bug

#pragma GCC optimize ("O3")
#pragma GCC target("sse4")
#include <bits/stdc++.h>
#define f first
#define s second
#define pb push_back
#define mp make_pair
#define ts to_string
#define ub upper_bound
#define lb lower_bound
const char nl = '\n';
using namespace std;
using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using str = string;
//The following debugging code was taken from Benjamin Qi's template :)
str ts(char c) { return str(1,c); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
template<class A> str ts(complex<A> c) {
    stringstream ss; ss << c; return ss.str(); }
str ts(vector<bool> v) {
    str res = "{"; for(int i = 0;i < (int)v.size(); i++) res += char('0'+v[i]);
    res += "}"; return res; }
template<size_t SZ> str ts(bitset<SZ> b) {
    str res = ""; for(int i = 0; i < b.size(); i++) res += char('0'+b[i]);
    return res; }
template<class A, class B> str ts(pair<A,B> p);
template<class T> str ts(T v) {
    bool fst = 1; str res = "{";
    for (const auto& x: v) {
        if (!fst) res += ", ";
        fst = 0; res += ts(x);
    }
    res += "}"; return res;
}
template<class A, class B> str ts(pair<A,B> p) {
    return "("+ts(p.f)+", "+ts(p.s)+")"; }
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
    cerr << ts(h); if (sizeof...(t)) cerr << ", ";
    DBG(t...); }

#ifdef LOCAL
#define dbg(...) cerr << "LINE(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 0
//freopen(".in", "r", stdin);
//freopen(".out", "w", stdout);
#endif
//CODE STARTS HERE-----------------------------------------------------------------------------------------//
const int N = 21;
int n;
char a[N][N];
queue<array<int, 6>> bfs;
int vis[N][N][N][N][4][4],d[N][N][N][N][4][4];
int dx[] = {0,1,0,-1}; int dy[] = {1,0,-1,0};
array<int, 6> forward(array<int, 6> q){
    array<int,6> ne = q;
    ne[0] += dx[ne[4]];
    ne[1] += dy[ne[4]];
    ne[2] += dx[ne[5]];
    ne[3] += dy[ne[5]];
    if(a[ne[0]][ne[1]] == 'H' || ne[0] < 0 || ne[0] >= n || ne[1] < 0 || ne[1] >= n){
        ne[0] -= dx[ne[4]];
        ne[1] -= dy[ne[4]];
    }
    if(a[ne[2]][ne[3]] == 'H'|| ne[2] < 0 || ne[2] >= n || ne[3] < 0 || ne[3] >= n){
        ne[2] -= dx[ne[5]];
        ne[3] -= dy[ne[5]];
    }
    if(q[0] == 0 && q[1] == 0){
        ne[0] = q[0], ne[1] = q[1];
    }
    if(q[2] == 0 && q[3] == 0){
        ne[2] = q[2], ne[3] = q[3];
    }
    return ne;
}
vector<array<int, 6>> FIND(array<int,6> q){
    vector<array<int, 6>> ret;
    array<int, 6> ne = forward(q);
    if(!vis[ne[0]][ne[1]][ne[2]][ne[3]][ne[4]][ne[5]]){
        ret.pb(ne);
        vis[ne[0]][ne[1]][ne[2]][ne[3]][ne[4]][ne[5]] = 1;
    }
    ne = q;
    ne[4] = (q[4] + 1) % 4;
    ne[5] = (q[5] + 1) % 4;
    if(!vis[ne[0]][ne[1]][ne[2]][ne[3]][ne[4]][ne[5]]){
        ret.pb(ne);
        vis[ne[0]][ne[1]][ne[2]][ne[3]][ne[4]][ne[5]] = 1;
    }
    ne = q;
    ne[4] = (q[4] + 3) % 4;
    ne[5] = (q[5] + 3) % 4;
    if(!vis[ne[0]][ne[1]][ne[2]][ne[3]][ne[4]][ne[5]]){
        ret.pb(ne);
        vis[ne[0]][ne[1]][ne[2]][ne[3]][ne[4]][ne[5]] = 1;
    }
    // dbg(ret);
    return ret;
}
signed main(){
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    // ifstream cin("cownav.in");
    // ofstream cout("cownav.out");
    cin >> n;
    for(int i =0 ; i < n; i++){
        for(int j =0 ; j < n; j++){
            cin >> a[i][j];
        }
    }
    bfs.push({n-1,n-1,n-1,n-1,2,3});
    vis[n-1][n-1][n-1][n-1][2][3] = 1;
    memset(d, 0x3f, sizeof(d));
    d[n-1][n-1][n-1][n-1][2][3] = 0;
    //0=up,1=right,2=down,3=left
    while(!bfs.empty()){
        array<int, 6> cur = bfs.front();
        // dbg(cur,d[cur[0]][cur[1]][cur[2]][cur[3]][cur[4]][cur[5]]);
        bfs.pop();
        vector<array<int, 6>> remain = FIND(cur);
        for(auto x : remain){
            bfs.push(x);
            d[x[0]][x[1]][x[2]][x[3]][x[4]][x[5]] = d[cur[0]][cur[1]][cur[2]][cur[3]][cur[4]][cur[5]] + 1;
        }
    }
    int ans = 1e9;
    for(int i = 0; i < 4; i++){
        for(int j = 0; j < 4; j++){
            ans = min(d[0][0][0][0][i][j],ans);
        }
    }
    cout << ans << nl;
}