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.

Examples

Input

3
111


Output

40


Input

6
110101


Output

616


Input

30
001110011011011101010111011100


Output

549320998
mod = 998244353
N = int(input())
X = input()
X_ = []
for i in range(N):
    if X[i]=='0':
        X_.append('1')
    else:
        X_.append('0')
X_ = ''.join(X_)

d = []
for n in range(1,N+1):
    if N%n==0 and (N//n)%2==1:
        d.append(n)

p_d = {}

for n in d:
    p_d[n] = 0
    S = (X[:n]+X_[:n])*(N//n//2)+X[:n]
    p_d[n] += int(X[:n],2)%mod
    if S<=X:
        p_d[n] += 1

ans = 0
for i in range(len(d)):
    n = d[i]
    for j in range(i):
        m = d[j]
        if n%m==0:
            p_d[n] -= p_d[m]
    ans += p_d[n]*2*n
ans %= mod
print(ans)