human
Bajtek, known for his unusual gifts, recently got an integer array x_0, x_1, …, x_{k-1}.

Unfortunately, after a huge array-party with his extraordinary friends, he realized that he'd lost it. After hours spent on searching for a new toy, Bajtek found on the arrays producer's website another array a of length n + 1. As a formal description of a says, a_0 = 0 and for all other i (1 ≤ i ≤ n) a_i = x_{(i-1)mod k} + a_{i-1}, where p mod q denotes the remainder of division p by q.

For example, if the x = [1, 2, 3] and n = 5, then:

  * a_0 = 0, 
  * a_1 = x_{0mod 3}+a_0=x_0+0=1, 
  * a_2 = x_{1mod 3}+a_1=x_1+1=3, 
  * a_3 = x_{2mod 3}+a_2=x_2+3=6, 
  * a_4 = x_{3mod 3}+a_3=x_0+6=7, 
  * a_5 = x_{4mod 3}+a_4=x_1+7=9. 


So, if the x = [1, 2, 3] and n = 5, then a = [0, 1, 3, 6, 7, 9].

Now the boy hopes that he will be able to restore x from a! Knowing that 1 ≤ k ≤ n, help him and find all possible values of k — possible lengths of the lost array.

Input

The first line contains exactly one integer n (1 ≤ n ≤ 1000) — the length of the array a, excluding the element a_0.

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^6).

Note that a_0 is always 0 and is not given in the input.

Output

The first line of the output should contain one integer l denoting the number of correct lengths of the lost array.

The second line of the output should contain l integers — possible lengths of the lost array in increasing order.

Examples

Input

5
1 2 3 4 5

Output

5
1 2 3 4 5 

Input

5
1 3 5 6 8

Output

2
3 5 

Input

3
1 5 3

Output

1
3 

Note

In the first example, any k is suitable, since a is an arithmetic progression.

Possible arrays x:

  * [1]
  * [1, 1]
  * [1, 1, 1]
  * [1, 1, 1, 1] 
  * [1, 1, 1, 1, 1]


In the second example, Bajtek's array can have three or five elements.

Possible arrays x:

  * [1, 2, 2]
  * [1, 2, 2, 1, 2]


For example, k = 4 is bad, since it leads to 6 + x_0 = 8 and 0 + x_0 = 1, which is an obvious contradiction.

In the third example, only k = n is good.

Array...
Solve the task in PYTHON.

Write me a Python code to find all possible values of k — possible lengths of the lost array?
assistant
#Here is Python code to find all possible values of k — possible lengths of the lost array.

#encoding:utf-8

class Rookie(object):

    def _input(self):
        l1 = raw_input()
        l2 = raw_input()
        n = int(l1.strip())
        a = l2.strip().split(' ')
        a = [int(_) for _ in a]
        return n, a

    def _output(self):
        print len(self.ans)
        #self.ans.reverse()
        print ' '.join([str(_) for _ in self.ans])
        pass

    def solve(self):
        n, a  = self._input()
        A = [a[i] - a[i-1] if i > 0 else a[i] for i in range(len(a))]
        self.ans = [i for i in range(1,n+1)]
        for i in range(n):
            s = A[i]  # ai+1 - ai
            for j in range(len(self.ans) - 1, -1, -1):
                k = self.ans[j]
                tar = (i + k) % k
                if s != A[tar]:
                    self.ans.pop(j)
        self._output()
if __name__ == '__main__':
    Rookie().solve()