Based on picklist selection, how to display corresponding pageblock on VF page

VF and APEX Code:

<apex:page controller="display">
    <apex:form >
      <!--<apex:actionFunction action="{!selectcountry}" name="fun"/>
      <apex:selectList size="1" value="{!country}" onchange="fun();">-->
      <apex:selectList size="1" value="{!country}">
      <apex:actionSupport event="onchange" action="{!selectcountry}"/>          <apex:selectOptions value="{!picklistvalues}">
          </apex:selectOptions>
      </apex:selectList>
      <apex:pageBlock >
       <!--renderd to display or hide the pageblocksection on any other element of VF page-->
       <apex:pageBlockSection title="India" rendered="{!Ind}">
           <b>India is a developing country</b>
       </apex:pageBlockSection>
       <apex:pageBlockSection title="Australia" rendered="{!Aus}">
           <b>Australia is a continent</b>
       </apex:pageBlockSection>
       <apex:pageBlockSection title="USA" rendered="{!Usa}">
           <b>USA is a developed country</b>
       </apex:pageBlockSection>
      </apex:pageBlock>
    </apex:form>      
</apex:page>

public class display { 
    
    //To store the picklist value which we have selected on VF page i.e (Ind, Aus, USA)
    public String country { get; set; }    
    
    //To display list of picklist values on VF page
    public List<selectOption> getPicklistvalues() {
        List<selectOption> options = new List<selectOption>();       
        options.add(new selectOption('India','India'));
        options.add(new selectOption('Australia','Australia'));
        options.add(new selectOption('USA','USA'));
        return options;
    }   

    //To make three pageblocksections invisible by default
    public Boolean indtf = false;
    public Boolean austf = false;
    public Boolean usatf = false;
       
    //To dynamically pass Boolean values to rendered attribute on pageblocksection
    public void setInd(Boolean b) {
        this.indtf = b;
    }
    public Boolean getInd() {
        return this.indtf;
    }    
    
    
    public void setAus(Boolean b) {
        this.austf = b;
    }
    public Boolean getAus() {
        return this.austf;
    }

    
    public void setUsa(Boolean b) {
        this.usatf = b;
    }
    public Boolean getUsa() {
        return this.usatf;
    }
 
    //Constructor, After loading the page to display india pageblocksection by default
    public display() {
        setInd(True);
        setAus(False);
        setUsa(False);
    }
    
    //After changing picklist value based on the selection to display either usa or aus pageblocksection
    //Through actionfunction or actionsupport this method will be called to VF page
    public PageReference selectcountry() {
        if(country == 'Australia') {
            setInd(False);
            setAus(True);
            setUsa(False);
        }
        else {
            setInd(False);
            setAus(False);
            setUsa(True);
        }
        return null;
    }
}