LogiQuest

247. Ways to Make an Expression

HardInterval DP

Given numbers separated by + − *, count the different results of all ways to fully parenthesise the expression and print the number of distinct values obtained.

Input format

A single expression without spaces (non-negative integers and + − *).

Output format

The number of distinct results.

Example 1

Input

2-1-1

Output

2

Example 2

Input

2*3-4*5

Output

4

Constraints

Up to 10 numbers.

Read input from standard input and print the answer to standard output. Your code is judged against 4 test cases, most of them hidden.

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