Alice and Bob take turns playing a game, with Alice starting first.
Initially, there are n stones in a pile.  On each player's turn, that player makes a move consisting of removing any non-zero square number of stones in the pile.
Also, if a player cannot make a move, he/she loses the game.
Given a positive integer n. Return True if and only if Alice wins the game otherwise return False, assuming both players play optimally.
Example 1:
Input: n = 1
Output: true
Explanation: Alice can remove 1 stone winning the game because Bob doesn't have any moves.
Example 2:
Input: n = 2
Output: false
Explanation: Alice can only remove 1 stone, after that Bob removes the last one winning the game (2 -> 1 -> 0).
Example 3:
Input: n = 4
Output: true
Explanation: n is already a perfect square, Alice can win with one move, removing 4 stones (4 -> 0).
Example 4:
Input: n = 7
Output: false
Explanation: Alice can't win the game if Bob plays optimally.
If Alice starts removing 4 stones, Bob will remove 1 stone then Alice should remove only 1 stone and finally Bob removes the last one (7 -> 3 -> 2 -> 1 -> 0). 
If Alice starts removing 1 stone, Bob will remove 4 stones then Alice only can remove 1 stone and finally Bob removes the last one (7 -> 6 -> 2 -> 1 -> 0).
Example 5:
Input: n = 17
Output: false
Explanation: Alice can't win the game if Bob plays optimally.
Constraints:
1 <= n <= 10^5
import math
class Solution:
    squares=[0]
    dp=[False]            
    def winnerSquareGame(self, n: int) -> bool:
        sqt=int(math.sqrt(n))
        for i in range(len(self.squares),sqt+1):
            self.squares.append(i*i)
        
        if n+1<=len(self.dp):
            return self.dp[n]
        
        old_len=len(self.dp)
        for i in range(old_len,n+1):
            self.dp.append(False)
        
        for i in range(old_len,n+1):
            flag=0
           # print(\"in loop i\")
            for j in range(1,int(math.sqrt(i))+1):
               # print(\"i and j are\",i,j)
                if not self.dp[i-self.squares[j]]:
                    self.dp[i]=True
                    flag=1
                    break
            if flag==0:
                self.dp[i]=False
       # print(dp)
        return self.dp[n]
                
                

import math
class Solution:
    squares=[0]
    dp=[False]            
    def winnerSquareGame(self, n: int) -> bool:
        sqt=int(math.sqrt(n))
        for i in range(len(self.squares),sqt+1):
            self.squares.append(i*i)
        
        if n+1<=len(self.dp):
            return self.dp[n]
        
        old_len=len(self.dp)
        for i in range(old_len,n+1):
            self.dp.append(False)
        
        for i in range(old_len,n+1):
            flag=0
           # print(\"in loop i\")
            for j in range(1,int(math.sqrt(i))+1):
               # print(\"i and j are\",i,j)
                if not self.dp[i-self.squares[j]]:
                    self.dp[i]=True
                    flag=1
                    break
            if flag==0:
                self.dp[i]=False
       # print(dp)
        return self.dp[n]
                
                
