The brave Knight came to the King and asked permission to marry the princess. The King knew that the Knight was brave, but he also wanted to know if he was smart enough. So he asked him to solve the following task.

There is a permutation p_i of numbers from 1 to 2n. You can make two types of operations. 

  1. Swap p_1 and p_2, p_3 and p_4, ..., p_{2n-1} and p_{2n}. 
  2. Swap p_1 and p_{n+1}, p_2 and p_{n+2}, ..., p_{n} and p_{2n}. 



The task is to find the minimal number of operations required to sort the given permutation.

The Knight was not that smart actually, but quite charming, so the princess asks you to help him to solve the King's task.

Input

The first line contains the integer n (1≤ n≤ 1000). The second line contains 2n integers p_i — the permutation of numbers from 1 to 2n.

Output

Print one integer — the minimal number of operations required to sort the permutation. If it is impossible to sort the permutation using these operations, print -1.

Examples

Input


3
6 3 2 5 4 1


Output


3


Input


2
3 4 2 1


Output


-1


Input


4
1 2 3 4 5 6 7 8


Output


0

Note

In the first example, you can sort the permutation in three operations: 

  1. Make operation 1: 3, 6, 5, 2, 1, 4. 
  2. Make operation 2: 2, 1, 4, 3, 6, 5. 
  3. Make operation 1: 1, 2, 3, 4, 5, 6. 
import collections
import string
import math
import copy
import os
import sys
from io import BytesIO, IOBase

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)


def input(): return sys.stdin.readline().rstrip("\r\n")


# n = 0
# m = 0

# n = int(input())

# li = [int(i) for i in input().split()]

# s = sorted(li)
"""
from dataclasses import dataclass

@dataclass
class point:
    x: float
    y: float
 
 
@dataclass
class line:
    A: float
    B: float
    C: float
 
    def gety(self, x):
        return (self.A*x+self.C)/-self.B
    
    def getx(self, y):
        return (self.B*y+self.C)/-self.A
 
    def k(self):
        return -self.A/self.B
 
    def b(self):
        return -self.C/self.B
 
    def dist(self, p: point):
        return abs((self.A*p.x+self.B*p.y+self.C)/(self.A**2+self.B**2)**0.5)
 
 
def calc_line(u: point, v: point):
    return line(A=u.y-v.y, B=v.x-u.x, C=u.y*(u.x-v.x)-u.x*(u.y-v.y))
 
 
def is_parallel(u: line, v: line) -> bool:
    f1 = False
    f2 = False
    try:
        k1 = u.k()
    except:
        f1 = True
    try:
        k2 = v.k()
    except:
        f2 = True
    if f1 != f2:
        return False
    return f1 or k1 == k2
 
 
def seg_len(_from: point, _to: point):
    return ((_from.x - _to.x)**2 + (_from.y - _to.y)**2) ** 0.5
 
def in_range(_from: point, _to: point, _point: point) -> bool:
    if _from.x < _to.x:
        if _from.y < _to.y:
            return _from.x <= _point.x <= _to.x and _from.y <= _point.y <= _to.y
        else:
            return _from.x <= _point.x <= _to.x and _from.y >= _point.y >= _to.y
    else:
        if _from.y < _to.y:
            return _from.x >= _point.x >= _to.x and _from.y <= _point.y <= _to.y
        else:
            return _from.x >= _point.x >= _to.x and _from.y >= _point.y >= _to.y
 
def intersect(u: line, v: line) -> point:
    tx = (u.B*v.C-v.B*u.C)/(v.B*u.A-u.B*v.A)
    if u.B!=0.0:
        ty = -u.A*tx/u.B - u.C/u.B
    else:
        ty = -v.A*tx/v.B - v.C/v.B
    return point(x=tx, y=ty)
 
def in_direction(_from: point, _to: point, _point: point) -> bool:
    if _from.x < _to.x:
        if _from.y < _to.y:
            return _to.x < _point.x  and _to.y < _point.y
        else:
            return _to.x < _point.x  and _point.y <= _to.y
    else:
        if _from.y < _to.y:
            return _to.x >= _point.x  and _to.y < _point.y
        else:
            return _to.x >= _point.x  and _point.y <= _to.y


"""
mo = int(1e9+7)


def exgcd(a, b):
    if not b:
        return 1, 0
    y, x = exgcd(b, a % b)
    y -= a//b * x
    return x, y


def getinv(a, m):
    x, y = exgcd(a, m)
    return -1 if x == 1 else x % m


def comb(n, b):
    res = 1
    b = min(b, n-b)
    for i in range(b):
        res = res*(n-i)*getinv(i+1, mo) % mo
        # res %= mo
    return res % mo


def quickpower(a, n):
    res = 1
    while n:
        if n & 1:
            res = res * a % mo
        n >>= 1
        a = a*a % mo
    return res


def dis(a, b):
    return abs(a[0]-b[0]) + abs(a[1]-b[1])


def getpref(x):
    if x > 1:
        return (x)*(x-1) >> 1
    else:
        return 0


def orafli(upp):
    primes = []
    marked = [False for i in range(upp+3)]
    prvs = [i for i in range(upp+3)]
    for i in range(2, upp):
        if not marked[i]:
            primes.append(i)
        for j in primes:
            if i*j >= upp:
                break
            marked[i*j] = True
            prvs[i*j] = j
            if i % j == 0:
                break
    return primes, prvs


def lower_ord(c: str) -> int:
    return ord(c)-97


def upper_ord(c: str) -> int:
    return ord(c) - 65


def read_list():
    return [int(i) for i in input().split()]


def read_int():
    s = input().split()
    if len(s) == 1:
        return int(s[0])
    else:
        return map(int, s)


def ask(s):
    print(f"? {s}", flush=True)


def answer(s):
    print(f"{s}", flush=True)

def transfer(f1, f2):
    ret = []
    for p, i in enumerate(f1):
        ret.append(f2[i])
    return ret

def chktrans(f1, f2):
    ret = []
    for p, i in enumerate(f1):
        if f1[p]!=f2[i]:
            return False
        else:
            ret.append(f2[i])
    return ret

import random

def solve():
    n = read_int()
    l = read_list()
    sl = sorted(l)
    if l == sl:
        print(0)
        return
    l1 = list(l)

    def swap1(ll):
        for i in range(n):
            ll[i<<1], ll[i<<1|1] = ll[i<<1|1],ll[i<<1]
        return ll

    def swap2(ll):
        for i in range(n):
            ll[i], ll[n+i] = ll[n+i],ll[i]
        return ll

    
    ans = 1145141919810
    ca1 = 1
    sta =  0
    swap1(l1)
    
    while l1!=l:
        if l1 == sl:
            ans = min(ca1, ans)
            break
        if sta:
            swap1(l1)
        else:
            swap2(l1)
        ca1+=1
        sta^=1

    l2 = list(l)
    swap2(l2)
    ca2 = 1
    sta= 1
    while l2!=l:
        if l2 == sl:
            ans = min(ca2, ans)
            break
        if sta:
            swap1(l2)
        else:
            swap2(l2)
        ca2+=1
        sta^=1
    if ans!=1145141919810:
        print(ans)
    else:
        print(-1)




    

    
# fi = open('C:\\cppHeaders\\CF2020.12.17\\test.data', 'r')
# def input(): return fi.readline().rstrip("\r\n")
# primes, prv = orafli(10001)
solve()
# t = int(input())

# for ti in range(t):
    # print(f"Case #{ti+1}: ", end='')
    # solve()
