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Build an Array With Stack Operations

You are given an integer array target and an integer n.

You are given an integer array target and an integer n.

You have an empty stack with the two following operations:

You also have a stream of the integers in the range [1, n].

Use the two stack operations to make the numbers in the stack (from the bottom to the top) equal to target. You should follow the following rules:

Return the stack operations needed to build target following the mentioned rules. If there are multiple valid answers, return any of them.

Build an Array With Stack Operations diagram

Example 1

Input: target = [1,3], n = 3

Output: ["Push","Push","Pop","Push"]

Explanation: Initially the stack s is empty. The last element is the top of the stack. Read 1 from the stream and push it to the stack. s = [1]. Read 2 from the stream and push it to the stack. s = [1,2]. Pop the integer on the top of the stack. s = [1]. Read 3 from the stream and push it to the stack. s = [1,3].

Example 2

Input: target = [1,2,3], n = 3

Output: ["Push","Push","Push"]

Explanation: Initially the stack s is empty. The last element is the top of the stack. Read 1 from the stream and push it to the stack. s = [1]. Read 2 from the stream and push it to the stack. s = [1,2]. Read 3 from the stream and push it to the stack. s = [1,2,3].

Example 3

Input: target = [1,2], n = 4

Output: ["Push","Push"]

Explanation: Initially the stack s is empty. The last element is the top of the stack. Read 1 from the stream and push it to the stack. s = [1]. Read 2 from the stream and push it to the stack. s = [1,2]. Since the stack (from the bottom to the top) is equal to target, we stop the stack operations. The answers that read integer 3 from the stream are not accepted.

Constraints

  • 1 <= target.length <= 100
  • 1 <= n <= 100
  • 1 <= target[i] <= n
  • target is strictly increasing.

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