How check distint with less value?

[EDN Admin]

Below is my xml file
<pre class="prettyprint <product>
<name>Pen</name>
<price>8</price>
</product>
<product>
<name>Bag</name>
<price>10</price>
</product>
<product>
<name>Pen</name>
<price>10</price>
</product>
<product>
<name>Pen</name>
<price>5</price>
</product>
<product>
<name>Bag</name>
<price>15</price>
</product>
<product>
<name>Pencil</name>
<price>5</price>
</product>
<products>
[/code]
I need to take distinct product with there minimum price ...using xslt 1.0
required output is
<pre class="prettyprint <products>
<product>
<name>Bag</name>
<price>10</price>
</product>
<product>
<name>Pen</name>
<price>5</price>
</product>
<product>
<name>Pencil</name>
<price>5</price>
</product>
<products>[/code]
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