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Problem
The program reads from standard input an expression. Only brackets are of interest: round `()`, square `[]`, and curly `{}`. All other characters are ignored.
The expression has **balanced** brackets if:
- every opening bracket has a matching closing bracket of the same type, later in the string;
- brackets do not interleave: the last opened bracket is the first to be closed.
For example, `([]{})` and `{[()]}` are balanced, but `([)]` is not.
Input format
Input
input.txt
The program reads from standard input a single line with the expression (at most 1000 characters long). The line may be empty.
Output format
Output
output.txt
The program prints to standard output: - `DA` if the brackets in the expression are balanced; - `NU` otherwise. An expression with no brackets at all is considered balanced.
Example
input
{[a+(b*c)]-d}
output
DA
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Sample cases (from the problem)
Sample Case 1
Input
{[a+(b*c)]-d}
Expected output
DA
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