There are n lamps on a line, numbered from 1 to n. Each one has an initial state off (0) or on (1).

You're given k subsets A_1, …, A_k of \{1, 2, ..., n\}, such that the intersection of any three subsets is empty. In other words, for all 1 ≤ i_1 < i_2 < i_3 ≤ k, A_{i_1} ∩ A_{i_2} ∩ A_{i_3} = ∅.

In one operation, you can choose one of these k subsets and switch the state of all lamps in it. It is guaranteed that, with the given subsets, it's possible to make all lamps be simultaneously on using this type of operation.

Let m_i be the minimum number of operations you have to do in order to make the i first lamps be simultaneously on. Note that there is no condition upon the state of other lamps (between i+1 and n), they can be either off or on.

You have to compute m_i for all 1 ≤ i ≤ n.

Input

The first line contains two integers n and k (1 ≤ n, k ≤ 3 ⋅ 10^5).

The second line contains a binary string of length n, representing the initial state of each lamp (the lamp i is off if s_i = 0, on if s_i = 1).

The description of each one of the k subsets follows, in the following format:

The first line of the description contains a single integer c (1 ≤ c ≤ n) — the number of elements in the subset.

The second line of the description contains c distinct integers x_1, …, x_c (1 ≤ x_i ≤ n) — the elements of the subset.

It is guaranteed that: 

  * The intersection of any three subsets is empty; 
  * It's possible to make all lamps be simultaneously on using some operations. 

Output

You must output n lines. The i-th line should contain a single integer m_i — the minimum number of operations required to make the lamps 1 to i be simultaneously on.

Examples

Input


7 3
0011100
3
1 4 6
3
3 4 7
2
2 3


Output


1
2
3
3
3
3
3


Input


8 6
00110011
3
1 3 8
5
1 2 5 6 7
2
6 8
2
3 5
2
4 7
1
2


Output


1
1
1
1
1
1
4
4


Input


5 3
00011
3
1 2 3
1
4
3
3 4 5


Output


1
1
1
1
1


Input


19 5
1001001001100000110
2
2 3
2
5 6
2
8 9
5
12 13 14 15 16
1
19


Output


0
1
1
1
2
2
2
3
3
3
3
4
4
4
4
4
4
4
5

Note

In the first example: 

  * For i = 1, we can just apply one operation on A_1, the final states will be 1010110; 
  * For i = 2, we can apply operations on A_1 and A_3, the final states will be 1100110; 
  * For i ≥ 3, we can apply operations on A_1, A_2 and A_3, the final states will be 1111111. 



In the second example: 

  * For i ≤ 6, we can just apply one operation on A_2, the final states will be 11111101; 
  * For i ≥ 7, we can apply operations on A_1, A_3, A_4, A_6, the final states will be 11111111. 
import java.util.*;
import java.io.*;
import java.math.*;
 
public class Solution {
    public static void main(String[] args) throws IOException {
        //PrintWriter out = new PrintWriter(new File("out.txt"));
        PrintWriter out = new PrintWriter(System.out);
        //Reader in = new Reader(new FileInputStream("in.txt"));
        Reader in = new Reader();
        Solution solver = new Solution();
        solver.solve(out, in);
        out.flush();
        out.close();
 
    }
 
 
    static int maxn = 5*(int)1e5+5;
    static long mod=(int)1e9+7;
    static int n, m, t, k, q;
    
    static int[] rank, clr, arr;
    static Node[] par;
    static ArrayList<Edge> adj[];
    static boolean[] vis;
    
    void solve(PrintWriter out, Reader in) throws IOException{
        n = in.nextInt();
        k = in.nextInt();
        
        String s = in.next();
        arr = new int[n+1];
        for (int i = 0; i < n; i++) {
            arr[i+1] = s.charAt(i)-'0';
        }
        
        adj = new ArrayList[k+1];
        for (int i = 1; i <= k; i++)
            adj[i] = new ArrayList<Edge>();
        
