You are given a sequence $a_1, a_2, \dots, a_n$, consisting of integers.

You can apply the following operation to this sequence: choose some integer $x$ and move all elements equal to $x$ either to the beginning, or to the end of $a$. Note that you have to move all these elements in one direction in one operation.

For example, if $a = [2, 1, 3, 1, 1, 3, 2]$, you can get the following sequences in one operation (for convenience, denote elements equal to $x$ as $x$-elements):   $[1, 1, 1, 2, 3, 3, 2]$ if you move all $1$-elements to the beginning;  $[2, 3, 3, 2, 1, 1, 1]$ if you move all $1$-elements to the end;  $[2, 2, 1, 3, 1, 1, 3]$ if you move all $2$-elements to the beginning;  $[1, 3, 1, 1, 3, 2, 2]$ if you move all $2$-elements to the end;  $[3, 3, 2, 1, 1, 1, 2]$ if you move all $3$-elements to the beginning;  $[2, 1, 1, 1, 2, 3, 3]$ if you move all $3$-elements to the end; 

You have to determine the minimum number of such operations so that the sequence $a$ becomes sorted in non-descending order. Non-descending order means that for all $i$ from $2$ to $n$, the condition $a_{i-1} \le a_i$ is satisfied.

Note that you have to answer $q$ independent queries.


-----Input-----

The first line contains one integer $q$ ($1 \le q \le 3 \cdot 10^5$) — the number of the queries. Each query is represented by two consecutive lines.

The first line of each query contains one integer $n$ ($1 \le n \le 3 \cdot 10^5$) — the number of elements.

The second line of each query contains $n$ integers $a_1, a_2, \dots , a_n$ ($1 \le a_i \le n$) — the elements.

It is guaranteed that the sum of all $n$ does not exceed $3 \cdot 10^5$.


-----Output-----

For each query print one integer — the minimum number of operation for sorting sequence $a$ in non-descending order.


-----Example-----
Input
3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7

Output
2
0
1



-----Note-----

In the first query, you can move all $1$-elements to the beginning (after that sequence turn into $[1, 1, 1, 3, 6, 6, 3]$) and then move all $6$-elements to the end.

In the second query, the sequence is sorted initially, so the answer is zero.

In the third query, you have to move all $2$-elements to the beginning.

Starter code:

Solutions:
def main():
    from sys import stdin, stdout
    for _ in range(int(stdin.readline())):
        n = int(stdin.readline())
        inp1 = [-1] * (n + 1)
        inp2 = [-1] * (n + 1)
        for i, ai in enumerate(map(int, stdin.readline().split())):
            if inp1[ai] < 0:
                inp1[ai] = i
            inp2[ai] = i
        inp1 = tuple((inp1i for inp1i in inp1 if inp1i >= 0))
        inp2 = tuple((inp2i for inp2i in inp2 if inp2i >= 0))
        n = len(inp1)
        ans = 0
        cur = 0
        for i in range(n):
            if i and inp1[i] < inp2[i - 1]:
                cur = 1
            else:
                cur += 1
                ans = max(ans, cur)
        stdout.write(f'{n - ans}\n')


main()


from sys import stdin
input = stdin.readline


def main():
    anses = []
    for _ in range(int(input())):
        n = int(input())
        a = list(map(int, input().split()))
        f = [0]*(n+1)
        d = sorted(list(set(a)))
        for q in range(1, len(d)+1):
            f[d[q-1]] = q
        for q in range(len(a)):
            a[q] = f[a[q]]
        n = len(d)
        starts, ends = [-1]*(n+1), [n+1]*(n+1)
        for q in range(len(a)):
            if starts[a[q]] == -1:
                starts[a[q]] = q
            ends[a[q]] = q
        s = [0]*(n+1)
        max1 = -float('inf')
        for q in range(1, n+1):
            s[q] = s[q-1]*(ends[q-1] < starts[q])+1
            max1 = max(max1, s[q])
        anses.append(str(len(d)-max1))
    print('\n'.join(anses))


main()


#                                               |
#   _` |  __ \    _` |   __|   _ \   __ \    _` |   _` |
#  (   |  |   |  (   |  (     (   |  |   |  (   |  (   |
# \__,_| _|  _| \__,_| \___| \___/  _|  _| \__,_| \__,_|

import sys
import math

def read_line():
	return sys.stdin.readline()[:-1]
 
def read_int():
	return int(sys.stdin.readline())
	
def read_int_line():
	return [int(v) for v in sys.stdin.readline().split()]

def read_float_line():
	return [float(v) for v in sys.stdin.readline().split()]

t = read_int()
for i in range(t):
	n = read_int()
	a = read_int_line()
	d = {}
	for i in range(n):
		if a[i] in d:
			d[a[i]].append(i)
		else:
			d[a[i]] = [i]

	dp = [1]*len(list(d.keys()))

