mirror of
https://github.com/Z3Prover/z3
synced 2025-04-06 17:44:08 +00:00
updates to monomial bounds
This commit is contained in:
Nikolaj Bjorner
parent
ba6c23bbc5
commit
08af965b56
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@ -123,6 +123,7 @@ public:
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m_stacked_simplex_strategy.pop(k);
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m_r_solver.m_settings.set_simplex_strategy(m_stacked_simplex_strategy);
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m_infeasible_linear_combination.reset();
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lp_assert(m_r_solver.basis_heading_is_correct());
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}
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@ -49,7 +49,7 @@ void lar_core_solver::fill_not_improvable_zero_sum_from_inf_row() {
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m_infeasible_sum_sign = m_r_solver.inf_sign_of_column(bj);
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m_infeasible_linear_combination.clear();
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for (auto & rc : m_r_solver.m_A.m_rows[m_r_solver.m_inf_row_index_for_tableau])
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m_infeasible_linear_combination.push_back(std::make_pair(rc.coeff(), rc.var()));
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m_infeasible_linear_combination.push_back({rc.coeff(), rc.var()});
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}
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void lar_core_solver::fill_not_improvable_zero_sum() {
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@ -179,7 +179,7 @@ namespace lp {
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lp_status lar_solver::get_status() const { return m_status; }
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void lar_solver::set_status(lp_status s) {
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void lar_solver::set_status(lp_status s) {
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TRACE("lar_solver", tout << "setting status to " << s << "\n";);
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m_status = s;
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}
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@ -224,9 +224,9 @@ namespace lp {
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}
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void lar_solver::push() {
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m_trail.push_scope();
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m_simplex_strategy = m_settings.simplex_strategy();
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m_simplex_strategy.push();
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m_columns_to_ul_pairs.push();
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m_crossed_bounds_column = null_lpvar;
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m_crossed_bounds_deps = nullptr;
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m_mpq_lar_core_solver.push();
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@ -260,16 +260,16 @@ namespace lp {
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TRACE("lar_solver", tout << "k = " << k << std::endl;);
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m_crossed_bounds_column = null_lpvar;
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m_crossed_bounds_deps = nullptr;
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unsigned n = m_columns_to_ul_pairs.peek_size(k);
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m_trail.pop_scope(k);
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unsigned n = m_columns_to_ul_pairs.size();
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m_var_register.shrink(n);
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pop_tableau(n);
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lp_assert(m_mpq_lar_core_solver.m_r_solver.m_costs.size() == A_r().column_count());
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lp_assert(m_mpq_lar_core_solver.m_r_solver.m_basis.size() == A_r().row_count());
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lp_assert(m_mpq_lar_core_solver.m_r_solver.basis_heading_is_correct());
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lp_assert(A_r().column_count() == n);
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TRACE("lar_solver_details",
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for (unsigned j = 0; j < n; j++) {
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print_column_info(j, tout) << "\n";
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}
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);
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m_columns_to_ul_pairs.pop(k);
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TRACE("lar_solver_details", for (unsigned j = 0; j < n; j++) print_column_info(j, tout) << "\n";);
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m_mpq_lar_core_solver.pop(k);
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remove_non_fixed_from_fixed_var_table();
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@ -612,26 +612,23 @@ namespace lp {
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}
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void lar_solver::set_upper_bound_witness(var_index j, u_dependency* dep) {
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ul_pair ul = m_columns_to_ul_pairs[j];
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ul.upper_bound_witness() = dep;
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m_columns_to_ul_pairs[j] = ul;
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m_trail.push(vector_value_trail(m_columns_to_ul_pairs, j));
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m_columns_to_ul_pairs[j].upper_bound_witness() = dep;
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}
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void lar_solver::set_lower_bound_witness(var_index j, u_dependency* dep) {
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ul_pair ul = m_columns_to_ul_pairs[j];
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ul.lower_bound_witness() = dep;
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m_columns_to_ul_pairs[j] = ul;
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m_trail.push(vector_value_trail(m_columns_to_ul_pairs, j));
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m_columns_to_ul_pairs[j].lower_bound_witness() = dep;
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}
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void lar_solver::register_monoid_in_map(std::unordered_map<var_index, mpq>& coeffs, const mpq& a, unsigned j) {
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auto it = coeffs.find(j);
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if (it == coeffs.end()) {
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if (it == coeffs.end())
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coeffs[j] = a;
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}
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else {
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else
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it->second += a;
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}
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}
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@ -1269,7 +1266,7 @@ namespace lp {
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}
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bool lar_solver::column_represents_row_in_tableau(unsigned j) {
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return m_columns_to_ul_pairs()[j].associated_with_row();
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return m_columns_to_ul_pairs[j].associated_with_row();
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}
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void lar_solver::make_sure_that_the_bottom_right_elem_not_zero_in_tableau(unsigned i, unsigned j) {
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@ -1371,20 +1368,6 @@ namespace lp {
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lp_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_costs.size());
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}
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void lar_solver::pop_tableau(unsigned old_size) {
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lp_assert(m_mpq_lar_core_solver.m_r_solver.m_costs.size() == A_r().column_count());
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lp_assert(m_mpq_lar_core_solver.m_r_solver.m_basis.size() == A_r().row_count());
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lp_assert(m_mpq_lar_core_solver.m_r_solver.basis_heading_is_correct());
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// We remove last variables starting from m_column_names.size() to m_vec_of_canonic_left_sides.size().
