Cirno gave AquaMoon a chessboard of size 1 × n. Its cells are numbered with integers from 1 to n from left to right. In the beginning, some of the cells are occupied with at most one pawn, and other cells are unoccupied.

In each operation, AquaMoon can choose a cell i with a pawn, and do either of the following (if possible): 

  * Move pawn from it to the (i+2)-th cell, if i+2 ≤ n and the (i+1)-th cell is occupied and the (i+2)-th cell is unoccupied. 
  * Move pawn from it to the (i-2)-th cell, if i-2 ≥ 1 and the (i-1)-th cell is occupied and the (i-2)-th cell is unoccupied. 



You are given an initial state of the chessboard. AquaMoon wants to count the number of states reachable from the initial state with some sequence of operations. But she is not good at programming. Can you help her? As the answer can be large find it modulo 998 244 353.

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10 000) — the number of test cases.

The first line contains a single integer n (1 ≤ n ≤ 10^5) — the size of the chessboard.

The second line contains a string of n characters, consists of characters "0" and "1". If the i-th character is "1", the i-th cell is initially occupied; otherwise, the i-th cell is initially unoccupied.

It is guaranteed that the sum of n over all test cases does not exceed 10^5.

Output

For each test case, print the number of states that reachable from the initial state with some sequence of operations modulo 998 244 353.

Example

Input


6
4
0110
6
011011
5
01010
20
10001111110110111000
20
00110110100110111101
20
11101111011000100010


Output


3
6
1
1287
1287
715

Note

In the first test case the strings "1100", "0110" and "0011" are reachable from the initial state with some sequence of operations.
# DEFINING SOME GOOD STUFF
import heapq
import sys
from math import *
import threading
from heapq import *
from itertools import count
from pprint import pprint
from collections import defaultdict

'''
    intialise defaultdict by any kind of value by default you want to take ( int -> 0 | list -> [] )
'''
from heapq import heapify, heappop, heappush

sys.setrecursionlimit(300000)
# threading.stack_size(10**8)
'''
-> if you are increasing recursionlimit then remember submitting using python3 rather pypy3
-> sometimes increasing stack size don't work locally but it will work on CF
'''

mod = 10 ** 9+7
inf = 10 ** 15
decision = ['NO', 'YES']
yes = 'YES'
no = 'NO'

# ------------------------------FASTIO----------------------------
import os

from io import BytesIO, IOBase

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n")+(not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")


# _______________________________________________________________#
class Factorial:
    def __init__(self, MOD):
        self.MOD = MOD
        self.factorials = [1, 1]
        self.invModulos = [0, 1]
        self.invFactorial_ = [1, 1]

    def calc(self, n):
        if n <= -1:
            print("Invalid argument to calculate n!")
            print("n must be non-negative value. But the argument was "+str(n))
            exit()
        if n < len(self.factorials):
            return self.factorials[n]
        nextArr = [0] * (n+1-len(self.factorials))
        initialI = len(self.factorials)
        prev = self.factorials[-1]
        m = self.MOD
        for i in range(initialI, n+1):
            prev = nextArr[i-initialI] = prev * i % m
        self.factorials += nextArr
        return self.factorials[n]

    def inv(self, n):
        if n <= -1:
            print("Invalid argument to calculate n^(-1)")
            print("n must be non-negative value. But the argument was "+str(n))
            exit()
        p = self.MOD
        pi = n % p
        if pi < len(self.invModulos):
            return self.invModulos[pi]
        nextArr = [0] * (n+1-len(self.invModulos))
        initialI = len(self.invModulos)
        for i in range(initialI, min(p, n+1)):
            next = -self.invModulos[p % i] * (p // i) % p
            self.invModulos.append(next)
        return self.invModulos[pi]

    def invFactorial(self, n):
        if n <= -1:
            print("Invalid argument to calculate (n^(-1))!")
            print("n must be non-negative value. But the argument was "+str(n))
            exit()
        if n < len(self.invFactorial_):
            return self.invFactorial_[n]
        self.inv(n)  # To make sure already calculated n^-1
        nextArr = [0] * (n+1-len(self.invFactorial_))
        initialI = len(self.invFactorial_)
        prev = self.invFactorial_[-1]
        p = self.MOD
        for i in range(initialI, n+1):
            prev = nextArr[i-initialI] = (prev * self.invModulos[i % p]) % p
        self.invFactorial_ += nextArr
        return self.invFactorial_[n]

class Combination:
    def __init__(self, MOD):
        self.MOD = MOD
        self.factorial = Factorial(MOD)

