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void normalLine(int line) {
double factor = mat[line][line];
for (double& x : mat[line]) x /= factor;
}
void takeAll(int n, int line) {
for (int i = 0; i < n; i++) {
if (i == line) continue;
double diff = mat[i][line];
for (int j = 0; j < sz(mat[i]); j++) {
mat[i][j] -= diff * mat[line][j];
}}}
int gauss(int n) {
vector<bool> done(n, false);
for (int i = 0; i < n; i++) {
int swappee = i; // Sucht Pivotzeile für bessere Stabilität.
for (int j = 0; j < n; j++) {
if (done[j]) continue;
if (abs(mat[j][i]) > abs(mat[i][i])) swappee = j;
}
swap(mat[i], mat[swappee]);
if (abs(mat[i][i]) > EPS) {
normalLine(i);
takeAll(n, i);
done[i] = true;
}}
// Ab jetzt nur checks bzgl. Eindeutigkeit/Existenz der Lösung.
for (int i = 0; i < n; i++) {
bool allZero = true;
for (int j = i; j < n; j++) allZero &= abs(mat[i][j]) <= EPS;
if (allZero && abs(mat[i][n]) > EPS) return INCONSISTENT;
if (allZero && abs(mat[i][n]) <= EPS) return MULTIPLE;
}
return UNIQUE;
}
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