#include <bits/stdc++.h>
using namespace std;
const int cd[4][2]={{0,1},{0,-1},{1,0},{-1,0}},b10m=(1<<10)-1;
int w,h,n,stg[4],trg[4],gid[20][20],tot;
char mapp[20][20];
vector<int> gr[400];
int extn[4],stat[4];
queue<int> que;
unordered_map<int,int> vis;
void extdfs(int cur,int eS,const int sS){
    if(cur==n){
        if(vis.count(eS)) return;
        que.push(eS);
        vis[eS]=vis[sS]+1;
        return;
    }
    for(int v:gr[stat[cur]]){
        bool ok=true;
        for(int i=0;i<cur;++i){
            if(extn[i]==v||(extn[i]==stat[cur]&&v==stat[i])){
                ok=false;
                break;
            }
        }
        extn[cur]=v;
        if(ok) extdfs(cur+1,(eS<<10)+v,sS);
    }
}
int bfs(){
    int stS=0,tgS=0;
    for(int i=0;i<n;++i) stS=(stS<<10)+stg[i];
    for(int i=0;i<n;++i) tgS=(tgS<<10)+trg[i];
    while(!que.empty()) que.pop();
    vis.clear();
    que.push(stS),vis[stS]=0;
    while(!que.empty()){
        int ssS,sS=que.front();que.pop();
        if(sS==tgS) return vis[sS];
        ssS=sS;
        for(int i=n-1;i>=0;--i) stat[i]=b10m&ssS,ssS>>=10;
        extdfs(0,0,sS);
    }
    return 0x3f3f3f3f;
}
int main(){
    ios::sync_with_stdio(false);
    while(cin>>w>>h>>n&&(w||h||n)){
        tot=0;
        cin.get();
        for(int i=1;i<=h;++i){
            string ss;
            getline(cin,ss);
            ss=" "+ss;
            for(int j=1;j<=w;++j){
                mapp[i][j]=ss[j];
                if(mapp[i][j]!='#'){
                    gid[i][j]=++tot;
                    gr[tot].clear();
                    gr[tot].push_back(tot);
                }
            }
        }
        for(int i=2;i<h;++i) for(int j=2;j<w;++j){
            if(mapp[i][j]=='#') continue;
            for(int k=0;k<4;++k){
                int ii=i+cd[k][0],jj=j+cd[k][1];
                if(mapp[ii][jj]!='#'){
                    gr[gid[i][j]].push_back(gid[ii][jj]);
                    gr[gid[ii][jj]].push_back(gid[i][j]);
                }
            }
            if(isupper(mapp[i][j])) trg[mapp[i][j]-'A']=gid[i][j];
            if(islower(mapp[i][j])) stg[mapp[i][j]-'a']=gid[i][j];
        }
        cout<<bfs()<<endl;
    }
    return 0;
}