Display the string in textbox in a datagridview cell right while typing?

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C#

WinForms

I have bound the Text property of a textbox to a column of a datagridview like the following:
dataGridView1.DataBindings.Add("Name", textBox1, "Text");
I have tried typing some text in the textbox but the value of the cell in the column bound to textBox1 (column "Name") didn't reflect the text in the textbox unless I clicked on the current cell and moved to other.
Is there any way to make it reflect the changes while typing in the textbox?
Thank you so much!