You have an array a with length n, you can perform operations. Each operation is like this: choose two adjacent elements from a, say x and y, and replace one of them with gcd(x, y), where gcd denotes the [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor).

What is the minimum number of operations you need to make all of the elements equal to 1?

Input

The first line of the input contains one integer n (1 ≤ n ≤ 2000) — the number of elements in the array.

The second line contains n space separated integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the elements of the array.

Output

Print -1, if it is impossible to turn all numbers to 1. Otherwise, print the minimum number of operations needed to make all numbers equal to 1.

Examples

Input

5
2 2 3 4 6


Output

5


Input

4
2 4 6 8


Output

-1


Input

3
2 6 9


Output

4

Note

In the first sample you can turn all numbers to 1 using the following 5 moves:

  * [2, 2, 3, 4, 6]. 
  * [2, 1, 3, 4, 6]
  * [2, 1, 3, 1, 6]
  * [2, 1, 1, 1, 6]
  * [1, 1, 1, 1, 6]
  * [1, 1, 1, 1, 1]



We can prove that in this case it is not possible to make all numbers one using less than 5 moves.
from collections import defaultdict, deque, Counter
from sys import stdin, stdout
from heapq import heappush, heappop
import math
import io
import os
import math
import bisect

#?############################################################


def isPrime(x):
    for i in range(2, x):
        if i*i > x:
            break
        if (x % i == 0):
            return False
    return True

#?############################################################


def ncr(n, r, p):
    num = den = 1
    for i in range(r):
        num = (num * (n - i)) % p
        den = (den * (i + 1)) % p
    return (num * pow(den, p - 2, p)) % p


#?############################################################

def primeFactors(n):
    l = []
    while n % 2 == 0:
        l.append(2)
        n = n / 2
    for i in range(3, int(math.sqrt(n))+1, 2):
        while n % i == 0:
            l.append(int(i))
            n = n / i
    if n > 2:
        l.append(n)
    return list(set(l))


#?############################################################

def power(x, y, p):
    res = 1
    x = x % p
    if (x == 0):
        return 0
    while (y > 0):
        if ((y & 1) == 1):
            res = (res * x) % p
        y = y >> 1
        x = (x * x) % p
    return res

#?############################################################


def sieve(n):
    prime = [True for i in range(n+1)]
    p = 2
    while (p * p <= n):
        if (prime[p] == True):
            for i in range(p * p, n+1, p):
                prime[i] = False
        p += 1
    return prime


#?############################################################

def digits(n):
    c = 0
    while (n > 0):
        n //= 10
        c += 1
    return c

#?############################################################


def ceil(n, x):
    if (n % x == 0):
        return n//x
    return n//x+1

#?############################################################


def mapin():
    return [int(x) for x in input().split()]

#?############################################################

def solve(a):
    n = len(a)
    dp = []
    for i in range(n+1):
        dp.append([0]*(n+1))
    for i in range(1, n+1):
        for j in range(i, n+1):
            if(j == i):
                dp[i][j] = a[i-1]
            else:
                dp[i][j] = math.gcd(dp[i][j-1], a[j-1])



    # for i in range(n+1):
    #     print(*dp[i])
    mi = 1e10
    for i in range(1, n+1):
        for j in range(i, n+1):
            if(dp[i][j] == 1):
                mi = min(mi, j-i)

    return mi

input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
# python3 15.py<in>op

t = 1
for i in range(t):
    n = int(input())
    
    a = mapin()
    te = 0
    for i in range(n):
        te = math.gcd(te, a[i])

    
    temp = solve(a)
    if(temp == 1e10):
        print(-1)
    elif(temp == 0):
        print(n-a.count(1))

    else:
        print(n-1+temp)
  