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// At this moment m_column_names is already popped
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while (A_r().column_count() > old_size)
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remove_last_column_from_tableau();
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lp_assert(m_mpq_lar_core_solver.m_r_solver.m_costs.size() == A_r().column_count());
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lp_assert(m_mpq_lar_core_solver.m_r_solver.m_basis.size() == A_r().row_count());
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lp_assert(m_mpq_lar_core_solver.m_r_solver.basis_heading_is_correct());
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}
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void lar_solver::clean_inf_heap_of_r_solver_after_pop() {
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vector<unsigned> became_feas;
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@ -1490,6 +1473,15 @@ namespace lp {
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return j;
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}
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struct lar_solver::add_column : public trail {
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lar_solver& s;
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add_column(lar_solver& s) : s(s) {}
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virtual void undo() {
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s.remove_last_column_from_tableau();
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s.m_columns_to_ul_pairs.pop_back();
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}
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};
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var_index lar_solver::add_var(unsigned ext_j, bool is_int) {
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TRACE("add_var", tout << "adding var " << ext_j << (is_int ? " int" : " nonint") << std::endl;);
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var_index local_j;
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@ -1500,9 +1492,9 @@ namespace lp {
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lp_assert(m_columns_to_ul_pairs.size() == A_r().column_count());
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local_j = A_r().column_count();
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m_columns_to_ul_pairs.push_back(ul_pair(false)); // not associated with a row
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while (m_usage_in_terms.size() <= ext_j) {
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m_trail.push(add_column(*this));
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while (m_usage_in_terms.size() <= ext_j)
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m_usage_in_terms.push_back(0);
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}
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add_non_basic_var_to_core_fields(ext_j, is_int);
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lp_assert(sizes_are_correct());
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return local_j;
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@ -1653,6 +1645,7 @@ namespace lp {
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unsigned j = A_r().column_count();
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ul_pair ul(true); // to mark this column as associated_with_row
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m_columns_to_ul_pairs.push_back(ul);
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m_trail.push(add_column(*this));
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add_basic_var_to_core_fields();
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A_r().fill_last_row_with_pivoting(*term,
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@ -2367,7 +2360,7 @@ namespace lp {
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SASSERT(m_crossed_bounds_deps == nullptr);
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set_status(lp_status::INFEASIBLE);
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m_crossed_bounds_column = j;
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const auto& ul = this->m_columns_to_ul_pairs()[j];
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const auto& ul = this->m_columns_to_ul_pairs[j];
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u_dependency* bdep = lower_bound? ul.lower_bound_witness() : ul.upper_bound_witness();
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SASSERT(bdep != nullptr);
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m_crossed_bounds_deps = m_dependencies.mk_join(bdep, dep);
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@ -42,6 +42,7 @@
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#include "util/debug.h"
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#include "util/stacked_value.h"
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#include "util/vector.h"
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#include "util/trail.h"
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namespace lp {
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@ -74,6 +75,7 @@ class lar_solver : public column_namer {
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};
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//////////////////// fields //////////////////////////
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trail_stack m_trail;
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lp_settings m_settings;
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lp_status m_status = lp_status::UNKNOWN;
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stacked_value<simplex_strategy_enum> m_simplex_strategy;
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@ -85,7 +87,8 @@ class lar_solver : public column_namer {
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bool m_need_register_terms = false;
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var_register m_var_register;
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var_register m_term_register;
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stacked_vector<ul_pair> m_columns_to_ul_pairs;
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struct add_column;
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svector<ul_pair> m_columns_to_ul_pairs;
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constraint_set m_constraints;
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// the set of column indices j such that bounds have changed for j
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indexed_uint_set m_columns_with_changed_bounds;
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@ -240,7 +243,6 @@ class lar_solver : public column_namer {
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void remove_last_column_from_basis_tableau(unsigned j);
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void remove_last_column_from_tableau();
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void pop_tableau(unsigned old_size);
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void clean_inf_heap_of_r_solver_after_pop();
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inline bool column_value_is_integer(unsigned j) const { return get_column_value(j).is_int(); }
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bool model_is_int_feasible() const;
