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
n = int(input())
s = input()
mod = 998244353
pr = []
for i in range(2,n+1):
  if n%i == 0:
    pr.append((i,n//i))
num = []
pr = pr[::-1]
for p,q in pr:
  if p%2 == 0:
    continue
  ntmp = 0
  x = s[:q]
  y = ""
  for i in x:
    if i == "0":
      y += "1"
    else:
      y += "0"
  for i in range(q):
    if x[i] == "1":
      ntmp = (ntmp+pow(2,q-1-i,mod))%mod
  k = (x+y)*((p-1)//2)+x
  if s >= k:
    ntmp += 1
  num.append((p,2*q,ntmp))
ans = 2*n
for i in range(n-1,-1,-1):
  if s[i] == "1":
    ans = (ans+pow(2,n-1-i,mod)*2*n)%mod
for i in range(len(num)):
  p1,x,number = num[i]
  for p2,y,number2 in num:
    if x == y:
      continue
    elif p2%p1 == 0 and (p2//p1)%2 == 1:
      number -= number2
  num[i] = p1,x,number
for p1,x,number in num:
  ans = (ans-(2*n-x)*number)%mod
print(ans)