A monopole magnet is a magnet that only has one pole, either north or south. They don't actually exist since real magnets have two poles, but this is a programming contest problem, so we don't care.

There is an n× m grid. Initially, you may place some north magnets and some south magnets into the cells. You are allowed to place as many magnets as you like, even multiple in the same cell.

An operation is performed as follows. Choose a north magnet and a south magnet to activate. If they are in the same row or the same column and they occupy different cells, then the north magnet moves one unit closer to the south magnet. Otherwise, if they occupy the same cell or do not share a row or column, then nothing changes. Note that the south magnets are immovable.

Each cell of the grid is colored black or white. Let's consider ways to place magnets in the cells so that the following conditions are met.

  1. There is at least one south magnet in every row and every column. 
  2. If a cell is colored black, then it is possible for a north magnet to occupy this cell after some sequence of operations from the initial placement. 
  3. If a cell is colored white, then it is impossible for a north magnet to occupy this cell after some sequence of operations from the initial placement. 



Determine if it is possible to place magnets such that these conditions are met. If it is possible, find the minimum number of north magnets required (there are no requirements on the number of south magnets).

Input

The first line contains two integers n and m (1≤ n,m≤ 1000) — the number of rows and the number of columns, respectively.

The next n lines describe the coloring. The i-th of these lines contains a string of length m, where the j-th character denotes the color of the cell in row i and column j. The characters "#" and "." represent black and white, respectively. It is guaranteed, that the string will not contain any other characters.

Output

Output a single integer, the minimum possible number of north magnets required.

If there is no placement of magnets that satisfies all conditions, print a single integer -1.

Examples

Input


3 3
.#.
###
##.


Output


1


Input


4 2
##
.#
.#
##


Output


-1


Input


4 5
....#
####.
.###.
.#...


Output


2


Input


2 1
.
#


Output


-1


Input


3 5
.....
.....
.....


Output


0

Note

In the first test, here is an example placement of magnets:

<image>

In the second test, we can show that no required placement of magnets exists. Here are three example placements that fail to meet the requirements. The first example violates rule 3 since we can move the north magnet down onto a white square. The second example violates rule 2 since we cannot move the north magnet to the bottom-left black square by any sequence of operations. The third example violates rule 1 since there is no south magnet in the first column.

<image>

In the third test, here is an example placement of magnets. We can show that there is no required placement of magnets with fewer north magnets.

<image>

In the fourth test, we can show that no required placement of magnets exists. Here are two example placements that fail to meet the requirements. The first example violates rule 1 since there is no south magnet in the first row. The second example violates rules 1 and 3 since there is no south magnet in the second row and we can move the north magnet up one unit onto a white square.

<image>

In the fifth test, we can put the south magnet in each cell and no north magnets. Because there are no black cells, it will be a correct placement.
import javax.imageio.ImageIO;
import java.awt.image.BufferedImage;
import java.io.*;
import java.math.BigInteger;
import java.net.PortUnreachableException;
import java.util.*;

// written by luchy0120

public class Main {
    public static void main(String[] args) throws Exception {

        new Main().run();
    }

    static int groups = 0;
    static int[] fa;
    static int[] sz;

    static void init(int n) {
        groups = n;
        fa = new int[n];
        for (int i = 1; i < n; ++i) {
            fa[i] = i;
        }
        sz = new int[n];
        Arrays.fill(sz, 1);
    }

    static int root(int p) {
        while (p != fa[p]) {
            fa[p] = fa[fa[p]];
            p = fa[p];
        }
        return p;
    }

    static void combine(int p, int q) {
        int i = root(p);
        int j = root(q);
        if (i == j) {
            return;
        }
        if (sz[i] < sz[j]) {
            fa[i] = j;
            sz[j] += sz[i];
        } else {
            fa[j] = i;
            sz[i] += sz[j];
        }
        groups--;
    }

    int child[];
    int color[],dfn[],low[],stack[],cnt[];
    boolean vis[];
    boolean iscut[];
    int deep,top,n,m,sum,ans;
    List<Integer> g[];
    int root = 0;
    //  无向图的强连通分量
    void tarjanNonDirect(int u1) {

        int stk[] = new int[10001];
        int fatk[] = new int[10001];
        int p = 0;
        stk[p] = u1;
        fatk[p] = -1;
        p= 1;
        ot: while(p>0) {
            int u  = stk[p-1];
            int fa = fatk[p-1];


            if(dfn[u]==0) {
                low[u] = dfn[u] = ++deep;
            }
            // stack[top++] = u;

