Why does this throw an exception

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C#

SQL

In SQL server, I created this sproc:

CREATE PROCEDURE [dbo].[GetOutletInfo] 
@PermitID int
AS SELECT * FROM Outlets WHERE PermitID=@PermitID
GO

then in my C# code, I run this:

var cn = new SqlConnection(connectionString);
SqlDataAdapter da;
DataSet ds = new DataSet();
da = new SqlDataAdapter("GetOutletInfo", cn);
da.SelectCommand.CommandType = CommandType.StoredProcedure;
da.SelectCommand.Parameters.Add("@PermitID", SqlDbType.Int).Value = PermitID;
da.Fill(ds, "GetOutletInfo");

Upon execution, the da.Fill throws this exception:
System.FormatException
HResult=0x80131537
Message=Failed to convert parameter value from a String to a Int32.
Source=System.Data.SqlClient

I have googled and scratched my head for hours trying different things, with no success. ANy pointers or insight will be appreciated. Thank you

What I have tried:

This query works (since it does not need a parameter)
SqlDataAdapter da;
DataSet ds = new DataSet();
da = new SqlDataAdapter("GetInspectionLettersQueue", cn);
da.SelectCommand.CommandType = CommandType.StoredProcedure;
da.Fill(ds, "GetInspectionLettersQueue");

I tried casting the parameter to int32 before adding it to the Parameters.Add command which did not work.