#include<stdio.h>#include<string.h>#include<math.h>#include<iostream>#include<algorithm>#include<map>#include<vector>using namespace std;#define pb push_back#define mp make_pair#define X first#define Y second#define inf 0xffffffftypedef long long lld;#define eps 1e-8#define pi acos(-1.0)#define mod 10000007char g[110][110];int in[110];int out[110];lld fac[110];lld c[110][110];lld dp[110][110];lld inv[110];lld Inv(lld x){ if(x == 1) return 1; return Inv(mod%x)*(mod-mod/x)%mod;}lld round(lld x){return (fac[x]*inv[x])%mod;}lld dfs(int x,int y){if(dp[x][y] != -1)return dp[x][y];dp[x][y]=0;if(x == 0){for(int j=1;j<=y;j++){if(j == 0)continue;lld add=round((lld)j);add=(add*c[y-1][j-1])%mod;add=(add*dfs(x,y-j))%mod;dp[x][y]=(dp[x][y]+add)%mod;}}else{for(int i=1;i<=x;i++)for(int j=0;j<=y;j++){if(i+j*2 <= 1)continue;lld add=round((lld)(i+j));add=(add*c[x-1][i-1])%mod;add=(add*c[y][j])%mod;add=(add*dfs(x-i,y-j))%mod;dp[x][y]=(dp[x][y]+add)%mod;}}return dp[x][y];}void init(){for(int i=1;i<=100;i++)inv[i]=Inv(i);inv[0]=1;c[0][0]=1;c[1][0]=c[1][1]=1;fac[0]=1;for(int i=1;i<=100;i++)fac[i]=(fac[i-1]*i)%mod;for(int i=2;i<=100;i++){c[i][0]=c[i][i]=1;for(int j=1;j<i;j++)c[i][j]=(c[i-1][j-1]+c[i-1][j])%mod;}memset(dp,-1,sizeof(dp));dp[0][0]=1;}int main(){init();int n;while(1){scanf("%d",&n);if(n == 0)break;for(int i=0;i<n;i++)scanf("%s",g[i]);memset(in,0,sizeof(in));memset(out,0,sizeof(out));for(int i=0;i<n;i++)for(int j=0;j<n;j++){if(i == j)continue;if(g[i][j] == 'Y'){in[j]++;out[i]++;}}bool ok=true;int x,y;x=y=0;for(int i=0;i<n;i++){if(in[i] >= 2 || out[i] >= 2)ok=false;if(in[i] == 0 && out[i] == 0)x++;if(in[i] == 0 && out[i] == 1)y++;}if(!ok){printf("0n");continue;}cout << dfs(x,y) << endl;}return 0;}
