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// defining the sub-directory so that it can be easily accessed from elsewhere as well.
define( 'WPSE_PAGE_TEMPLATE_SUB_DIR', 'page-singaku' );

function wpse312159_page_template_add_subdir( $templates = array() ) {
    // Generally this doesn't happen, unless another plugin / theme does modifications
    // of their own. In that case, it's better not to mess with it again with our code.
    if( empty( $templates ) || ! is_array( $templates ) || count( $templates ) < 3 )
        return $templates;

    $page_tpl_idx = 0;
    if( $templates[0] === get_page_template_slug() ) {
        // if there is custom template, then our page-{slug}.php template is at the next index
        $page_tpl_idx = 1;
    }

    $page_tpls = array( WPSE_PAGE_TEMPLATE_SUB_DIR . '/' . $templates[$page_tpl_idx] );

    // As of WordPress 4.7, the URL decoded page-{$slug}.php template file is included in the
    // page template hierarchy just before the URL encoded page-{$slug}.php template file.
    // Also, WordPress always keeps the page id different from page slug. So page-{slug}.php will
    // always be different from page-{id}.php, even if you try to input the {id} as {slug}.
    // So this check will work for WordPress versions prior to 4.7 as well.
    if( $templates[$page_tpl_idx] === urldecode( $templates[$page_tpl_idx + 1] ) ) {
        $page_tpls[] = WPSE_PAGE_TEMPLATE_SUB_DIR . '/' . $templates[$page_tpl_idx + 1];
    }

    array_splice( $templates, $page_tpl_idx, 0, $page_tpls );

    return $templates;
}
add_filter( 'page_template_hierarchy', 'wpse312159_page_template_add_subdir' );

function tbdn_get_page_template() {
    $id = get_queried_object_id();
    $template = get_page_template_slug();
    $pagename = get_query_var('pagename');

    if ( ! $pagename && $id ) {
        // If a static page is set as the front page, $pagename will not be set. Retrieve it from the queried object
        $post = get_queried_object();
        if ( $post )
            $pagename = $post->post_name;
    }

    $templates = array();

    if ( $template && 0 === validate_file( $template ) )
        $templates[] = $template;
    // if there's a custom template then still give that priority

    if ( $pagename )
        $templates[] = "page-shingaku/page-$pagename.php";

    if ( $pagename )
        $templates[] = "toshin-net/page-$pagename.php";

    if ( $pagename )
        $templates[] = "believe/page-$pagename.php";
    // change the default search for the page-$slug template to use our directory
    // you could also look in the theme root directory either before or after this

    if ( $id )
        $templates[] = "page-shingaku/page-$id.php";
    $templates[] = 'page.php';

    if ( $id )
        $templates[] = "toshin-net/page-$id.php";
    $templates[] = 'page.php';

    if ( $id )
        $templates[] = "believe/page-$id.php";
    $templates[] = 'page.php';

    /* Don't call get_query_template again!!!
       // return get_query_template( 'page', $templates );
       We also reproduce the key code of get_query_template() - we don't want to call it or we'll get stuck in a loop .
       We can remove lines of code that we know won't apply for pages, leaving us with...
    */

    $template = locate_template( $templates );

    return $template;
}

add_filter( 'page_template', 'tbdn_get_page_template' );