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.
public class Main {

	public static void main(String[] args) {
		new Main();
	}

	public Main() {
		FastScanner fs = new FastScanner();
		java.io.PrintWriter out = new java.io.PrintWriter(System.out);
		solve(fs, out);
		out.flush();
	}

	public void solve(FastScanner fs, java.io.PrintWriter out) {
		int t = fs.nextInt();
		calc(2_000_000);
		while(t --> 0) {
			int n = fs.nextInt();
			char[] s = fs.next().toCharArray();
			int zero = 0, one = 0;
			for (char c : s) if (c == '0') ++ zero;
			for (int i = 1;i < s.length; ++ i) {
				if (s[i - 1] == '1' && s[i] == '1') {
					++ one;
					s[i - 1] = s[i] = '0';
				}
			}
			out.println(comb(zero + one, zero));
		}
	}
	
	final int MOD = 998_244_353;
	int plus(int n, int m) {
		int sum = n + m;
		if (sum >= MOD) sum -= MOD;
		return sum;
	}
	int minus(int n, int m) {
		int sum = n - m;
		if (sum < 0) sum += MOD;
		return sum;
	}
	int times(int n, int m) {
		return (int)((long)n * m % MOD);
	}
	int divide(int n, int m) {
		return times(n, IntMath.pow(m, MOD - 2, MOD));
	}
	int[] fact, invf;
	void calc(int len) {
		len += 2;
		fact = new int[len];
		invf = new int[len];
		fact[0] = fact[1] = invf[0] = invf[1] = 1;
		for (int i = 2;i < fact.length;++ i) fact[i] = times(fact[i - 1], i);
		invf[len - 1] = divide(1, fact[len - 1]);
		for (int i = len - 1;i > 1;-- i) invf[i - 1] = times(i, invf[i]);
	}
	int comb(int n, int m) {
		if (n < m) return 0;
		return times(fact[n], times(invf[n - m], invf[m]));
	}
}

class FastScanner {

	private final java.io.InputStream in = System.in;
	private final byte[] buffer = new byte[8192];
	private int ptr = 0;
	private int buflen = 0;

	private boolean hasNextByte() {
		if (ptr < buflen) return true;
		ptr = 0;
		try {
			buflen = in.read(buffer);
		} catch (java.io.IOException e) {
			e.printStackTrace();
		}
		return buflen > 0;
	}

	private byte readByte() {
		return hasNextByte() ? buffer[ptr++ ] : -1;
	}

	private static boolean isPrintableChar(byte c) {
		return 32 < c || c < 0;
	}

	private static boolean isNumber(int c) {
		return '0' <= c && c <= '9';
	}

	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++ ;
		return hasNextByte();
	}

	public String next() {
		if (!hasNext()) throw new java.util.NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		byte b;
		while (isPrintableChar(b = readByte()))
			sb.appendCodePoint(b);
		return sb.toString();
	}

	public final char nextChar() {
		if (!hasNext()) throw new java.util.NoSuchElementException();
		return (char)readByte();
	}

	public final long nextLong() {
		if (!hasNext()) throw new java.util.NoSuchElementException();
		long n = 0;
		try {
			byte b = readByte();
			if (b == '-') {
				while (isNumber(b = readByte()))
					n = n * 10 + '0' - b;
				return n;
			} else if (!isNumber(b)) throw new NumberFormatException();
			do
				n = n * 10 + b - '0';
			while (isNumber(b = readByte()));
		} catch (java.util.NoSuchElementException e) {}
		return n;
	}

	public final int nextInt() {
		if (!hasNext()) throw new java.util.NoSuchElementException();
		int n = 0;
		try {
			byte b = readByte();
			if (b == '-') {
				while (isNumber(b = readByte()))
					n = n * 10 + '0' - b;
				return n;
			} else if (!isNumber(b)) throw new NumberFormatException();
			do
				n = n * 10 + b - '0';
			while (isNumber(b = readByte()));
		} catch (java.util.NoSuchElementException e) {}
		return n;
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}
}

class Arrays {

	public static void sort(final int[] array) {
		sort(array, 0, array.length);
	}

	public static void sort(final int[] array, int fromIndex, int toIndex) {
		if (toIndex - fromIndex  <= 512) {
			java.util.Arrays.sort(array, fromIndex, toIndex);
			return;
		}
		sort(array, fromIndex, toIndex, 0, new int[array.length]);
	}

	private static final void sort(int[] a, final int from, final int to, final int l, final int[] bucket) {
		if (to - from  <= 512) {
			java.util.Arrays.sort(a, from, to);
			return;
		}
		final int BUCKET_SIZE = 256;
		final int INT_RECURSION = 4;
		final int MASK = 0xff;
		final int shift = l << 3;
		final int[] cnt = new int[BUCKET_SIZE + 1];
		final int[] put = new int[BUCKET_SIZE];
		for (int i = from; i < to; i++) ++ cnt[(a[i] >>> shift & MASK) + 1];
		for (int i = 0; i < BUCKET_SIZE; i++) cnt[i + 1] += cnt[i];
		for (int i = from; i < to; i++) {
			int bi = a[i] >>> shift & MASK;
			bucket[cnt[bi] + put[bi]++] = a[i];
		}
		for (int i = BUCKET_SIZE - 1, idx = from; i >= 0; i--) {
			int begin = cnt[i];
			int len = cnt[i + 1] - begin;
			System.arraycopy(bucket, begin, a, idx, len);
			idx += len;
	    }
		final int nxtL = l + 1;
		if (nxtL < INT_RECURSION) {
			sort(a, from, to, nxtL, bucket);
			if (l == 0) {
				int lft, rgt;
				lft = from - 1; rgt = to;
				while (rgt - lft > 1) {
					int mid = lft + rgt >> 1;
					if (a[mid] < 0) lft = mid;
					else rgt = mid;
				}
				reverse(a, from, rgt);
				reverse(a, rgt, to);
	        }
	    }
	}

