# 895 Maximum Frequency Stack

Design a stack-like data structure to push elements to the stack and pop the most frequent element from the stack.

Implement the `FreqStack` class:

• `FreqStack()` constructs an empty frequency stack.
• `void push(int val)` pushes an integer `val` onto the top of the stack.
• `int pop()` removes and returns the most frequent element in the stack.
• If there is a tie for the most frequent element, the element closest to the stack's top is removed and returned.

Example 1:

``````Input
["FreqStack", "push", "push", "push", "push", "push", "push", "pop", "pop", "pop", "pop"]
[[], , , , , , , [], [], [], []]
Output
[null, null, null, null, null, null, null, 5, 7, 5, 4]

Explanation
FreqStack freqStack = new FreqStack();
freqStack.push(5); // The stack is 
freqStack.push(7); // The stack is [5,7]
freqStack.push(5); // The stack is [5,7,5]
freqStack.push(7); // The stack is [5,7,5,7]
freqStack.push(4); // The stack is [5,7,5,7,4]
freqStack.push(5); // The stack is [5,7,5,7,4,5]
freqStack.pop();   // return 5, as 5 is the most frequent. The stack becomes [5,7,5,7,4].
freqStack.pop();   // return 7, as 5 and 7 is the most frequent, but 7 is closest to the top. The stack becomes [5,7,5,4].
freqStack.pop();   // return 5, as 5 is the most frequent. The stack becomes [5,7,4].
freqStack.pop();   // return 4, as 4, 5 and 7 is the most frequent, but 4 is closest to the top. The stack becomes [5,7].
``````

Constraints:

• `0 <= val <= 109`
• At most `2 * 104` calls will be made to push and pop.
• It is guaranteed that there will be at least one element in the stack before calling `pop`.
``````Stack of stack

push(5) - { 1: }
push(7) - { 1:[5,7]] }
push(5) - { 1:[5,7]],  2:] }
push(7) - { 1:[5,7]],  2:[5,7] }
push(4) - { 1:[5,7,4], 2:[5,7] }
push(5) - { 1:[5,7,4], 2:[5,7], 3: }
pop()   - { 1:[5,7,4], 2:[5,7] } => 5
pop()   - { 1:[5,7,4], 2: } => 7
pop()   - { 1:[5,7,4] } => 5
pop()   - { 1:[5,7]] } => 4
``````
 `````` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 `````` ``````class FreqStack: def __init__(self): self.val_freq = defaultdict(int) self.freq_list = defaultdict(list) self.max_freq = 0 def push(self, val: int) -> None: self.val_freq[val] += 1 new_freq = self.val_freq[val] if new_freq > self.max_freq: self.max_freq = new_freq self.freq_list[new_freq].append(val) def pop(self) -> int: val = self.freq_list[self.max_freq].pop() self.val_freq[val] -= 1 if not self.freq_list[self.max_freq]: self.max_freq -= 1 return val # Your FreqStack object will be instantiated and called as such: # obj = FreqStack() # obj.push(val) # param_2 = obj.pop()``````