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@ -393,6 +395,7 @@ class lar_solver : public column_namer {
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inline column_index to_column_index(unsigned v) const { return column_index(external_to_column_index(v)); }
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bool external_is_used(unsigned) const;
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void pop(unsigned k);
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unsigned num_scopes() const { return m_term_count.stack_size(); }
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bool compare_values(var_index j, lconstraint_kind kind, const mpq& right_side);
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var_index add_term(const vector<std::pair<mpq, var_index>>& coeffs, unsigned ext_i);
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void register_existing_terms();
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@ -503,7 +506,7 @@ class lar_solver : public column_namer {
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if (tv::is_term(j)) {
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j = m_var_register.external_to_local(j);
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}
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return m_columns_to_ul_pairs()[j].upper_bound_witness();
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return m_columns_to_ul_pairs[j].upper_bound_witness();
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}
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inline const impq& get_upper_bound(column_index j) const {
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@ -591,7 +594,7 @@ class lar_solver : public column_namer {
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if (tv::is_term(j)) {
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j = m_var_register.external_to_local(j);
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}
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return m_columns_to_ul_pairs()[j].lower_bound_witness();
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return m_columns_to_ul_pairs[j].lower_bound_witness();
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}
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inline tv column2tv(column_index const& c) const {
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@ -12,8 +12,6 @@
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#include "math/lp/nla_intervals.h"
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#include "math/lp/numeric_pair.h"
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#define UNIT_PROPAGATE_BOUNDS 0
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namespace nla {
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monomial_bounds::monomial_bounds(core* c):
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@ -21,16 +19,17 @@ namespace nla {
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dep(c->m_intervals.get_dep_intervals()) {}
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void monomial_bounds::propagate() {
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for (lpvar v : c().m_to_refine)
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for (lpvar v : c().m_to_refine) {
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propagate(c().emon(v));
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if (add_lemma())
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break;
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}
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}
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bool monomial_bounds::is_too_big(mpq const& q) const {
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return rational(q).bitsize() > 256;
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}
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/**
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* Accumulate product of variables in monomial starting at position 'start'
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*/
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@ -53,8 +52,9 @@ namespace nla {
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* a bounds axiom.
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*/
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bool monomial_bounds::propagate_value(dep_interval& range, lpvar v) {
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auto val = c().val(v);
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if (dep.is_below(range, val)) {
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// auto val = c().val(v);
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bool propagated = false;
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if (should_propagate_upper(range, v, 1)) {
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auto const& upper = dep.upper(range);
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auto cmp = dep.upper_is_open(range) ? llc::LT : llc::LE;
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++c().lra.settings().stats().m_nla_propagate_bounds;
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@ -72,9 +72,9 @@ namespace nla {
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lemma |= ineq(v, cmp, upper);
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TRACE("nla_solver", dep.display(tout << c().val(v) << " > ", range) << "\n" << lemma << "\n";);
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}
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return true;
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propagated = true;
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}
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else if (dep.is_above(range, val)) {
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if (should_propagate_lower(range, v, 1)) {
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auto const& lower = dep.lower(range);
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auto cmp = dep.lower_is_open(range) ? llc::GT : llc::GE;
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++c().lra.settings().stats().m_nla_propagate_bounds;
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@ -92,11 +92,45 @@ namespace nla {
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lemma |= ineq(v, cmp, lower);
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TRACE("nla_solver", dep.display(tout << c().val(v) << " < ", range) << "\n" << lemma << "\n";);
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}
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return true;
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propagated = true;
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}
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else {
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return propagated;
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}
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bool monomial_bounds::should_propagate_lower(dep_interval const& range, lpvar v, unsigned p) {
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if (dep.lower_is_inf(range))
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return false;
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}
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u_dependency* d = nullptr;
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rational bound;
