Problem: There is an evil creature in a square on N-by-M grid (2 \leq N, M \leq 100), and you want to kill it using a laser generator located in a different square. Since the location and direction of the laser generator are fixed, you may need to use several mirrors to reflect laser beams. There are some obstacles on the grid and you have a limited number of mirrors. Please find out whether it is possible to kill the creature, and if possible, find the minimum number of mirrors.

There are two types of single-sided mirrors; type P mirrors can be placed at the angle of 45 or 225 degrees from east-west direction, and type Q mirrors can be placed with at the angle of 135 or 315 degrees. For example, four mirrors are located properly, laser go through like the following.

<image>

Note that mirrors are single-sided, and thus back side (the side with cross in the above picture) is not reflective. You have A type P mirrors, and also A type Q mirrors (0 \leq A \leq 10). Although you cannot put mirrors onto the squares with the creature or the laser generator, laser beam can pass through the square. Evil creature is killed if the laser reaches the square it is in.



Input

Each test case consists of several lines.

The first line contains three integers, N, M, and A. Each of the following N lines contains M characters, and represents the grid information. '#', '.', 'S', 'G' indicates obstacle, empty square, the location of the laser generator, and the location of the evil creature, respectively. The first line shows the information in northernmost squares and the last line shows the information in southernmost squares. You can assume that there is exactly one laser generator and exactly one creature, and the laser generator emits laser beam always toward the south.

Output

Output the minimum number of mirrors used if you can kill creature, or -1 otherwise.

Examples

Input

3 3 2
S#.
...
.#G


Output

2


Input

3 3 1
S#.
...
.#G


Output

-1


Input

3 3 1
S#G
...
.#.


Output

2


Input

4 3 2
S..
...
..#
.#G


Output

-1

Solution (in CPP):

Solution:
#define  _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES

#pragma comment (linker, "/STACK:526000000")

#include "bits/stdc++.h"

using namespace std;
typedef string::const_iterator State;
#define eps 1e-5L
#define MAX_MOD 1000000007LL
#define GYAKU 500000004LL
#define seg_size 262144LL
#define MOD 998244353LL
#define pb push_back
#define mp make_pair
typedef long long ll;
#define REP(a,b) for(long long (a) = 0;(a) < (b);++(a))
#define ALL(x) (x).begin(),(x).end()

// geometry library

typedef complex<long double> Point;
typedef pair<complex<long double>, complex<long double>> Line;

typedef struct Circle {
    complex<long double> center;
    long double r;
}Circle;

//内積、 dot(a,b) = |a||b|cos()
long double dot(Point a, Point b) {
    return (a.real() * b.real() + a.imag() * b.imag());
}
//外積、cross(a,b) = |a||b|sin()
long double cross(Point a, Point b) {
    return (a.real() * b.imag() - a.imag() * b.real());
}

//線分と点の距離
long double Dist_Line_Point(Line a, Point b) {
    if (dot(a.second - a.first, b - a.first) < eps) return abs(b - a.first);
    if (dot(a.first - a.second, b - a.second) < eps) return abs(b - a.second);
    return abs(cross(a.second - a.first, b - a.first)) / abs(a.second - a.first);
}

//線分の交差判定
int is_intersected_ls(Line a, Line b) {
    return (cross(a.second - a.first, b.first - a.first) * cross(a.second - a.first, b.second - a.first) < 0) &&
        (cross(b.second - b.first, a.first - b.first) * cross(b.second - b.first, a.second - b.first) < 0);
}

//線分の交点
Point intersection_l(Line a, Line b) {
    Point da = a.second - a.first;
    Point db = b.second - b.first;
    return a.first + da * cross(db, b.first - a.first) / cross(db, da);
}

//線分と線分の距離
long double Dist_Line_Line(Line a, Line b) {
    if (is_intersected_ls(a, b) == 1) {
        return 0;
    }
    return min({ Dist_Line_Point(a,b.first), Dist_Line_Point(a,b.second),Dist_Line_Point(b,a.first),Dist_Line_Point(b,a.second) });
}

//円と円の交点
pair<Point, Point> intersection_Circle_Circle(Circle a, Circle b) {
    long double dist = abs(a.center - b.center);
    assert(dist <= eps + a.r + b.r);
    assert(dist+eps >= abs(a.r - b.r));
    Point target = b.center - a.center;
    long double pointer = target.real() * target.real() + target.imag() * target.imag();
    long double aa = pointer + a.r * a.r - b.r * b.r;
    aa /= 2.0L;
    Point l{ (aa * target.real() + target.imag() * sqrt(pointer * a.r * a.r - aa * aa))/pointer,
            (aa* target.imag() - target.real() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer};
    Point r{ (aa * target.real() - target.imag() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer,
        (aa * target.imag() + target.real() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer };
    r = r + a.center;
    l = l + a.center;
    return mp(l, r);
}

