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You are given a directed acyclic graph of 'N' vertices(0 to 'N' - 1) and 'M' weighted edges.

Return an array that stores the distance(sum of weights) of the shortest path from vertex 0 to all vertices, and if it is impossible to reach any vertex, then assign -1 as distance.

For Example:

'N' = 3, 'M' = 3, 'edges' = [0, 1, 2], [1, 2, 3], [0, 2, 6]].

Distance (0 to 0) = 0.
Distance (0 to 1) = 2.
Distance (0 to 2) = 0->1 + 1->2 = 2+3 = 5.
So our answer is [0, 2, 5].

A Directed Acyclic Graph (DAG) is a directed graph that contains no cycles.

Topological Sorting of DAG is a linear ordering of vertices such that for every directed edge from vertex ‘u’ to vertex ‘v’, vertex ‘u’ comes before ‘v’ in the ordering. Topological Sorting for a graph is not possible if the graph is not a DAG.

Given a DAG consisting of ‘V’ vertices and ‘E’ edges, you need to find out any topological sorting of this DAG. Return an array of size ‘V’ representing the topological sort of the vertices of the given DAG.

For example, Consider the DAG shown in the picture.

In this graph, there are directed edges from 0 to 1 and 0 to 3, so 0 should come before 1 and 3. Also, there are directed edges from 1 to 2 and 3 to 2 so 1 and 3 should come before 2.

So, The topological sorting of this DAG is {0 1 3 2}.

Note that there are multiple topological sortings possible for a DAG. For the graph given above one another topological sorting is: {0, 3, 1, 2}

Note:

1. It is guaranteed that the given graph is DAG.
2. There will be no multiple edges and self-loops in the given DAG.
3. There can be multiple correct solutions, you can find any one of them. 
4. Don’t print anything, just return an array representing the topological sort of the vertices of the given DAG.

You are given a string 'exp' which is a valid infix expression.

Convert the given infix expression to postfix expression.

Note:

Infix notation is a method of writing mathematical expressions in which operators are placed between operands. 

For example, "3 + 4" represents the addition of 3 and 4.

Postfix notation is a method of writing mathematical expressions in which operators are placed after the operands. 

For example, "3 4 +" represents the addition of 3 and 4.

Expression contains digits, lower case English letters, ‘(’, ‘)’, ‘+’, ‘-’, ‘*’, ‘/’, ‘^’. 

Example:

Input: exp = ‘3+4*8’

Output: 348*+

Explanation:
Here multiplication is performed first and then the addition operation. Hence postfix expression is  3 4 8 * +.

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