sort an XML file into a tree structure by XSL 1.0 - xslt-1.0

Question

I want to convert an XML file with scattered element to an tree struct XML file.
if the 'identifier' of a menu is exist in another menu's items in input XML file, the menu context should be copied into the 'menu_list' element in output XML file.
Can any one please help me how do I achieve this using XSL1.0.
Input XML file:
<input>
<menu>
<identifier>1</identifier>
<items>
<item>2</item>
<item>3</item>
</items>
</menu>
<menu>
<identifier>2</identifier>
<items>
<item>21</item>
<item>22</item>
</items>
</menu>
<menu>
<identifier>3</identifier>
<items>
<item>31</item>
<item>32</item>
</items>
</menu>
<menu>
<identifier>21</identifier>
<items>
<item>211</item>
<item>212</item>
</items>
</menu>
<menu>
<identifier>22</identifier>
<items>
<item>221</item>
<item>222</item>
</items>
</menu>
<menu>
<identifier>31</identifier>
<items>
<item>311</item>
<item>312</item>
</items>
</menu>
<menu>
<identifier>32</identifier>
<items>
<item>321</item>
<item>322</item>
</items>
</menu>
</input>
Output XML file:
<input>
<menu>
<identifier>1</identifier>
<items>
<item>2</item>
<item>3</item>
</items>
<menu_list>
<menu>
<identifier>2</identifier>
<items>
<item>21</item>
<item>22</item>
</items>
<menu_list>
<menu>
<identifier>21</identifier>
<items>
<item>211</item>
<item>212</item>
</items>
</menu>
<menu>
<identifier>22</identifier>
<items>
<item>221</item>
<item>222</item>
</items>
</menu>
</menu_list>
</menu>
<menu>
<identifier>3</identifier>
<items>
<item>31</item>
<item>32</item>
</items>
<menu_list>
<menu>
<identifier>31</identifier>
<items>
<item>311</item>
<item>312</item>
</items>
</menu>
<menu>
<identifier>32</identifier>
<items>
<item>321</item>
<item>322</item>
</items>
</menu>
</menu_list>
</menu>
</menu_list>
</menu>
</input>

Answer 1

Try it this way:
XSLT 1.0
<xsl:stylesheet version="1.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
<xsl:output method="xml" version="1.0" encoding="UTF-8" indent="yes"/>
<xsl:strip-space elements="*"/>
<xsl:key name="children" match="menu" use="identifier" />
<xsl:key name="parent" match="menu" use="items/item" />
<xsl:template match="/input">
<xsl:copy>
<xsl:apply-templates select="menu[not(key('parent', identifier))]"/>
</xsl:copy>
</xsl:template>
<xsl:template match="menu">
<xsl:copy>
<xsl:copy-of select="*"/>
<xsl:variable name="children" select="key('children', items/item)"/>
<xsl:if test="$children">
<menu_list>
<xsl:apply-templates select="$children"/>
</menu_list>
</xsl:if>
</xsl:copy>
</xsl:template>
</xsl:stylesheet>