#include<cstdio>
#include<cstring>
#include<cctype>
#include<queue>
using namespace std;
const int maxs=20;
const int maxn=150;
const int dx[]={1,-1,0,0,0};
const int dy[]={0,0,1,-1,0};
inline int ID(int a,int b,int c)
{
	return (a<<16)|(b<<8)|c;
}
int s[3],t[3];
int deg[maxn],G[maxn][5];
inline bool error(int a, int b, int a2, int b2)
{
	return a2==b2||(a2==b&&b2==a);
}
int d[maxn][maxn][maxn];
int bfs()
{
	queue<int> q;
	memset(d,-1,sizeof(d));
	q.push(ID(s[0],s[1],s[2]));
	d[s[0]][s[1]][s[2]]=0;
	while(!q.empty())
	{
		int u=q.front();
		q.pop();
		int a=(u>>16)&0xff,b=(u>>8)&0xff,c=u&0xff;
		if(a==t[0]&&b==t[1]&&c==t[2]) return d[a][b][c];
		for(int i=0;i<deg[a];i++)
		{
			int a2=G[a][i];
			for(int j=0;j<deg[b];j++)
			{
				int b2=G[b][j];
				if(error(a,b,a2,b2)) continue;
				for(int k=0;k<deg[c];k++)
				{
					int c2=G[c][k];
					if(error(a,c,a2,c2)) continue;
					if(error(b,c,b2,c2)) continue;
					if(d[a2][b2][c2]!=-1) continue;
					d[a2][b2][c2]=d[a][b][c]+1;
					q.push(ID(a2,b2,c2));
				}
			}
		}
	}
	return -1;
}
int main()
{
#ifdef local
	freopen("pro.in","r",stdin);
#endif
	int w,h,n; 
	while(scanf("%d%d%d\n",&w,&h,&n)==3&&n)
	{
		char maze[20][20];
		for(int i=0;i<h;i++)
			fgets(maze[i], 20, stdin);
		int cnt,x[maxn],y[maxn],id[maxs][maxs];
		cnt=0;
		for(int i=0;i<h;i++)
			for(int j=0;j<w;j++)
				if(maze[i][j]!='#')
				{
					x[cnt]=i;
					y[cnt]=j;
					id[i][j]=cnt;
					if(islower(maze[i][j])) s[maze[i][j]-'a']=cnt;
					else if(isupper(maze[i][j])) t[maze[i][j]-'A']=cnt;
					cnt++;
				}
		for(int i=0;i<cnt;i++)
		{
			deg[i]=0;
			for(int j=0;j<5;j++)
			{
				int nx=x[i]+dx[j],ny=y[i]+dy[j];
				if(maze[nx][ny]!='#') G[i][deg[i]++]=id[nx][ny];
			}
		}
		if(n<=2) { deg[cnt] = 1; G[cnt][0] = cnt; s[2] = t[2] = cnt++; }
		if(n<=1) { deg[cnt] = 1; G[cnt][0] = cnt; s[1] = t[1] = cnt++; }
		printf("%d\n", bfs());
	}
	return 0;
}