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bool is_strict;
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if (!c().has_lower_bound(v, d, bound, is_strict))
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return true;
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auto const& lower = dep.lower(range);
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if (p > 1)
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bound = power(bound, p);
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if (bound < lower)
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return true;
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if (bound > lower)
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return false;
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return !is_strict && dep.lower_is_open(range);
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}
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bool monomial_bounds::should_propagate_upper(dep_interval const& range, lpvar v, unsigned p) {
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if (dep.upper_is_inf(range))
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return false;
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u_dependency* d = nullptr;
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rational bound;
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bool is_strict;
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if (!c().has_upper_bound(v, d, bound, is_strict))
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return true;
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auto const& upper = dep.upper(range);
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if (p > 1)
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bound = power(bound, p);
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if (bound > upper)
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return true;
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if (bound < upper)
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return false;
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return !is_strict && dep.upper_is_open(range);
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}
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/**
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@ -135,68 +169,86 @@ namespace nla {
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SASSERT(p > 0);
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if (p == 1)
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return propagate_value(range, v);
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auto val_v = c().val(v);
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auto val = power(val_v, p);
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rational r;
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if (dep.is_below(range, val)) {
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if (should_propagate_upper(range, v, p)) { // v.upper^p > range.upper
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SASSERT(c().has_upper_bound(v));
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lp::explanation ex;
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dep.get_upper_dep(range, ex);
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// p even, range.upper < 0, v^p >= 0 -> infeasible
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if (p % 2 == 0 && rational(dep.upper(range)).is_neg()) {
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++c().lra.settings().stats().m_nla_propagate_bounds;
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new_lemma lemma(c(), "range requires a non-negative upper bound");
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lemma &= ex;
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return true;
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}
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else if (rational(dep.upper(range)).root(p, r)) {
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// v = -2, [-4,-3]^3 < v^3 -> add bound v <= -3
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// v = -2, [-1,+1]^2 < v^2 -> add bound v >= -1
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if ((p % 2 == 1) || val_v.is_pos()) {
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++c().lra.settings().stats().m_nla_propagate_bounds;
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auto le = dep.upper_is_open(range) ? llc::LT : llc::LE;
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if (c().params().arith_nl_internal_bounds()) {
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auto* d = dep.get_upper_dep(range);
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propagate_bound(v, le, r, d);
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}
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else {
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new_lemma lemma(c(), "propagate value - root case - upper bound of range is below value");
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lemma &= ex;
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lemma |= ineq(v, le, r);
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}
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return true;
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}
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if (p % 2 == 0 && val_v.is_neg()) {
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++c().lra.settings().stats().m_nla_propagate_bounds;
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SASSERT(!r.is_neg());
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auto ge = dep.upper_is_open(range) ? llc::GT : llc::GE;
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if (c().params().arith_nl_internal_bounds()) {
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auto* d = dep.get_upper_dep(range);
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propagate_bound(v, ge, -r, d);
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}
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else {
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new_lemma lemma(c(), "propagate value - root case - upper bound of range is below negative value");
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lemma &= ex;
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lemma |= ineq(v, ge, -r);
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}
|
||||
return true;
|
||||
}
|
||||
}
|
||||
// TBD: add bounds as long as difference to val is above some epsilon.
|
||||
}
|
||||
else if (dep.is_above(range, val)) {
|
||||
if (rational(dep.lower(range)).root(p, r)) {
|
||||
// v.upper < 0, but v^p > range.upper -> infeasible.
|
||||
if (p % 2 == 0 && c().get_upper_bound(v) < 0) {
|
||||
++c().lra.settings().stats().m_nla_propagate_bounds;
|
||||
lp::explanation ex;
|
||||
dep.get_lower_dep(range, ex);
|
||||
auto ge = dep.lower_is_open(range) ? llc::GT : llc::GE;
|
||||
auto le = dep.lower_is_open(range) ? llc::LT : llc::LE;
|
||||
new_lemma lemma(c(), "propagate value - root case - lower bound of range is above value");
|
||||
new_lemma lemma(c(), "range requires a non-negative upper bound");
|
||||
lemma &= ex;
|
||||
lemma |= ineq(v, ge, r);
|
||||
if (p % 2 == 0)
|
||||
lemma |= ineq(v, le, -r);
|
||||
lemma.explain_existing_upper_bound(v);
|
||||
return true;
|
||||
}
|
||||
// TBD: add bounds as long as difference to val is above some epsilon.
