################<I/O Region >##############################################


def inp():
    return sys.stdin.readline().strip()


def map_inp(v_type):
    return map(v_type, inp().split())


def list_inp(v_type):
    return list(map_inp(v_type))


######################################## Solution ####################################

for _ in range(int(inp())):
    n = int(inp())
    arr = list_inp(int)
    ans = 0
    for i in range(n):
        ans = max(ans,abs(arr[i] - (i + 1)))
    print(ans)