            for (; h[u] != -1; h[u] = ne[h[u]]) {
                int v = to[h[u]];
                if (dfn[v] == 0) {
                    //tarjanNonDirect(v);

                    fatk[p] = u;
                    stk[p++] = v;
                    continue ot;
                } else {
                    low[u] = Math.min(low[u], dfn[v]);
                    // 没有特判是否直接指向父亲
                    // 回边，使用dfn【v】更新low【u】,因为可能是指向父亲，而父亲的low可能比较小
                }
            }
            --p;

            if (fa != -1) {
                low[fa] = Math.min(low[fa], low[u]);
                if (low[u] >= dfn[fa]) {
                    if (fa != root || ++child[fa] > 1) {     // 不是root，直接记为cut，是root，判断是否有两个儿子
                        iscut[fa] = true;
                    }
                    ++dcc_cnt;
                    // 一个割点可能会被多个点双共享
                    //  int z = -1;
                    //    do {
                    //        z = stack[--top];
                    //      dcc[dcc_cnt].add(z);
                    //    } while(z != v);
                    //   dcc[dcc_cnt].add(u);
                }


            }

        }
    }
    int gd = 0;
    int id =-1;
    int scc_cnt = 0;
    int sccno[];

//    void solve() {
//
//    }




//    int get_room(int i,int j){
//        return i/3*3 + j/3;
//    }

//    int a[][] = new int[9][9];
//    int space = 0;
//
//    boolean vis_row[][] = new boolean[9][10];
//    boolean vis_col[][] = new boolean[9][10];
//    boolean vis_room[][] = new boolean[9][10];
//    int val[][][] =new int[9][9][];
//    int prepare[][];
//
//    void dfs(int rt){
//
//    }

    int h[],to[],ne[];int ct =0;
    void add(int u,int v){
        // u--;v--;
        to[ct] = v;
        ne[ct] = h[u];
        h[u] = ct++;

    }

    int dcc_cnt = 0;
    int time = 0;








    private static double f(double x) {
        return Math.pow(Math.abs(x), 0.5) + (5*(Math.pow(x, 3)));
    }

    void dfs(int rt,int fa){
        size[rt]  =1;
        for(int i=h[rt];i!=-1;i=ne[i]){
            int v = to[i];
            if(v==fa) continue;
            dep[v] = dep[rt]+1;
            dfs(v,rt);
            size[rt] += size[v];
        }
    }

    int size[];int dep[];



    long get(int i,int i1,int j,int j1){
        return s[i1][j1] - s[i-1][j1] - s[i1][j-1] + s[i-1][j-1];
    }
    long mod = 1000000007;
    long sv(int i,int i1,int j,int j1,int qie){

        if(dp[i][i1][j][j1][qie]!=0) return dp[i][i1][j][j1][qie];
        if(qie==0) return 1;
        long t = 0;
        for(int k=i+1;k<=i1;++k){
            long num = get(i,k-1,j,j1);
            long num1 = get(k,i1,j,j1);
            if(num>0&&num1>0){
                t += sv(k,i1,j,j1,qie-1);
                t %= mod;
            }
        }
        for(int k=j+1;k<=j1;++k){
            long num = get(i,i1,j,k-1);
            long num1 = get(i,i1,k,j1);
            if(num>0&&num1>0){
                t += sv(i,i1,k,j1,qie-1);
                t %= mod;
            }
        }
        return dp[i][i1][j][j1][qie] = t;
    }

    long s[][];
    long dp[][][][][];
    public int ways(String[] p, int k) {
        int l  = p.length;
        int ll = p[0].length();

        dp = new long[l+1][l+1][ll+1][ll+1][k+1];
        s  = new long[l+1][ll+1];

        for(int i=1;i<=l;++i){
            for(int j=1;j<=ll;++j){
                int c = 0;
                if(p[i-1].charAt(j-1)=='A'){
                    c++;
                }
                s[i][j] = s[i-1][j] + s[i][j-1] - s[i-1][j-1] + c;
            }
        }

        return (int)sv(1,l,1,ll,k-1);