//end of geometry

template<typename A>
A pows(A val, ll b) {
    assert(b >= 1);
    A ans = val;
    b--;
    while (b) {
        if (b % 2) {
            ans *= val;
        }
        val *= val;
        b /= 2LL;
    }
    return ans;
}

template<typename A>
class Compressor {
public:
    bool is_zipped = false;
    map<A, ll> zipper;
    map<ll, A> unzipper;
    queue<A> fetcher;
    Compressor(){
        is_zipped = false;
        zipper.clear();
        unzipper.clear();
    }
    void add(A now) {
        assert(is_zipped == false);
        zipper[now] = 1;
        fetcher.push(now);
    }
    void exec() {
        assert(is_zipped == false);
        int cnt = 0;
        for (auto i = zipper.begin(); i != zipper.end(); ++i) {
            i->second = cnt;
            unzipper[cnt] = i->first;
            cnt++;
        }
        is_zipped = true;
    }
    ll fetch() {
        assert(is_zipped == true);
        A hoge = fetcher.front();
        fetcher.pop();
        return zipper[hoge];
    }
    ll zip(A now) {
        assert(is_zipped == true);
        assert(zipper.find(now) != zipper.end());
        return zipper[now];
    }
    A unzip(ll a) {
        assert(is_zipped == true);
        assert(a < unzipper.size());
        return unzipper[a];
    }
    ll next(A now) {
        auto x = zipper.upper_bound(now);
        if (x == zipper.end()) return zipper.size();
        return (ll)((*x).second);
    }
    ll back(A now) {
        auto x = zipper.lower_bound(now);
        if (x == zipper.begin()) return -1;
        x--;
        return (ll)((*x).second);
    }
};

template<typename A>
class Matrix {
public:
    vector<vector<A>> data;
    Matrix(vector<vector<A>> a) :data(a){

    }
    Matrix operator + (const Matrix obj) {
        vector<vector<A>> ans;
        assert(obj.data.size() == this->data.size());
        assert(obj.data[0].size() == this->data[0].size());
        REP(i, obj.data.size()) {
            ans.push_back(vector<A>());
            REP(q, obj.data[i].size()) {
                A hoge = obj.data[i][q] + (this -> data[i][q]);
                ans.back().push_back(hoge);
            }
        }
        return Matrix(ans);
    }
    Matrix operator - (const Matrix obj) {
        vector<vector<A>> ans;
        assert(obj.data.size() == this->data.size());
        assert(obj.data[0].size() == this->data[0].size());
        REP(i, obj.data.size()) {
            ans.push_back(vector<A>());
            REP(q, obj.data[i].size()) {
                A hoge = this->data[i][q] - obj.data[i][q];
                ans.back().push_back(hoge);
            }
        }
        return Matrix(ans);
    }
    Matrix operator * (const Matrix obj) {
        vector<vector<A>> ans;
        assert(obj.data.size() == this->data[0].size());
        REP(i, this -> data.size()) {
            ans.push_back(vector<A>());
            REP(q, obj.data[0].size()) {
                A hoge = (this -> data[i][0]) * (obj.data[0][q]);
                for(int t = 1;t < obj.data[i].size();++t){
                    hoge += this -> data[i][t] * obj.data[t][q];
                }
                ans.back().push_back(hoge);
            }
        }
        return Matrix(ans);
    }
    Matrix &operator *= (const Matrix obj) {
        *this = (*this * obj);
        return *this;
    }
    Matrix& operator += (const Matrix obj) {
        *this = (*this + obj);
        return *this;
    }
    Matrix& operator -= (const Matrix obj) {
        *this = (*this - obj);
        return *this;
    }
};

class modint {
public:
    using u64 = std::uint_fast64_t;
    u64 value = 0;
    u64 mod;
    modint(ll a, ll b): value(((a%b) + 2 * b) % b),mod(b) {