    def ncr(self, n, k):
        if k < 0 or n < k:
            return 0
        k = min(k, n-k)
        f = self.factorial
        return f.calc(n) * f.invFactorial(max(n-k, k)) * f.invFactorial(min(k, n-k)) % self.MOD
# _______________________________________________________________#



def npr(n, r):
    return (factorial(n)%mod) // (factorial(n-r)%mod) if n >= r else 0


def ncr(n, r):
    # print(n, r)
    return (factorial(n)%mod) // (((factorial(r)) * (factorial(n-r)))%mod) if n >= r else 0


def lower_bound(li, num):
    answer = -1
    start = 0
    end = len(li)-1

    while (start <= end):
        middle = (end+start) // 2
        if li[middle] >= num:
            answer = middle
            end = middle-1
        else:
            start = middle+1
    return answer  # min index where x is not less than num


def upper_bound(li, num):
    answer = -1
    start = 0
    end = len(li)-1

    while (start <= end):
        middle = (end+start) // 2

        if li[middle] <= num:
            answer = middle
            start = middle+1

        else:
            end = middle-1
    return answer  # max index where x is not greater than num


def abs(x):
    return x if x >= 0 else -x


def binary_search(li, val):
    # print(lb, ub, li)
    ans = -1
    lb = 0
    ub = len(li)-1
    while (lb <= ub):
        mid = (lb+ub) // 2
        # print('mid is',mid, li[mid])
        if li[mid] > val:
            ub = mid-1
        elif val > li[mid]:
            lb = mid+1
        else:
            ans = mid  # return index
            break
    return ans


def kadane(x):  # maximum sum contiguous subarray
    sum_so_far = 0
    current_sum = 0
    for i in x:
        current_sum += i
        if current_sum < 0:
            current_sum = 0
        else:
            sum_so_far = max(sum_so_far, current_sum)
    return sum_so_far


def pref(li):
    pref_sum = [0]
    for i in li:
        pref_sum.append(pref_sum[-1]+i)
    return pref_sum


def SieveOfEratosthenes(n):
    prime = [{1, i} for i in range(n+1)]
    p = 2
    while (p <= n):
        for i in range(p * 2, n+1, p):
            prime[i].add(p)
        p += 1
    return prime


def primefactors(n):
    factors = []
    while (n % 2 == 0):
        factors.append(2)
        n //= 2
    for i in range(3, int(sqrt(n))+1, 2):  # only odd factors left
        while n % i == 0:
            factors.append(i)
            n //= i
    if n > 2:  # incase of prime
        factors.append(n)
    return factors


def prod(li):
    ans = 1
    for i in li:
        ans *= i
    return ans


def sumk(a, b):
    print('called for', a, b)
    ans = a * (a+1) // 2
    ans -= b * (b+1) // 2
    return ans

def sumi(n):
    ans = 0
    if len(n) > 1:
        for x in n:
            ans += int(x)
        return ans
    else:
        return int(n)

def checkwin(x, a):
    if a[0][0] == a[1][1] == a[2][2] == x:
        return 1
    if a[0][2] == a[1][1] == a[2][0] == x:
        return 1
    if (len(set(a[0])) == 1 and a[0][0] == x) or (len(set(a[1])) == 1 and a[1][0] == x) or (len(set(a[2])) == 1 and a[2][0] == x):
        return 1
    if (len(set(a[0][:])) == 1 and a[0][0] == x) or (len(set(a[1][:])) == 1 and a[0][1] == x) or (len(set(a[2][:])) == 1 and a[0][0] == x):
        return 1
    return 0

# _______________________________________________________________#




# def main():
karmanya = int(input())
# karmanya = 1
# divisors = SieveOfEratosthenes(200010)
# print(divisors)
while karmanya != 0:
    karmanya -= 1
    n = int(input())
    # n,m = map(int, input().split())
    a = [int(x) for x in list(input())]
    # a = list(map(int, input().split()))
    # b = list(map(int, input().split()))
    # c = list(map(int, input().split()))
    # d = defaultdict(list)
    cnt = 0
    groups, zeroes = 0, 0
    for i in range(n):
        if a[i] == 1:
            cnt += 1
        else:
            zeroes += 1
            groups += cnt//2
            cnt = 0
        if i == n-1 and a[i] == 1:
            groups += cnt//2

    thismod = 998244353
    f = Combination(thismod)
    print(f.ncr(groups+zeroes, zeroes))





























# t = threading.Thread(target=main)
# t.start()
# t.join()