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
import sys
input = sys.stdin.readline

mod=998244353

N=int(input())
X=input()

import math
xr=math.ceil(math.sqrt(N))

LIST=[]
for i in range(1,xr+1):
    if N%i==0:
        LIST.append(i)
        LIST.append(N//i)

REP=[l for l in set(LIST) if (N//l)%2==1 and l!=N]

REP.sort(reverse=True)


ANS=2*N*(int(X,2)+1)%mod

def invstr(X,r):
    return bin(int(X,2)^((1<<r)-1))[2:].zfill(r)

from collections import defaultdict
score=defaultdict(int)

for r in REP:
    score[r]+=2*r-2*N

    for j in REP:
        if r%j==0 and j<r:
            score[j]-=score[r]
  
for r in REP:
    sc=score[r]

    #print(r,score)

    XSTR=X[:r]

    kosuu=int(XSTR,2)

    if (XSTR+invstr(XSTR,r))*(N//(r*2))+XSTR<=X:
        kosuu+=1

    ANS+=kosuu*sc

print(ANS%mod)