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#include <bits/stdc++.h>
using namespace std;

typedef long long int lli;

const int MAXN = 3005;
const lli MOD = 1'000'000'007;

char in[MAXN];

vector<int> t[MAXN];

// lli unsafe_mod(lli x) {
// 	while (x >= MOD)
// 		x -= MOD;
// 	
// 	return x;
// }

#define unsafe_mod(x) ((x) % MOD)

struct Node {
	lli no=0, nl=0, np=0, ok=0;
	
// 	void mod() {
// 		no = unsafe_mod(no);
// 		nl = unsafe_mod(nl);
// 		np = unsafe_mod(np);
// 		ok = unsafe_mod(ok);
// 	}
};

Node res[2 * MAXN];
int numl;

Node rem_res[2 * MAXN];
int rem_numl;

void update(int a) {
	if (a == 1) {
		for (int i=numl+1; i>=0; i--) {
			res[i].ok = unsafe_mod(res[i].ok + res[i].nl);
			res[i].nl = 0;
			
			res[i].np = unsafe_mod(res[i].np + res[i].no);
			res[i].no = 0;
			
			if (i > 0)
				res[i].no = unsafe_mod(res[i].no + res[i-1].nl + res[i-1].no);
		}
	}
	else {
		for (int i=0; i<=numl+1; i++) {
			res[i].ok = unsafe_mod(res[i].ok + res[i].np);
			res[i].np = 0;
			
			res[i].nl = unsafe_mod(res[i].nl + res[i].no);
			res[i].no = 0;
			
			res[i].no = unsafe_mod(res[i].no + res[i+1].np + res[i+1].no);
		}
	}
}

lli compute_score(int x, int y, bool reuse) {
	if (reuse) {
		numl = rem_numl;
		for (int i=0; i<=numl; i++)
			res[i] = rem_res[i];
	} else {
		numl = 1;
		res[0].no = 1;
		
		for (int a : t[x]) {
			if (a == 1)
				numl++;
			update(a);
		}
	
		for (int i=0; i<=numl; i++)
			rem_res[i] = res[i];
		rem_numl = numl;
	}
	
	for (int a : t[y]) {
		if (a == 1)
			numl++;
		update(a);
	}
	
	lli w = unsafe_mod(res[0].no + res[0].nl + res[0].np + res[0].ok - 1 + MOD);
	
	for (int i=0; i<=numl; i++)
		res[i] = Node();
	
	return w;
}

int main() {
	int n;
	scanf("%d%*c", &n);
	
	for (int i=0; i<n; i++) {
		scanf("%s", in);
		int l = 0;
		
		for (int j=0; in[j]!=0; j++) {
			l++;
			
			if (in[j] == 'L') {
				t[i].push_back(1);
			}
			else {
				t[i].push_back(-1);
			}
		}
	}
	
	for (int i=0; i<n; i++) {
		for (int j=0; j<n; j++) {
			printf("%lld ", compute_score(i, j, (j!=0)));
		}
		printf("\n");
	}
	
	return 0;
}