    }
    modint operator+(const modint rhs) const{
        return modint(*this) += rhs;
    }
    modint operator-(const modint rhs) const{
        return modint(*this) -= rhs;
    }
    modint operator*(const modint rhs) const {
        return modint(*this) *= rhs;
    }
    modint operator/(const modint rhs) const{
        return modint(*this) /= rhs;
    }
    modint& operator+=(const modint rhs) {
        assert(rhs.mod == mod);
        value += rhs.value;
        if (value >= mod) {
            value -= mod;
        }
        return *this;
    }
    modint& operator-=(const modint rhs) {
        assert(rhs.mod == mod);
        if (value < rhs.value) {
            value += mod;
        }
        value -= rhs.value;
        return *this;
    }
    modint& operator*=(const modint rhs) {
        assert(rhs.mod == mod);
        value = (value *  rhs.value) % mod;
        return *this;
    }
    modint& operator/=(modint rhs) {
        assert(rhs.mod == mod);
        ll rem = mod - 2;
        while (rem) {
            if (rem % 2) {
                *this *= rhs;
            }
            rhs *= rhs;
            rem /= 2LL;
        }
        return *this;
    }
    friend ostream& operator<<(ostream& os, modint& p) {
        os << p.value;
        return (os);
    }
};

void init() {
    iostream::sync_with_stdio(false);
    cout << fixed << setprecision(20);
}

unsigned long xor128() {
    static unsigned long x = 123456789, y = 362436069, z = 521288629, w = 88675123;
    unsigned long t = (x ^ (x << 11));
    x = y; y = z; z = w;
    return (w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)));
}

#define int ll
bool dp[4][100][100][11][11];
int grid[100][100];
int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };
int P[4] = { 1,0,3,2 };
int Q[4] = { 3,2,1,0 };
void solve(){
    int n, m, a;
    cin >> n >> m >> a;
    pair<int, int> goal;
    queue<tuple<int, int, int, int, int>> next;
    REP(i, n) {
        string s;
        cin >> s;
        REP(q, m) {
            if (s[q] == '#') {
                grid[i][q] = 1;
            }
            if (s[q] == 'S') {
                grid[i][q] = 2;
                if (i + 1 >= n) {
                    cout << -1 << endl;
                    return;
                }
                dp[0][i + 1][q][a][a] = 1;
                next.push(make_tuple(0, i + 1, q, a, a));
            }
            if (s[q] == 'G') {
                goal = mp(i, q);
            }
        }
    }
    while (next.empty() == false) {
        auto verify = [n, m](int x, int y) {
            if (x >= 0 && x < n && y >= 0 && y < m&&grid[x][y] != 1) return 1;
            return 0;
        };
        tuple<int, int, int, int, int> now = next.front();
        next.pop();
        if (grid[get<1>(now)][get<2>(now)] == 1) continue;
        if (grid[get<1>(now)][get<2>(now)] == 2 && get<0>(now) == 2) continue;
        {
            int x = get<1>(now) + dx[get<0>(now)];
            int y = get<2>(now) + dy[get<0>(now)];
            if(verify(x,y))
            if (dp[get<0>(now)][x][y][get<3>(now)][get<4>(now)] == 0) {
                dp[get<0>(now)][x][y][get<3>(now)][get<4>(now)] = 1;
                next.push(make_tuple(get<0>(now), x, y, get<3>(now), get<4>(now)));
            }
        }
        if (grid[get<1>(now)][get<2>(now)] == 2) continue;
        if (get<3>(now) > 0) {
            int t = P[get<0>(now)];
            int x = get<1>(now) + dx[t];
            int y = get<2>(now) + dy[t];
            if (verify(x, y))
                if (dp[t][x][y][get<3>(now) - 1][get<4>(now)] == 0) {
                    dp[t][x][y][get<3>(now) - 1][get<4>(now)] = 1;
                    next.push(make_tuple(t, x, y, get<3>(now) - 1, get<4>(now)));
                }
        }
        if (get<4>(now) > 0) {
            int t = Q[get<0>(now)];
            int x = get<1>(now) + dx[t];
            int y = get<2>(now) + dy[t];
            if (verify(x, y))
                if (dp[t][x][y][get<3>(now)][get<4>(now) - 1] == 0) {
                    dp[t][x][y][get<3>(now)][get<4>(now) - 1] = 1;
                    next.push(make_tuple(t, x, y, get<3>(now), get<4>(now) - 1));
                }
        }
    }
    int ans = 30;
    REP(i, a + 1) {
        REP(q, a + 1) {
            REP(j, 4) {
                if (dp[j][goal.first][goal.second][i][q]) {
                    ans = min(ans, a - i + a - q);
                }
            }
        }
    }
    if (ans == 30)ans = -1;
    cout << ans << endl;
}

#undef int
int main() {
    init();
    solve();
}