winform多个button旋钮 初始一种颜色，点一个按钮变色，其他不变，再点其他按钮，点中按钮变色，其他回复初始颜色

winform多个button按钮 初始一种颜色，点一个按钮变色，其他不变，再点其他按钮，点中按钮变色，其他回复初始颜色
这是我写代码，希望能简化一点，一个事件就能解决的最好
namespace WinForm
{
    public partial class UserControl1 : UserControl
    {
        public UserControl1()
        {
            InitializeComponent();
            this.button1.Click+=button1_Click;
            this.button2.Click += button2_Click;
            this.button3.Click += button3_Click;
            this.button4.Click += button4_Click;
        }
        public void invit() 
        {

            button1.BackColor = Color.Red;
            button2.BackColor = Color.Red;
            button3.BackColor = Color.Red;
            button4.BackColor = Color.Red;  

        }

        private void button1_Click(object sender, EventArgs e)
        {
            invit();
            button1.BackColor = System.Drawing.Color.Lime;    
            
        }

        private void button2_Click(object sender, EventArgs e)
        {
            invit();
            button2.BackColor = System.Drawing.Color.Lime;    
        }
        private void button3_Click(object sender, EventArgs e)
        {
            invit();
            button3.BackColor = System.Drawing.Color.Lime;          
        }
        private void button4_Click(object sender, EventArgs e)
        {
            invit();
            button4.BackColor = System.Drawing.Color.Lime;
        }
    }
}
------解决思路----------------------

private void button_Click(object sender, EventArgs e)
        {
            invit();
            ((Button)sender).BackColor = System.Drawing.Color.Lime;    
        }
 public UserControl1()
        {
            InitializeComponent();
            this.button1.Click+=button_Click;
            this.button2.Click += button_Click;
            this.button3.Click += button_Click;
            this.button4.Click += button_Click;
        }