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diff --git a/demo3/vertical/tbtnavi_demo/include/mapbox/variant_io.hpp b/demo3/vertical/tbtnavi_demo/include/mapbox/variant_io.hpp
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+++ b/demo3/vertical/tbtnavi_demo/include/mapbox/variant_io.hpp
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+#ifndef MAPBOX_UTIL_VARIANT_IO_HPP
+#define MAPBOX_UTIL_VARIANT_IO_HPP
+
+#include <iosfwd>
+
+#include <mapbox/variant.hpp>
+
+namespace mapbox {
+namespace util {
+
+namespace detail {
+// operator<< helper
+template <typename Out>
+class printer
+{
+public:
+ explicit printer(Out& out)
+ : out_(out) {}
+ printer& operator=(printer const&) = delete;
+
+ // visitor
+ template <typename T>
+ void operator()(T const& operand) const
+ {
+ out_ << operand;
+ }
+
+private:
+ Out& out_;
+};
+}
+
+// operator<<
+template <typename CharT, typename Traits, typename... Types>
+VARIANT_INLINE std::basic_ostream<CharT, Traits>&
+operator<<(std::basic_ostream<CharT, Traits>& out, variant<Types...> const& rhs)
+{
+ detail::printer<std::basic_ostream<CharT, Traits>> visitor(out);
+ apply_visitor(visitor, rhs);
+ return out;
+}
+} // namespace util
+} // namespace mapbox
+
+#endif // MAPBOX_UTIL_VARIANT_IO_HPP