Pretty-print XML tree to file after adding node

Question

I have seen several posts advising solutions on pretty-printing the entire XMl after parsing. In my case, I add a new node to the original file, print the result out into a new file. How do I maintain the same indentation with respect to the original node.

Original file:

<?xml version="1.0"?>
<data>
    <country name="Liechtenstein">
        <rank updated="yes">2</rank>
        <year>2008</year>
        <gdppc>141100</gdppc>
        <neighbor name="Austria" direction="E"/>
        <neighbor name="Switzerland" direction="W"/>
    </country>
    <country name="Singapore">
        <rank updated="yes">5</rank>
        <year>2011</year>
        <gdppc>59900</gdppc>
        <neighbor name="Malaysia" direction="N"/>
    </country>
    <country name="Panama">
        <rank updated="yes">69</rank>
        <year>2011</year>
        <gdppc>13600</gdppc>
        <neighbor name="Costa Rica" direction="W"/>
        <neighbor name="Colombia" direction="E"/>
    </country>
</data>

Code to add a new country node:

file_path = "xmlsample1.xml"
tree = ET.parse(file_path)
root = tree.getroot()

new_country = ET.SubElement(root, 'country')
new_rank = ET.SubElement(new_country, 'rank')
new_rank.text = '120'

tree.write('output.xml')

This is what the output.xml looks like:

<data>
    <country name="Liechtenstein">
        <rank updated="yes">2</rank>
        <year>2008</year>
        <gdppc>141100</gdppc>
        <neighbor name="Austria" direction="E" />
        <neighbor name="Switzerland" direction="W" />
    </country>
    <country name="Singapore">
        <rank updated="yes">5</rank>
        <year>2011</year>
        <gdppc>59900</gdppc>
        <neighbor name="Malaysia" direction="N" />
    </country>
    <country name="Panama">
        <rank updated="yes">100</rank>
        <year>2011</year>
        <gdppc>13600</gdppc>
        <neighbor name="Costa Rica" direction="W" />
        <neighbor name="Colombia" direction="E" />
    </country>
<country><rank>120</rank></country></data>

How to make it looks like this (i.e. country follows the same level indentation):

<data>
    <country name="Liechtenstein">
        <rank updated="yes">2</rank>
        <year>2008</year>
        <gdppc>141100</gdppc>
        <neighbor name="Austria" direction="E" />
        <neighbor name="Switzerland" direction="W" />
    </country>
    <country name="Singapore">
        <rank updated="yes">5</rank>
        <year>2011</year>
        <gdppc>59900</gdppc>
        <neighbor name="Malaysia" direction="N" />
    </country>
    <country name="Panama">
        <rank updated="yes">100</rank>
        <year>2011</year>
        <gdppc>13600</gdppc>
        <neighbor name="Costa Rica" direction="W" />
        <neighbor name="Colombia" direction="E" />
    </country>
    <country>
        <rank>120</rank>
    </country>
</data>