    }



    void solve() {
       int n = ni();
       int m = ni();
       char c[][] = nm(n,m);
       int sh = 0;
       boolean ok  = true;
       for(int i=0;i<n;++i){
           boolean kb = true;int lst =-1;
           for(int j=0;j<m;++j){
               kb &= c[i][j]=='.';
               if(c[i][j]=='#'){
                   if(lst==-1){
                       lst = j;
                   }else if(j>lst+1){
                       ok = false;
                       break;
                   }else{
                       lst = j;
                   }
               }
           }
           if(kb) sh++;
       }
       int sc = 0;
       for(int j=0;j<m;++j){
           boolean kb = true;int lst = -1;
           for(int i=0;i<n;++i){
               kb &= c[i][j]=='.';
               if(c[i][j]=='#'){
                   if(lst==-1){
                       lst = i;
                   }else if(i>lst+1){
                       ok = false;
                       break;
                   }else{
                       lst = i;
                   }
               }
           }
           if(kb) sc++;
       }
       if(sh>=1&&sc==0||sh==0&&sc>=1||!ok){
           println(-1);return;
       }

       Queue<int[]> q = new ArrayDeque<>();

       int dx[] = {0,0,1,-1};
       int dy[] = {1,-1,0,0};
       int ct =0;
       for(int i=0;i<n;++i){
           for(int j=0;j<m;++j) {
               if (c[i][j] == '#'){
                    q.clear();q.offer(new int[]{i,j});
                    while(q.size()>0){
                        int cur[] = q.poll();

                        for(int k=0;k<4;++k){
                            int nx = cur[0] + dx[k];
                            int ny = cur[1] + dy[k];

                            if(nx>=0&&ny>=0&&nx<n&&ny<m&&c[nx][ny]=='#'){
                                c[nx][ny] = '.';
                                q.offer(new int[]{nx,ny});
                            }

                        }



                    }
                    ct++;
                }
           }
       }
       println(ct);





//        int t  =ni();
//        for(int i=0;i<t;++i){
//            int f[]  = na(3);
//            StringBuilder sb  =new StringBuilder();
//            if(f[1]>0){
//                int v = 0;
//
//
//                    for(int j=0;j<f[0]+1;++j){
//                        sb.append(0);
//                    }
//
//
//
//
//                    for(int j=0;j<f[2]+1;++j){
//                        sb.append(1);
//                    }
//
//                    f[1]--;
//
//                for(int j=0;j<f[1];++j){
//                    sb.append(v); v ^= 1;
//                }
//
//                println(sb);
//            }else{
//                if(f[0]>0){
//
//                    for(int j=0;j<f[0]+1;++j){
//                        sb.append(0);
//                    }
//                    println(sb);
//                }
//                if(f[2]>0){
//
//                    for(int j=0;j<f[2]+1;++j){
//                        sb.append(1);
//                    }
//                    println(sb);
//                }
//
//
//            }
//
//
//        }

    }


      //  println(width);
//      //  println(height);
//        int i  =ni();
//        int j  =ni();


//        for(int i=0;i<height;++i){
//            for(int j=0;j<width;++j){
//               int me =  bi.getRGB(i,j);
//               print(me==-1?0:1);
//            }
//            println();
//        }

//        int minx = bi.getMinX();
//        int miny = bi.getMinY();
//        System.out.println("width=" + width + ",height=" + height + ".");
//        System.out.println("minx=" + minx + ",miniy=" + miny + ".");
//        int b[][][] = new int[64][64][3];
//
//        for (int i = minx; i < width; i++) {
//            for (int j = miny; j < height; j++) {
//                int pixel = bi.getRGB(i, j);
//              //  print(pixel);
//               // b[j][i] = pixel;
//
//                b[j][i][0] = (pixel & 0xff0000) >> 16;
//                b[j][i][1] = (pixel & 0xff00) >> 8;
//                b[j][i][2] = (pixel & 0xff);
//
//            }
//            println();
//        }
//
//        for(int i=0;i<64;++i){
//            print("\"");
//            for(int j=0;j<64;++j){
//                print(b[i][j][0]<=50?"*":" ");
//            }
//            println("\",");
//        }
//        //println(b[0][0]);


//
//
//
//
//
//            }
//        }
    //    print("No");




//        int n = ni();
//        int m  = n*(n+1)/2;
//        int k = ni();
//        int p = 0;
//
//        double x[] = new double[n];
//        double y[] = new double[n];
//
//        for(int i=0;i<n;++i){
//            x[i] = nd();
//            y[i] = nd();
//        }
//
//        List<Item> li = new ArrayList<>();
//        for(int i=0;i<n;++i){
//            for(int j=i+1;j<n;++j){
//               double r =  (x[i]-x[j])*(x[i]-x[j]) + (y[i]-y[j])*(y[i]-y[j]);
//               li.add(new Item(r,i,j));
//            }
//        }
//        Collections.sort(li,(xx,yy)->Double.compare(xx.s,yy.s));
//
//        init(n + 1);
//
//        int s = 0;
//        int c = n;
//        for (int i = 0; i < li.size(); ++i) {
//            int p1 = li.get(i).a;
//            int p2 = li.get(i).b;
//            if (root(p1) != root(p2)) {
//                combine(p1, p2);
//                c--;
//                if(c==k-1){
//                    print(roundS(Math.sqrt(li.get(i).s),2));
//                    break;
//                }
//            }
//        }

