The Prince's Path

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Challenge created by conioh

Note the clarification below

The Prince of Zakarta has a problem. The princess has been kidnapped by the demon. To save the princess he needs to travel through a path similar to figure below, where each line leads to different cities denoted by circles.


At most cities he faces two paths to two different cities. But in the bottom row, there's only one path forward to the end.

In each city the Prince will either find a devil power or good power. The Prince will initially start with the power of the first city he visits. If he passes the city with devil power d then his power will be reduced by d i.e. P - d. Similarly, if he passes the city with good power g his power will be increased by g i.e. P + g.

If, after the first city, his power ever becomes 0 or less, he will Die. The Prince has all the information needed, but he needs your help to tell him whether he can save the Princess.

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