LED push button results help

Hello everyone. I'm working on a project that requires 3 LEDS to be lit as follows:

Button pushed LED1 is lit

Button pushed again LED1 stays lit while LED2 is lit

Button pushed again LED 1 & 2 stay lit while LED3 is lit

Button Pushed 4th time All three LED lights flash on and off

Button pushed 5th time all lights turn off

This is the current code I am using. Could someone please help me re-write this to work for the above results? Thank you

/// this constant won't change:
const int  buttonPin = 2;    // the pin that the pushbutton is attached to
const int ledPin = 12;       // the pin that the LED is attached to
const int ledPin2 = 11; 
const int ledPin3 = 10; 

// Variables will change:
int buttonPushCounter = 0;   // counter for the number of button presses
int buttonState = 0;         // current state of the button
int lastButtonState = 0;     // previous state of the button

void setup() {
  // initialize the button pin as a input:
  pinMode(buttonPin, INPUT);
  // initialize the LED as an output:
  pinMode(ledPin, OUTPUT);
  // initialize serial communication:
  pinMode(ledPin2, OUTPUT);
  pinMode(ledPin3, OUTPUT);
  Serial.begin(9600);
}


void loop() {
  // read the pushbutton input pin:
  buttonState = digitalRead(buttonPin);

  // compare the buttonState to its previous state
  if (buttonState != lastButtonState) {
    // if the state has changed, increment the counter
    if (buttonState == HIGH) {
      // if the current state is HIGH then the button went from off to on:
      buttonPushCounter++;
      Serial.println("on");
      Serial.print("number of button pushes: ");
      Serial.println(buttonPushCounter);
    } else {
      // if the current state is LOW then the button went from on to off:
      Serial.println("off");
    }
    // Delay a little bit to avoid bouncing
    delay(50);
  }
  // save the current state as the last state, for next time through the loop
  lastButtonState = buttonState;


  // turns on the LED every four button pushes by checking the modulo of the
  // button push counter. the modulo function gives you the remainder of the
  // division of two numbers:
  if (buttonPushCounter  == 1) {
    digitalWrite(ledPin, HIGH);
  } else {
    digitalWrite(ledPin, LOW);
  }
    if (buttonPushCounter  == 2) {
    digitalWrite(ledPin2, HIGH);
  } else {
    digitalWrite(ledPin, LOW);
  }
  if (buttonPushCounter  == 3) {
    digitalWrite(ledPin3, HIGH);
  } else {
    digitalWrite(ledPin, LOW);
  }

}

Please read this:-
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It will tell you how to ask a question here.

Specifically if you are posting code then say what the code does and what you would like it to do differently.

This looks like a school assignment, is it?

Tip :- Do not try and do everything in one long function, break things up into separate functions. You can also select a portion of code useing the switch / case structure rather than a fist full of 'if' statements.