Man, Elephant and Mouse

A very popular game in Nlogonia is called Man, Elephant and Mouse. It is typically played with only two players, and works as follows: each player secretly selects one of these three symbols, and after a countdown, both simultaneously reveal the symbol chosen through hand signals, extending in front his hands signaling the choice.

Man is represented by the closed hand, like the head of a man. The elephant is represented by the open hand showing five fingers, like the paw of the nlogonense elephant. Finally, the Rat is represented by the closed hand with the index finger and middle finger outstretched, as the ears of the little animal.

Figure 1: The three symbols of the game Man, Elephant and Mouse.

To determine the winner is very simple: the man always loses to the elephant (it is crushed under his paw), the elephant always loses to the mouse (because he is afraid of him and runs away) and the mouse always loses to the Man (which spreads traps to capture it). If two players use the same symbol, a tie occurs and the game is played again.

The inhabitants of Nlogonia, that are born strategists of Man, Elephant and Mouse, are using the following technique in the national championship, held every year: they always start playing man until the moment that this symbol cause tie with the most of their opponents. They then change its approach to the the winning symbol considering that they were using previously. Thus, players will switch to Elephant Man, then to Mouse, then they back again to Man.

To assist a famous foreign competitor in a game similar to this game Man, Elephant and Mouse, you will develop a program that counts how many players will use each symbol. Suppose all N players are arranged in a row and identified by their position, from 1 to N. Your program should handle with M commands of two types: change of symbol and count the frequency of these symbols. Both commands take a contiguous range of players in the queue to be considered.