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:
//package its_ulure;

import java.io.*;
import java.util.*;

public class Main{
    FastReader in;
    PrintWriter out;
    final long mod = 1000000009;
    final int MAXN = 1000000;
    final int lgN = 20;
    final long INF = (long)1e18 + 1;
    final int MAX_Ai = 1000001;
    public static void main(String[] args) throws java.lang.Exception{
        new Main().run();
    }
    void run() throws Exception{
        in = new FastReader(System.in);
        out = new PrintWriter(System.out);
        int t = 1;
        while(t-->0)
            solve();
        out.flush();
        out.close();
    }
    int find(int i, int j, int n, int[] cost){
    	int ans = 0;
        for(int p = 0; p < n; p++) {
        	if(((1 << p) & i) == ((1 << p) & j))
        		ans += cost[n - p - 1];
        	if(ans > 100)
        		break;
        }
        return ans;
    }
    int to_integer(String st, int n){
        int i = 0, p = 0;
        int ans = 0;
        for(i = n - 1; i >= 0; i--, p++)
            ans += (st.charAt(i) - '0') * (1 << p);
        return ans;
    }
    void solve(){
        int n = ni();
        int m = ni();
        int q = ni();
        int mx = 1 << n;
        int[][] arr = new int[mx][mx];
        int i = 0, j = 0;
        int[] cost = new int[n];
        for(i = 0; i < n; i++)
            cost[i] = ni();
        for(i = 0; i < mx; i++){
            for(j = 0; j < mx; j++)
                arr[i][j] = find(i, j, n, cost);
        }
        int[] cnt = new int[mx];
        for(i = 0; i < m; i++)
            cnt[to_integer(n(), n)]++;
        int[][] ans = new int[105][mx];
        for(i = 0; i < mx; i++){
            for(j = 0; j < mx; j++) {
                int x = Math.min(arr[i][j], 101);
                ans[x][i] += cnt[j];
            }
            for(j = 1; j < 103; j++)
            	ans[j][i] += ans[j - 1][i];
        }
        while(q-- > 0){
            int val = to_integer(n(), n);
            int k = ni();
            pn(ans[k][val]);
        }
    }



    static final Comparator<Pair> com = new Comparator<Pair>(){
        public int compare(Pair a, Pair b){
            if(Integer.compare(a.x, b.x) != 0)
                return Integer.compare(a.x, b.x);
            else
                return Integer.compare(a.y, b.y);
        }
    };
    
    class Pair{
        int x;
        int y;
        int z;
        Pair(int p, int q, int r){
            x = p;
            y = q;
            z = r;
        }
    }
    class Edge{
        int u , v;
        Edge(int a, int b){
            u = a;
            v = b;
        }
        int other(int x) {
            return u ^ v ^ x;
        }
    }
    long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
    int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}
    int bitcount(long n){return (n==0)?0:(1+bitcount(n&(n-1)));}
    void p(Object o){out.print(o);}
    void pn(Object o){out.println(o);}
    void pni(Object o){out.println(o);out.flush();}
    String n(){return in.next();}
    String nln(){return in.nextLine();}
    int ni(){return Integer.parseInt(in.next());}
    long nl(){return Long.parseLong(in.next());}
    double nd(){return Double.parseDouble(in.next());}
 
    long mul(long a,long b){
        if(a>=mod)a%=mod;
        if(b>=mod)b%=mod;
        a*=b;
        if(a>=mod)a%=mod;
        return a;
    }
    long modPow(long a, long p){
        long o = 1;
        while(p>0){
            if((p&1)==1)o = mul(o,a);
            a = mul(a,a);
            p>>=1;
        }
        return o;
    }
 
    class FastReader{
        private InputStream stream; 
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
 
        public FastReader(InputStream stream) {
            this.stream = stream;
        }
 
        public int read() {
            if (numChars == -1)
                throw new UnknownError();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new UnknownError();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int peek() {
            if (numChars == -1)
                return -1;
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    return -1;
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar];
        }
 
        public void skip(int x) {
            while (x-- > 0)
                read();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }
 
        public long nextLong() {
            return Long.parseLong(next());
        }
 
        public String nextString() {
            return next();
        }
 
        public String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
 
            return res.toString();
        }
 
        public String nextLine() {
            StringBuffer buf = new StringBuffer();
            int c = read();
            while (c != '\n' && c != -1) {
                if (c != '\r')
                    buf.appendCodePoint(c);
                c = read();
            }
            return buf.toString();
        }
 
        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
 
        public boolean hasNext() {
            int value;
            while (isSpaceChar(value = peek()) && value != -1)
                read();
            return value != -1;
        }
 
        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}