|
||||
SASSERT(p % 2 == 1 || c().get_upper_bound(v) >= 0);
|
||||
|
||||
if (rational(dep.upper(range)).root(p, r)) {
|
||||
// v = -2, [-4,-3]^3 < v^3 -> add bound v <= -3
|
||||
// v = -2, [-1,+1]^2 < v^2 -> add bound v >= -1
|
||||
++c().lra.settings().stats().m_nla_propagate_bounds;
|
||||
auto le = dep.upper_is_open(range) ? llc::LT : llc::LE;
|
||||
if (c().params().arith_nl_internal_bounds()) {
|
||||
auto* d = dep.get_upper_dep(range);
|
||||
if (p % 2 == 0)
|
||||
d = dep.mk_join(d, c().lra.get_column_upper_bound_witness(v));
|
||||
propagate_bound(v, le, r, d);
|
||||
}
|
||||
else {
|
||||
new_lemma lemma(c(), "propagate value - root case - upper bound of range is below value");
|
||||
lemma &= ex;
|
||||
if (p % 2 == 0)
|
||||
lemma.explain_existing_upper_bound(v);
|
||||
lemma |= ineq(v, le, r);
|
||||
}
|
||||
return true;
|
||||
}
|
||||
}
|
||||
|
||||
if (should_propagate_lower(range, v, p)) { // v.lower^p < range.lower
|
||||
//
|
||||
// range.lower < 0 -> v.lower >= root(p, range.lower)
|
||||
// range.lower >= 0, p odd -> v.lower >= root(p, range.lower)
|
||||
// range.lower >= 0, p even, v.lower >= 0 -> v.lower >= root(p, range.lower)
|
||||
// default:
|
||||
// v.lower >= root(p, range.lower) || (p even & v.upper <= -root(p, range.lower))
|
||||
//
|
||||
// pre-condition: p even -> range.lower >= 0
|
||||
//
|
||||
if (rational(dep.lower(range)).root(p, r)) {
|
||||
++c().lra.settings().stats().m_nla_propagate_bounds;
|
||||
auto ge = dep.lower_is_open(range) ? llc::GT : llc::GE;
|
||||
auto le = dep.lower_is_open(range) ? llc::LT : llc::LE;
|
||||
if (c().params().arith_nl_internal_bounds()) {
|
||||
if (rational(dep.lower(range)).is_neg() || p % 2 == 1) {
|
||||
auto* d = dep.get_lower_dep(range);
|
||||
propagate_bound(v, ge, r, d);
|
||||
return true;
|
||||
}
|
||||
if (c().get_lower_bound(v) >= 0) {
|
||||
auto* d = dep.get_lower_dep(range);
|
||||
d = dep.mk_join(d, c().lra.get_column_lower_bound_witness(v));
|
||||
propagate_bound(v, ge, r, d);
|
||||
return true;
|
||||
}
|
||||
}
|
||||
lp::explanation ex;
|
||||
dep.get_lower_dep(range, ex);
|
||||
new_lemma lemma(c(), "propagate value - root case - lower bound of range is above value");
|
||||
lemma &= ex;
|
||||
lemma |= ineq(v, ge, r);
|
||||
if (p % 2 == 0)
|
||||
lemma |= ineq(v, le, -r);
|
||||
return true;
|
||||
}
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
|
@ -316,28 +368,30 @@ namespace nla {
|
|||
continue;
|
||||
monic& m = c().emon(v);
|
||||
unit_propagate(m);
|
||||
if (c().lra.get_status() == lp::lp_status::INFEASIBLE) {
|
||||
lp::explanation exp;
|
||||
c().lra.get_infeasibility_explanation(exp);
|
||||
new_lemma lemma(c(), "propagate fixed - infeasible lra");
|
||||
lemma &= exp;
|
||||
if (add_lemma())
|
||||
break;
|
||||
}
|
||||
if (c().m_conflicts > 0)
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
bool monomial_bounds::add_lemma() {
|
||||
if (c().lra.get_status() != lp::lp_status::INFEASIBLE)
|
||||
return false;
|
||||
lp::explanation exp;
|
||||
c().lra.get_infeasibility_explanation(exp);
|
||||
new_lemma lemma(c(), "propagate fixed - infeasible lra");
|
||||
lemma &= exp;
|
||||
return true;
|
||||
}
|
||||
|