	s = list(d.keys())
	s.sort()

	for i in range(len(s)-2,-1,-1):
		if d[s[i]][-1] < d[s[i+1]][0]:
			dp[i] = dp[i+1]+1
		else:
			dp[i] = 1
	ans = len(s)-max(dp)
	print(ans)



import os
import sys


def solve(arr):
    items = sorted(set(arr))
    min_max = [(float("inf"), float("-inf"))] * len(items)
    item_to_idx = {k: idx for idx, k in enumerate(items)}
    for idx, a in enumerate(arr):
        m, M = min_max[item_to_idx[a]]
        min_max[item_to_idx[a]] = (min(idx, m), max(idx, M))

    best = 1
    current = 1
    for i in range(1, len(items)):
        _, prev_M = min_max[i - 1]
        m, _ = min_max[i]
        if prev_M <= m:
            current += 1
        else:
            current = 1

        best = max(best, current)

    return len(items) - best


def pp(input):
    T = int(input())
    for t in range(T):
        input()
        arr = list(map(int, input().strip().split()))
        print(solve(arr))


if "paalto" in os.getcwd():
    from string_source import string_source, codeforces_parse

    pp(
        string_source(
            """3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7"""
        )
    )
else:
    pp(sys.stdin.readline)


import sys as _sys


def main():
    q = int(input())
    for i_q in range(q):
        n, = _read_ints()
        a = tuple(_read_ints())
        result = find_min_sorting_cost(sequence=a)
        print(result)


def _read_line():
    result = _sys.stdin.readline()
    assert result[-1] == "\n"
    return result[:-1]


def _read_ints():
    return list(map(int, _read_line().split(" ")))


def find_min_sorting_cost(sequence):
    sequence = tuple(sequence)
    
    if not sequence:
        return 0
    
    indices_by_values = {x: [] for x in sequence}
    for i, x in enumerate(sequence):
        indices_by_values[x].append(i)
    
    borders_by_values = {
        x: (indices[0], indices[-1]) for x, indices in list(indices_by_values.items())
    }
    
    borders_sorted_by_values = [borders for x, borders in sorted(borders_by_values.items())]
    
    max_cost_can_keep_n = curr_can_keep_n = 1
    for prev_border, curr_border in zip(borders_sorted_by_values, borders_sorted_by_values[1:]):
        if curr_border[0] > prev_border[1]:
            curr_can_keep_n += 1
        else:
            if curr_can_keep_n > max_cost_can_keep_n:
                max_cost_can_keep_n = curr_can_keep_n
            curr_can_keep_n = 1
    if curr_can_keep_n > max_cost_can_keep_n:
        max_cost_can_keep_n = curr_can_keep_n
    
    return len(set(sequence)) - max_cost_can_keep_n


def __starting_point():
    main()

__starting_point()

import copy
def DeleteRepetitionsIn(Array):
    AlreadyRead = {}
    index = 0
    ConstantArray = copy.deepcopy(Array)
    for a in range(len(ConstantArray)):
        if Array[index] not in AlreadyRead:
            AlreadyRead[Array[index]] = ""
            index += 1
            continue
        Array = Array[0:index] + Array[index + 1:len(Array)]

    return Array

def DeleteRepetitionsIn2(Array):
    AlreadyRead = {}
    for elem in Array:
        if elem in AlreadyRead:
            continue
        AlreadyRead[elem] = ""
    return list(AlreadyRead)

Results = []
ArraysNumber = int(input())
for e in range(ArraysNumber):
    AbsolutelyUselessNumber = int(input())
    Array = list(map(int, input().split()))
    if len(Array) == 1:
        Results.append(0)
        continue

    #print(Array)
    TheRightOrder = DeleteRepetitionsIn2(Array)
    TheRightOrder.sort()
    TheCurrentOrder = {}
    for i in range(len(Array)):
        if Array[i] not in TheCurrentOrder:
            TheCurrentOrder[Array[i]] = [i, i]
            continue
        TheCurrentOrder[Array[i]][1] = i

    #print(TheRightOrder)
    #print(TheCurrentOrder)
    #print(Array)

    TheCurrentResult = 1
    TheMaxResult = 1
    for i in range(len(TheRightOrder)):
        #print("a =", TheCurrentResult)
        #print("b =", TheMaxResult)
        if i == len(TheRightOrder) - 1:
            if TheCurrentResult >= TheMaxResult:
                TheMaxResult = TheCurrentResult
            continue
        if TheCurrentOrder[TheRightOrder[i]][1] > TheCurrentOrder[TheRightOrder[i + 1]][0]:
            if TheCurrentResult >= TheMaxResult:
                TheMaxResult = TheCurrentResult

            TheCurrentResult = 1
            continue

        TheCurrentResult += 1

    Results.append(len(TheRightOrder) - TheMaxResult)

for i in Results:
    print(i)