2D camera follow lock Y-Axis

Hi.I am trying this script.With below script camera follows character all fine…But I want y-axis following to be locked so that i can make platformer game like mario. Please help.

using UnityEngine;
using System.Collections;

public class SmoothFollow : MonoBehaviour
{
public Transform target;
public float smoothDampTime = 0.2f;
[HideInInspector]
public new Transform transform;
public Vector3 cameraOffset;
public bool useFixedUpdate = false;

private CharacterControl _playerController;
private Vector3 _smoothDampVelocity;


void Awake()
{
	transform = gameObject.transform;
	_playerController = target.GetComponent<CharacterControl>();
}


void LateUpdate()
{
	if( !useFixedUpdate )
		updateCameraPosition();
}


void FixedUpdate()
{
	if( useFixedUpdate )
		updateCameraPosition();
}


void updateCameraPosition()
{
	if( _playerController == null )
	{
		transform.position = Vector3.SmoothDamp( transform.position, target.position - cameraOffset, ref _smoothDampVelocity, smoothDampTime );
		return;
	}
	
	if( _playerController.velocity.x > 0 )
	{
		transform.position = Vector3.SmoothDamp( transform.position, target.position - cameraOffset, ref _smoothDampVelocity, smoothDampTime );
	}
	else
	{
		var leftOffset = cameraOffset;
		leftOffset.x *= -1;
		transform.position = Vector3.SmoothDamp( transform.position, target.position - leftOffset, ref _smoothDampVelocity, smoothDampTime );
	}
}

}

Just store the initial camera Y position and assign it later to the movement vector;

private float startingY;

private void Start()
{
    startingY = transform.position.y;
}

private void Update()
{
    Vector3 position = Vector3.SmoothDamp( transform.position, target.position - leftOffset, ref _smoothDampVelocity, smoothDampTime );
    position.y = startingY;
    transform.position = position;
}