||||
void monomial_bounds::unit_propagate(monic & m) {
|
||||
if (m.is_propagated())
|
||||
return;
|
||||
lpvar w, fixed_to_zero;
|
||||
|
||||
if (!is_linear(m, w, fixed_to_zero)) {
|
||||
if (c().params().arith_nl_internal_bounds())
|
||||
propagate(m);
|
||||
if (!is_linear(m, w, fixed_to_zero))
|
||||
return;
|
||||
}
|
||||
|
||||
c().emons().set_propagated(m);
|
||||
|
||||
|
|
|
|||
|
|
@ -17,6 +17,8 @@ namespace nla {
|
|||
class monomial_bounds : common {
|
||||
dep_intervals& dep;
|
||||
|
||||
bool should_propagate_lower(dep_interval const& range, lpvar v, unsigned p);
|
||||
bool should_propagate_upper(dep_interval const& range, lpvar v, unsigned p);
|
||||
void propagate_bound(lpvar v, lp::lconstraint_kind cmp, rational const& q, u_dependency* d);
|
||||
void var2interval(lpvar v, scoped_dep_interval& i);
|
||||
bool is_too_big(mpq const& q) const;
|
||||
|
|
@ -34,6 +36,7 @@ namespace nla {
|
|||
void analyze_monomial(monic const& m, unsigned& num_free, lpvar& free_v, unsigned& power) const;
|
||||
bool is_free(lpvar v) const;
|
||||
bool is_zero(lpvar v) const;
|
||||
bool add_lemma();
|
||||
|
||||
// monomial propagation
|
||||
void unit_propagate(monic & m);
|
||||
|
|
|
|||
|
|
@ -44,7 +44,7 @@ inline bool compare(const std::pair<mpq, var_index> & a, const std::pair<mpq, va
|
|||
class ul_pair {
|
||||
u_dependency* m_lower_bound_witness = nullptr;
|
||||
u_dependency* m_upper_bound_witness = nullptr;
|
||||
bool m_associated_with_row = false;
|
||||
bool m_associated_with_row = false;
|
||||
public:
|
||||
// TODO - seems more straight-forward to just expose ul_pair as a struct with direct access to attributes.
|
||||
|
||||
|
|
@ -62,8 +62,8 @@ public:
|
|||
|
||||
bool operator==(const ul_pair & p) const {
|
||||
return m_lower_bound_witness == p.m_lower_bound_witness
|
||||
&& m_upper_bound_witness == p.m_upper_bound_witness &&
|
||||
m_associated_with_row == p.m_associated_with_row;
|
||||
&& m_upper_bound_witness == p.m_upper_bound_witness
|
||||
&& m_associated_with_row == p.m_associated_with_row;
|
||||
}
|
||||
// empty constructor
|
||||
ul_pair() {}
|
||||
|
|
|
|||
|
|
@ -2021,7 +2021,6 @@ public:
|
|||
final_check_status check_nla_continue() {
|
||||
m_a1 = nullptr; m_a2 = nullptr;
|
||||
lbool r = m_nla->check();
|
||||
|
||||
switch (r) {
|
||||
case l_false:
|
||||
add_lemmas();
|
||||
|
|
@ -3293,9 +3292,8 @@ public:
|
|||
for (auto ev : m_explanation)
|
||||
set_evidence(ev.ci(), m_core, m_eqs);
|
||||
|
||||
SASSERT(!m_core.empty() || !m_eqs.empty());
|
||||
|
||||
// SASSERT(validate_conflict(m_core, m_eqs));
|
||||
// VERIFY(validate_conflict(m_core, m_eqs));
|
||||
if (is_conflict) {
|
||||
ctx().set_conflict(
|
||||
ctx().mk_justification(
|
||||
|
|
@ -3509,6 +3507,8 @@ public:
|
|||
|
||||
bool validate_conflict(literal_vector const& core, svector<enode_pair> const& eqs) {
|
||||
if (params().m_arith_mode != arith_solver_id::AS_NEW_ARITH) return true;
|
||||
|
||||
VERIFY(!m_core.empty() || !m_eqs.empty());
|
||||
scoped_arith_mode _sa(ctx().get_fparams());
|
||||
context nctx(m, ctx().get_fparams(), ctx().get_params());
|
||||
add_background(nctx);
|
||||
|
|
|
|||
Loading…
Reference in a new issue