Board Game

题面翻译

$\texttt{Polycarp}$ 和 $\texttt{Vasiliy}$ 各有一个棋子，它们分别在 $(x_p,y_p)$ 和 $(x_v,y_v)$。每人只能移动自己的棋子。

若 $\texttt {Polycarp}$ 的棋子在 $(x,y)$，则 $\texttt {Polycarp}$ 一次移动可以将其移动到 $(x-1,y)$ 或者 $(x,y-1)$；若 $\texttt {Vasiliy}$ 的棋子在 $(x,y)$，则 $\texttt {Vasiliy}$ 一次移动可以将其移动到 $(x-1,y),(x,y-1)$ 或 $(x-1,y-1)$。二人都不能移动到不合法位置。

如果 $(x,y)$ 满足以下任一条，那么它是不合法的：

• $x<0$。

• $y<0$。

• 别人的棋子在 $(x,y)$。

每次操作可以在以下事情中任选一件做：

• 移动一次棋子

• 什么都不做

$\texttt{Polycarp}$ 先手，两人轮流操作。

将棋子移动到 $(0,0)$ 的人获得胜利。

现在假设 $\texttt{Polycarp}$ 和 $\texttt{Vasiliy}$ 都足够聪明，问谁能胜利。

$0\le x_p,y_p,x_v,y_v\le 10^5$，保证最开始时两个棋子不在同一位置并且没有棋子在 $(0,0)$。

题目描述

Polycarp and Vasiliy love simple logical games. Today they play a game with infinite chessboard and one pawn for each player. Polycarp and Vasiliy move in turns, Polycarp starts. In each turn Polycarp can move his pawn from cell $(x,y)$ to $(x-1,y)$ or $(x,y-1)$ . Vasiliy can move his pawn from $(x,y)$ to one of cells: $(x-1,y),(x-1,y-1)$ and $(x,y-1)$ . Both players are also allowed to skip move.

There are some additional restrictions — a player is forbidden to move his pawn to a cell with negative $x$ -coordinate or $y$ -coordinate or to the cell containing opponent's pawn The winner is the first person to reach cell $(0,0)$ .

You are given the starting coordinates of both pawns. Determine who will win if both of them play optimally well.

输入格式

The first line contains four integers: $x_{p},y_{p},x_{v},y_{v}$ ( $0<=x_{p},y_{p},x_{v},y_{v}<=10^{5})$ — Polycarp's and Vasiliy's starting coordinates.

It is guaranteed that in the beginning the pawns are in different cells and none of them is in the cell $(0,0)$ .

输出格式

Output the name of the winner: "Polycarp" or "Vasiliy".

样例 #1

样例输入 #1

2 1 2 2

样例输出 #1

Polycarp

样例 #2

样例输入 #2

4 7 7 4

样例输出 #2

Vasiliy

提示

In the first sample test Polycarp starts in $(2,1)$ and will move to $(1,1)$ in the first turn. No matter what his opponent is doing, in the second turn Polycarp can move to $(1,0)$ and finally to $(0,0)$ in the third turn.