        ArrayList<Integer> pos[] = new ArrayList[n+1];
        for (int i = 1; i <= n; i++)
            pos[i] = new ArrayList<Integer>();
        
        for (int z = 1; z <= k; z++) {
            int c = in.nextInt();
            
            for (int i = 0; i < c; i++) {
                pos[in.nextInt()].add(z);
            }
        }
        
        int u = 0, v = 0;
        for (int i = 1; i <= n; i++) {
            if (pos[i].size() == 2) {
                u = pos[i].get(0);
                v = pos[i].get(1);
                adj[u].add(new Edge(v, i));
                adj[v].add(new Edge(u, i));
            }
        }
        
        clr = new int[k+1];
        vis = new boolean[k+1];
        for (int i = 1; i <= k; i++) {
            if (!vis[i]) {
                clr[i] = 1;
                DFS(i);
            }
        }
        
        int[] ans = new int[n+1];
        rank = new int[k+1];
        par = new Node[k+1];
        for (int i = 1; i <= k; i++) {
            par[i] = new Node(i, clr[i], clr[i]^1);
        }
        for (int i = 1; i <= k; i++) vis[i] = false;
        
        for (int i = 1; i <= n; i++) {
            if (pos[i].size() == 2) {
                u = pos[i].get(0); v = pos[i].get(1);
                u = find(u); v = find(v);
                if (u == v) {
                    vis[u] = true;
                } else {
                    ans[i] -= (vis[u]?getans(u):0) + (vis[v]?getans(v):0);
                    //out.print(u+" "+v+" "+(vis[u]?getans(u):0) +" "+ (vis[v]?getans(v):0)+" ");
                    vis[u] = vis[v] = true;
                    union(u, v);
                    u = find(u);
                    //out.println(u+" "+getans(u)+" "+i);
                    ans[i] += getans(u);
                }
            } else if (pos[i].size() == 1) {
                u = pos[i].get(0);
                v = clr[u]^arr[i];
                u = find(u);
                if (vis[u]) ans[i] -= getans(u);
                //out.print(vis[u]+" "+u+" "+getans(u));
                vis[u] = true;
                if (v == 1) par[u].redf = true;
                else par[u].bluef = true;
                ans[i] += getans(u);
                //out.println(" "+getans(u)+" "+u+" "+i+" "+v);
            }
            ans[i] += ans[i-1];
            out.println(ans[i]);
        }
    }
    
    //<>
    
    static void DFS(int s) {
        vis[s] = true;
        for (Edge e:adj[s]) {
            if (!vis[e.to]) {
                int tmp = clr[s]+arr[e.w];
                clr[e.to] = (tmp%2)^1;
                DFS(e.to);
            }
        }
    }
    
    static int getans(int x) {
        if (par[x].redf) return par[x].red;
        else if (par[x].bluef) return par[x].blue;
        return Math.min(par[x].red, par[x].blue);
    }
    
    static int find(int x) {
        if (x != par[x].rt) par[x].rt = find(par[x].rt);
        return par[x].rt;
    }
    
    static void union(int xroot, int yroot) {
        
        if (rank[xroot] < rank[yroot]) {
            par[xroot].rt = yroot;
        } else if (rank[xroot] > rank[yroot]) {
            par[yroot].rt = xroot;
            int tmp = xroot;
            xroot = yroot;
            yroot = tmp;
        } else {
            par[xroot].rt = yroot;
            rank[yroot]++;
        }
        par[yroot].red += par[xroot].red;
        par[yroot].blue += par[xroot].blue;
        par[yroot].bluef |= par[xroot].bluef;
        par[yroot].redf  |= par[xroot].redf;
    }
    
    static class Node {
        int rt, red, blue;
        boolean bluef, redf;
        
        Node (int rt, int red, int blue) {
            this.rt = rt;
            this.red = red;
            this.blue = blue;
        }
    }
    
    static class Edge {
        int to, w;
        
        Edge(int to, int w) {
            this.to = to;
            this.w  = w;
        }
    }
    
    static class Reader {
 
        private InputStream mIs;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
    
        public Reader() {
            this(System.in);
        }
    
        public Reader(InputStream is) {
            mIs = is;
        }
    
        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
    
        }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = mIs.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }
    
        public 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();
        }
    
        public String next() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
    
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
    
        public 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;
        }
    
        public 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;
        }
    
        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    
        public boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
 
    }
}
