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
from collections import deque, defaultdict
import copy
import bisect
sys.setrecursionlimit(10 ** 9)
import math
import heapq
from itertools import product, permutations,combinations
import fractions
from operator import itemgetter

import sys
def input():
	return sys.stdin.readline().strip()

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

def make_divisors(n):
	divisors = []
	for i in range(1, int(n**0.5)+1):
		if n % i == 0:
			divisors.append(i)
			if i != n // i:
				divisors.append(n//i)
	return divisors

mod = 998244353
pow2 = [1]
for i in range(N):
	pow2.append((pow2[-1]*2) % mod)

yakusu_n = make_divisors(2*N)
yakusu_n.sort()



ans = 0
before = 0

#print(yakusu_n)
num_dict = defaultdict(int)
for n in yakusu_n:
	if N % (2*n) != 0 and N % n == 0:
		num = 0
		for i in range(n):
			if X[i] == "1":
				num += pow2[n - 1 - i]
		Y = list(X[:n])
		for i in range(n):
			if Y[i] == "0":
				Y.append("1")
			else:
				Y.append("0")
		Y = "".join(Y)
		Y = Y*(N//n)
		Y = Y[0:N]
		if X >= Y:
			num += 1
		#print(num, X>=Y)
		num_yakusu = make_divisors(n)
		for z in num_yakusu:
			num -= num_dict[z]
		num_dict[n] = num
		num *= 2*n
		num %= mod
		ans += num
		ans %= mod
		#print(n, ans, before, Y, X)

print(ans)