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 [1, 4, -2] satisfies the requirements.

Note that x_i may be negative.
import java.lang.*;
import java.util.*;
import java.io.*;

public class LostArr{

  static String arrToStr(Integer[]arr){
     StringBuffer sb = new StringBuffer();
     int len = arr.length;
     for(int i=0;i<len;i++){
        sb.append(arr[i]);
	if(i<(len-1)){
	   sb.append(' ');
	}
     }
     return sb.toString();
  }

    Integer[]getValidLens(int n, int[]a){
	Vector<Integer>retV = new Vector<Integer>();
	Vector<Integer>currV = new Vector<Integer>();
	for(int i=1;i<=n;i++){
	    if(i==1){
		currV.add(a[0]);
	    }else{
		currV.add(a[i-1]-a[i-2]);
	    }
	    if(testLen(i,n,a,currV)){
		retV.add(i);
	    }
	}
	Integer[]retArr = new Integer[0];
	retArr = retV.toArray(retArr);
	//	System.out.format("validLens lenght %s\n",retArr.length);
	return retArr;
    }

    boolean checkA(int aInd, int xLen, int[]a, Vector<Integer>xV){
	boolean retV = false;
	int xInd = aInd%xLen;
	int xVal = xV.elementAt(xInd);
	int prevA = 0;
	if(aInd>0){
	    prevA = a[aInd-1];
	}
	int newA = prevA + xVal;
	//	System.out.format("checkA, prevA %d, xVal %d, aVal %d\n",prevA,xVal,a[aInd]);
	if(newA==a[aInd]){
	    retV = true;
	}
	return retV;
    }

    boolean testLen(int len, int n, int[]a, Vector<Integer>currV){
	boolean retV = true;
	for(int i=0;i<n;i++){
	    boolean aCorr = checkA(i,len,a,currV);
	    if(!aCorr){
		retV = false;
		break;
	    }
	}
	//	System.out.format("testLen, returns %b\n",retV);
	return retV;
    }
    
    static int[]strToIntArr(String s){
	//	s = s.substring(1,s.length()-1);
	String[] sArr = s.split(" ");
	int len = sArr.length;
	int[] retArr = new int[len];
	for(int i=0;i<len;i++){
	    retArr[i] = Integer.parseInt(sArr[i]);
	}
	return retArr;
    }
    
    public static void main(String[]args) throws Exception{
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
	String nLn = br.readLine();
	String aLn = br.readLine();
	int n = Integer.parseInt(nLn);
	int[]a = strToIntArr(aLn);
	LostArr la = new LostArr();
	Integer[]validLens = la.getValidLens(n,a);
	String arrStr = arrToStr(validLens);
	String lenStr = Integer.toString(validLens.length);
	bw.write(lenStr);
	bw.newLine();
	bw.write(arrStr);
	bw.newLine();
	bw.flush();
    }
}
