Problem: Childan is making up a legendary story and trying to sell his forgery — a necklace with a strong sense of "Wu" to the Kasouras. But Mr. Kasoura is challenging the truth of Childan's story. So he is going to ask a few questions about Childan's so-called "personal treasure" necklace.

This "personal treasure" is a multiset S of m "01-strings".

A "01-string" is a string that contains n characters "0" and "1". For example, if n=4, strings "0110", "0000", and "1110" are "01-strings", but "00110" (there are 5 characters, not 4) and "zero" (unallowed characters) are not.

Note that the multiset S can contain equal elements.

Frequently, Mr. Kasoura will provide a "01-string" t and ask Childan how many strings s are in the multiset S such that the "Wu" value of the pair (s, t) is not greater than k. 

Mrs. Kasoura and Mr. Kasoura think that if s_i = t_i (1≤ i≤ n) then the "Wu" value of the character pair equals to w_i, otherwise 0. The "Wu" value of the "01-string" pair is the sum of the "Wu" values of every character pair. Note that the length of every "01-string" is equal to n.

For example, if w=[4, 5, 3, 6], "Wu" of ("1001", "1100") is 7 because these strings have equal characters only on the first and third positions, so w_1+w_3=4+3=7.

You need to help Childan to answer Mr. Kasoura's queries. That is to find the number of strings in the multiset S such that the "Wu" value of the pair is not greater than k.

Input

The first line contains three integers n, m, and q (1≤ n≤ 12, 1≤ q, m≤ 5⋅ 10^5) — the length of the "01-strings", the size of the multiset S, and the number of queries.

The second line contains n integers w_1, w_2, …, w_n (0 ≤ w_i ≤ 100) — the value of the i-th caracter.

Each of the next m lines contains the "01-string" s of length n — the string in the multiset S.

Each of the next q lines contains the "01-string" t of length n and integer k (0≤ k≤ 100) — the query.

Output

For each query, print the answer for this query.

Examples

Input

2 4 5
40 20
01
01
10
11
00 20
00 40
11 20
11 40
11 60


Output

2
4
2
3
4


Input

1 2 4
100
0
1
0 0
0 100
1 0
1 100


Output

1
2
1
2

Note

In the first example, we can get:

"Wu" of ("01", "00") is 40.

"Wu" of ("10", "00") is 20.

"Wu" of ("11", "00") is 0.

"Wu" of ("01", "11") is 20.

"Wu" of ("10", "11") is 40.

"Wu" of ("11", "11") is 60.

In the first query, pairs ("11", "00") and ("10", "00") satisfy the condition since their "Wu" is not greater than 20.

In the second query, all strings satisfy the condition.

In the third query, pairs ("01", "11") and ("01", "11") satisfy the condition. Note that since there are two "01" strings in the multiset, the answer is 2, not 1.

In the fourth query, since k was increased, pair ("10", "11") satisfies the condition too.

In the fifth query, since k was increased, pair ("11", "11") satisfies the condition too.

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.*;
import java.util.Map.Entry;

public class Main
{
	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;
	private PrintWriter pw;
	private long mod = 1000000 + 3;

	private StringBuilder ans_sb;

	private void soln()
	{
		int n = nextInt();
		int m = nextInt();
		int q = nextInt();
		int pow = (int) Math.pow(2, n);
		long[][] arr = new long[pow][105];
		int[] arr1 = nextIntArray(n);
		int[] a1 = new int[pow];
		for (int i = 0; i < m; i++) {
			String s = nextLine();
			int val = 0;
			int pow1 = 1;
			for (int j = n - 1; j >= 0; j--) {
				if (s.charAt(j) == '1') {
					val += pow1;
				}
				pow1 = pow1 * 2;
			}
			a1[val]++;
		}
		// debug(a1);
		int[] vs = new int[pow];
		for (int i = 0; i < pow; i++) {
			int j = i;
			int kk = 0;
			while (j != 0) {
				int x = j % 2;
				if (x == 0)
					vs[i] += arr1[n - kk - 1];
				j /= 2;
				kk++;
			}
			while (kk < n) {
				vs[i] += arr1[n - kk - 1];
				kk++;
			}
		}
		// debug(vs);
		for (int i = 0; i < pow; i++) {
			for (int j = 0; j <= i; j++) {
				int xor = (i ^ j);
				int va = vs[xor];
				if (va <= 100) {
					if (a1[j] != 0)
						arr[i][va] += (long) a1[j];
					if (a1[i] != 0 && i != j)
						arr[j][va] += (long) a1[i];
					// debug(i+" "+j+" "+va);
				}
			}
		}
		// debug(arr);
		for (int i = 0; i < pow; i++) {
			for (int j = 1; j <= 100; j++) {
				arr[i][j] += arr[i][j - 1];
			}
		}
		while (q-- > 0) {
			String[] s = nextLine().split(" ");
			int k = Integer.parseInt(s[1]);
			int val = 0;
			int pow1 = 1;
			for (int j = n - 1; j >= 0; j--) {
				if (s[0].charAt(j) == '1') {
					val += pow1;
				}
				pow1 = pow1 * 2;
			}
			pw.println(arr[val][k]);
		}
	}

	private String solveEqn(long a, long b)
	{
		long x = 0, y = 1, lastx = 1, lasty = 0, temp;
		while (b != 0) {
			long q = a / b;
			long r = a % b;
			a = b;
			b = r;
			temp = x;
			x = lastx - q * x;
			lastx = temp;
			temp = y;
			y = lasty - q * y;
			lasty = temp;
		}
		return lastx + " " + lasty;
	}

	private void debug(Object... o)
	{
		System.out.println(Arrays.deepToString(o));
	}

	private long pow(long a, long b, long c)
	{
		if (b == 0)
			return 1;
		long p = pow(a, b / 2, c);
		p = (p * p) % c;
		return (b % 2 == 0) ? p : (a * p) % c;
	}

	private long gcd(long n, long l)
	{
		if (l == 0)
			return n;
		return gcd(l, n % l);
	}

	public static void main(String[] args) throws Exception
	{
		new Thread(null, new Runnable()
		{
			@Override
			public void run()
			{
				new Main().solve();
			}
		}, "1", 1 << 26).start();
		// new Main().solve();
	}

	public StringBuilder solve()
	{
		InputReader(System.in);
		/*
		 * try { InputReader(new FileInputStream("C:\\Users\\hardik\\Desktop\\in.txt"));
		 * } catch(FileNotFoundException e) {}
		 */
		pw = new PrintWriter(System.out);
		// ans_sb = new StringBuilder();
		soln();

		pw.close();
		// System.out.println(ans_sb);
		return ans_sb;
	}

	public void InputReader(InputStream stream1)
	{
		stream = stream1;
	}

	private boolean isWhitespace(int c)
	{
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	private boolean isEndOfLine(int c)
	{
		return c == '\n' || c == '\r' || c == -1;
	}

	private int read()
	{
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	private int nextInt()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	private long nextLong()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	private String nextToken()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	private String nextLine()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString();
	}

	private int[] nextIntArray(int n)
	{
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nextInt();
		}
		return arr;
	}

	private long[] nextLongArray(int n)
	{
		long[] arr = new long[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nextLong();
		}
		return arr;
	}

	private void pArray(int[] arr)
	{
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private void pArray(long[] arr)
	{
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private boolean isSpaceChar(int c)
	{
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}

	private char nextChar()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		char c1 = (char) c;
		while (!isSpaceChar(c))
			c = read();
		return c1;
	}

	private interface SpaceCharFilter
	{
		public boolean isSpaceChar(int ch);
	}
}