The network of spies consists of N intelligence officers. They are numbered with the code numbers from 1 to N so that nobody could discover them. The number 1 belongs to the radiowoman Kat. There is exactly N - 1 communication channels between the spies. It is known that a message from any spy to Kat can reach her. All channels are unidirectional.

A channel can have one of two types: protected and almost protected. It is known that a message will not be intercepted almost surely by the hostile security service if at least half of the channels along the path to radiowoman Kat are protected. What is the minimum number of channels to be made protected from almost protected, so that any message from any spy will not be intercepted almost surely ? What are those channels?

The first line of the input contains the integer number N (1 ≤ N ≤ 200000). The following N - 1 lines contain the description of the communication channels. Each channel is described by a pair of the code numbers of spies (the direction of the channel is from the first spy to the second one) and the parameter p_i. If p_i =

protected

, the channel is protected and if p_i =

almost protected

, the channel is almost protected.

Write the number of channels to be converted to protected to the first line of the output. To the next line write numbers of channels to be made protected. If there are several solutions, choose any of them.

sample input	sample output
5 5 1 almost protected 3 1 almost protected 2 3 protected 4 3 almost protected	2 1 2