	public static void sort(final long[] array) {
		sort(array, 0, array.length);
	}

	public static void sort(final long[] array, int fromIndex, int toIndex) {
		if (toIndex - fromIndex  <= 512) {
			java.util.Arrays.sort(array, fromIndex, toIndex);
			return;
		}
		sort(array, fromIndex, toIndex, 0, new long[array.length]);
	}

	private static final void sort(long[] a, final int from, final int to, final int l, final long[] bucket) {
		final int BUCKET_SIZE = 256;
		final int LONG_RECURSION = 8;
		final int MASK = 0xff;
		final int shift = l << 3;
		final int[] cnt = new int[BUCKET_SIZE + 1];
		final int[] put = new int[BUCKET_SIZE];
		for (int i = from; i < to; i++) ++ cnt[(int) ((a[i] >>> shift & MASK) + 1)];
		for (int i = 0; i < BUCKET_SIZE; i++) cnt[i + 1] += cnt[i];
		for (int i = from; i < to; i++) {
			int bi = (int) (a[i] >>> shift & MASK);
			bucket[cnt[bi] + put[bi]++] = a[i];
		}
		for (int i = BUCKET_SIZE - 1, idx = from; i >= 0; i--) {
			int begin = cnt[i];
			int len = cnt[i + 1] - begin;
			System.arraycopy(bucket, begin, a, idx, len);
			idx += len;
	    }
		final int nxtL = l + 1;
		if (nxtL < LONG_RECURSION) {
			sort(a, from, to, nxtL, bucket);
			if (l == 0) {
				int lft, rgt;
				lft = from - 1; rgt = to;
				while (rgt - lft > 1) {
					int mid = lft + rgt >> 1;
					if (a[mid] < 0) lft = mid;
					else rgt = mid;
				}
				reverse(a, from, rgt);
				reverse(a, rgt, to);
	        }
	    }
	}

	public static void reverse(int[] array) {
		reverse(array, 0, array.length);
	}

	public static void reverse(int[] array, int fromIndex, int toIndex) {
		for (-- toIndex;fromIndex < toIndex;++ fromIndex, -- toIndex) {
			int swap = array[fromIndex];
			array[fromIndex] = array[toIndex];
			array[toIndex] = swap;
		}
	}

	public static void reverse(long[] array) {
		reverse(array, 0, array.length);
	}

	public static void reverse(long[] array, int fromIndex, int toIndex) {
		for (-- toIndex;fromIndex < toIndex;++ fromIndex, -- toIndex) {
			long swap = array[fromIndex];
			array[fromIndex] = array[toIndex];
			array[toIndex] = swap;
		}
	}
}

class IntMath {

	public static int gcd(int a, int b) {
		while (a != 0)
			if ((b %= a) != 0) a %= b;
			else return a;
		return b;
	}

	public static int gcd(int... array) {
		int ret = array[0];
		for (int i = 1; i < array.length; ++i)
			ret = gcd(ret, array[i]);
		return ret;
	}

	public static long gcd(long a, long b) {
		while (a != 0)
			if ((b %= a) != 0) a %= b;
			else return a;
		return b;
	}

	public static long gcd(long... array) {
		long ret = array[0];
		for (int i = 1; i < array.length; ++i)
			ret = gcd(ret, array[i]);
		return ret;
	}

	public static long lcm(long a, long b) {
		return a / gcd(a, b) * b;
	}

	public static int pow(int a, int b) {
		int ans = 1;
		for (int mul = a; b > 0; b >>= 1, mul *= mul)
			if ((b & 1) != 0) ans *= mul;
		return ans;
	}

	public static long pow(long a, long b) {
		long ans = 1;
		for (long mul = a; b > 0; b >>= 1, mul *= mul)
			if ((b & 1) != 0) ans *= mul;
		return ans;
	}

	public static int pow(int a, long b, int mod) {
		if (b < 0) b = b % (mod - 1) + mod - 1;
		long ans = 1;
		for (long mul = a; b > 0; b >>= 1, mul = mul * mul % mod)
			if ((b & 1) != 0) ans = ans * mul % mod;
		return (int)ans;
	}

	public static int pow(long a, long b, int mod) {
		return pow((int)(a % mod), b, mod);
	}

	public static int floorsqrt(long n) {
		return (int)Math.sqrt(n + 0.1);
	}

	public static int ceilsqrt(long n) {
		return n <= 1 ? (int)n : (int)Math.sqrt(n - 0.1) + 1;
	}
}
