无法使用基本身份验证保护gorilla/mux子路由

import (
    "net/http"
    "github.com/gorilla/mux"
)

func BasicAuthMiddleware(next http.Handler) http.Handler {
    return http.HandlerFunc(func(w http.ResponseWriter, r *http.Request) {
        username, password, ok := r.BasicAuth()
        if !ok || !checkCredentials(username, password) {
            w.Header().Set("WWW-Authenticate", `Basic realm="Restricted"`)
            w.WriteHeader(http.StatusUnauthorized)
            w.Write([]byte("Unauthorized\n"))
            return
        }
        next.ServeHTTP(w, r)
    })
}

func MyHandler(w http.ResponseWriter, r *http.Request) {
    w.Write([]byte("Authenticated\n"))
}

func main() {
    r := mux.NewRouter()

    // 添加基本身份验证中间件到子路由
    subRouter := r.PathPrefix("/protected").Subrouter()
    subRouter.Use(BasicAuthMiddleware)

    // 添加处理函数到子路由
    subRouter.HandleFunc("/", MyHandler)

    http.ListenAndServe(":8080", r)
}