The diagram shows an example of a mountain profile. This consists of upstrokes which go upwards from left to right, and downstrokes which go downwards from left to right. The horizontal line at the bottom is known as sea level. A mountain profile of order n consists of \(n\) upstrokes and \(n\) downstrokes, with the condition that the profile begins and ends at sea level and never goes below sea level. Mountain profiles can be coded by using U to indicate an upstroke and D to indicate a downstroke. The example shown has the code UDUUUDUDDUDD. Which of the following statements is/are true? I If a valid code is written in reverse order, the result is always a valid code. II If each U in a valid code is replaced by D and each D by U, the result is always a valid code. III If U is added at the beginning of a valid code and D is added at the end of the code, the result is always a valid code.

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