Problem:
Score : 800 points

Problem Statement

Given are integers N and X. For each integer k between 0 and X (inclusive), find the answer to the following question, then compute the sum of all those answers, modulo 998244353.

Let us repeat the following operation on the integer k. Operation: if the integer is currently odd, subtract 1 from it and divide it by 2; otherwise, divide it by 2 and add 2^{N-1} to it. How many operations need to be performed until k returns to its original value? (The answer is considered to be 0 if k never returns to its original value.)

Constraints

1 \leq N \leq 2\times 10^5

0 \leq X < 2^N

X is given in binary and has exactly N digits. (In case X has less than N digits, it is given with leading zeroes.)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
X

Output

Print the sum of the answers to the questions for the integers between 0 and X (inclusive), modulo 998244353.

Sample Input 1

3
111

Sample Output 1

40

For example, for k=3, the operation changes k as follows: 1,0,4,6,7,3. Therefore the answer for k=3 is 6.

Sample Input 2

6
110101

Sample Output 2

616

Sample Input 3

30
001110011011011101010111011100

Sample Output 3

549320998

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

N = int(input())
X = int(input(),2)

counted = [0]*(N+1)

ans = 0
for i in range(1,N+1):
    if (not N%i) and (N//i)%2:
        temp = (X>>(N-i)) + 1
        for j in range(1,i):
            if not i%j:
                temp -= counted[j]
        
        #print(i,X>>(N-i),temp, N//i, ans)
        ans += temp * i * 2
        ans %= 998244353
        counted[i] = temp
        #print(ans)


print(ans)