  //  }
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//    }


//    static long mul(long a, long b, long p)
//    {
//        long res=0,base=a;
//        while(b>0)
//        {
//            if((b&1L)>0)
//                res=(res+base)%p;
//            base=(base+base)%p;
//            b>>=1;
//        }
//        return res;
//    }


    static long mod_pow(long k,long n,long p){
        long res = 1L;
        long temp = (k%p+p)%p;
        while(n!=0L){
            if((n&1L)==1L){
                res = ((res*temp)%p+p)%p;
            }
            temp = ((temp * temp)%p+p)%p;
            n = n>>1L;
        }
        return res%p;
    }
    public static String roundS(double result, int scale){
        String fmt = String.format("%%.%df", scale);
        return String.format(fmt, result);
    }


//    void solve() {
//
//        for(int i=0;i<9;++i) {
//            for (int j = 0; j < 9; ++j) {
//                int v = ni();
//                a[i][j] = v;
//                if(v>0) {
//                    vis_row[i][v] = true;
//                    vis_col[j][v] = true;
//                    vis_room[get_room(i, j)][v] = true;
//                }else{
//                    space++;
//                }
//            }
//        }
//
//
//        prepare = new int[space][2];
//
//        int p = 0;
//
//        for(int i=0;i<9;++i) {
//            for (int j = 0; j < 9; ++j) {
//                if(a[i][j]==0){
//                    prepare[p][0] = i;
//                    prepare[p][1]= j;p++;
//                    List<Integer> temp =new ArrayList<>();
//                    for(int k=1;k<=9;++k){
//                        if(!vis_col[j][k]&&!vis_row[i][k]&&!vis_room[get_room(i,j)][k]){
//                            temp.add(k);
//                        }
//                    }
//                    int sz = temp.size();
//                    val[i][j] = new int[sz];
//                    for(int k=0;k<sz;++k){
//                        val[i][j][k] = temp.get(k);
//                    }
//                }
//            }
//        }
//        Arrays.sort(prepare,(x,y)->{
//           return Integer.compare(val[x[0]][x[1]].length,val[y[0]][y[1]].length);
//        });
//        dfs(0);
//
//
//
//
//
//
//
//
//
//
//    }




    InputStream is;
    PrintWriter out;

    void run() throws Exception {
        //is = new FileInputStream(new File("C:\\Users\\Luqi\\Downloads\\P3387_9.in"));
        is = System.in;
        out = new PrintWriter(System.out);

        solve();
        out.flush();
    }

    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;

    private int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) return -1;
        }
        return inbuf[ptrbuf++];
    }

    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }

    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
        return b;
    }

    private double nd() {
        return Double.parseDouble(ns());
    }

    private char nc() {
        return (char) skip();
    }

    private char ncc() {
        int b = readByte();
        return (char) b;
    }

    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private String nline() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!isSpaceChar(b) || b == ' ') {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[][] nm(int n, int m) {
        char[][] a = new char[n][];
        for (int i = 0; i < n; i++) a[i] = ns(m);
        return a;
    }

    private int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = ni();
        return a;
    }

    private long[] nal(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = nl();
        return a;
    }

    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) {
        }
        ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') num = (num << 3) + (num << 1) + (b - '0');
            else return minus ? -num : num;
            b = readByte();
        }
    }

    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) {
        }
        ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') num = num * 10 + (b - '0');
            else return minus ? -num : num;
            b = readByte();
        }
    }

    void print(Object obj) {
        out.print(obj);
    }

    void println(Object obj) {
        out.println(obj);
    }

    void println() {
        out.println();
    }

    void printArray(int a[],int from){
        int l = a.length;
        for(int i=from;i<l;++i){
            print(a[i]);
            if(i!=l-1){
                print(" ");
            }
        }
        println();
    }

    void printArray(long a[],int from){
        int l = a.length;
        for(int i=from;i<l;++i){
            print(a[i]);
            if(i!=l-1){
                print(" ");
            }
        }
        println();
    }
}