C++ :

#include <cstdio>
#include <cstring>
#include <algorithm>
#define INF 0x1f1f1f1f
#define MAXV 600
#define MAXE 5000

using namespace std;

int flag[MAXV], head[MAXV], size, edgeID[MAXE];
int que[MAXV + 10], front, rear, pre[MAXV];
int dist[MAXV], maxFlow[MAXV];

struct Edge {
	int v, next, opp;     //边上的另一个顶点, 下一条边, 反向边 
	int cost, cap, f;      //花费、容量、流量 
	Edge(){}
	Edge(int _v, int _cost, int _cap, int _f, int _next, int _opp):
		v(_v), cost(_cost), cap(_cap), f(_f), next(_next), opp(_opp){}
}edge[MAXE];

void init() {
	size = 0;
	memset(head, -1, sizeof(head));
}

void add_edge(int u, int v, int cap, int cost, int f = 0) {
	edge[size] = Edge(v, cost, cap, f, head[u], size + 1);
	edgeID[size] = u;
	head[u] = size++;
	edge[size] = Edge(u, -cost, 0, f, head[v], size - 1);
	edgeID[size] = v;
	head[v] = size++;
}

int SPFA(int S, int T) {      //找花费最小的一条路 
	int i, u, v;
	front = rear = 0;
	memset(flag, 0, sizeof(flag));              
	memset(dist, 0x1f, sizeof(dist));
	memset(pre, -1, sizeof(pre));               
	dist[S] = 0;	                                                  
	flag[S] = 1;
	maxFlow[S] = INF;
	que[rear++] = S;
	while (front != rear) {
		u = que[front++];
		if(front >= MAXV) front = 0;
		flag[u] = 0;
		for(i = head[u]; i != -1; i = edge[i].next) {
			v = edge[i].v;
			if (edge[i].cap > edge[i].f && dist[v] > dist[u] + edge[i].cost){
				dist[v] = dist[u] + edge[i].cost;
				maxFlow[v] = min(edge[i].cap - edge[i].f, maxFlow[u]);
				pre[v] = i;          //记录前驱在edge中的下标
				if (!flag[v]) {
					que[rear++] = v;
					if (rear >= MAXV) rear = 0;
					flag[v] = 1;
				}
			}
		}
	}
	if (dist[T] == INF) return 0;
	else return 1;
}

int MFMC(int S, int T) {
	int sumCost, sumFlow, k;
	sumCost = sumFlow = 0;
	while (SPFA(S, T)) {
		k= T;
		while (pre[k] >= 0) {
			edge[pre[k]].f += maxFlow[T];
			edge[edge[pre[k]].opp].f = -edge[pre[k]].f;
			k = edgeID[pre[k]];
		}
		sumFlow += maxFlow[T];
		sumCost += dist[T] * maxFlow[T];
	}
	return sumCost;
}

char board[16][16];
int main()
{
	init();
	int r, c, n, src, sink;
	scanf("%d%d",&r,&c);
	for(int i = 0;i < r; ++i)
		scanf("%s",board[i]);

	const char D[] = "ULDR";
	const int dx[] = {0, -1, 0, 1};
	const int dy[] = {-1, 0, 1, 0};
	n = r * c;
	src = 2*n; sink = 2*n + 1;


	for(int i = 0;i < n; ++i){
		add_edge(src, i, 1, 0);
		add_edge(i + n, sink, 1, 0);
	}

	for(int x = 0;x < c; ++x){
		for(int y = 0;y < r; ++y){
			for(int d = 0;d < 4; ++d){
				int nx = (x + dx[d] + c) % c;
				int ny = (y + dy[d] + r) % r;

				if(board[y][x] == D[d]){
					add_edge((y*c+x), ny*c+nx+n, 1, 0);
				}else{
					add_edge((y*c+x), ny*c+nx+n, 1, 1);
				}
			}
		}
	}
	printf("%d\n",MFMC(src, sink));

}