A series of eight games, numbered $\text{G1}$ to $\text{G8}$ R is organized as part of a college fest. In each game, only four players - A, B, C, D - participate and only one of them emerges as the winner. Five persons - P, Q, R, S, T - from among the audience took part in a contest wherein each person predicts the winner of each of the eight games in the series.

A person gets $300$ for the right prediction and loses $100$ for a wrong prediction. The following table gives the predictions of each of the five person as to who the winners would be. For example in game $\text{G1,}$ R predicted player B to win, while both P and T predicted player C to win and both Q and S predicted player D to win.

At the end of eight games, it turned out that if any person had predicted that a single player would win each of the eight games, he would not have gain or lost any amount. At the end of the series of eight games, Q received the maximum amount of $1600,$ while T neither gained nor lost any amount. Had R made one more correct prediction and Q made one more incorrect prediction, the amounts gained by them at the end of the games would have interchanged.

2. How many correct predictions made by S?

- $5$
- $3$
- $4$
- $2$

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