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# Problem 259

Reachable Numbers

A positive integer will be called reachable if it can result from an arithmetic expression obeying the following rules:

• Uses the digits 1 through 9, in that order and exactly once each.
• Any successive digits can be concatenated (for example, using the digits 2, 3 and 4 we obtain the number 234).
• Only the four usual binary arithmetic operations (addition, subtraction, multiplication and division) are allowed.
• Each operation can be used any number of times, or not at all.
• Unary minus is not allowed.
• Any number of (possibly nested) parentheses may be used to define the order of operations.

For example, 42 is reachable, since (1/23) * ((4*5)-6) * (78-9) = 42.

What is the sum of all positive reachable integers?

• 按照从小到大顺序使用数字1至9恰好各一次。
• 任意相邻数字可以连接起来使用（例如，将数字2、3、4连接起来得到234）。
• 只能使用四则运算（加法、减法、乘法、除法）。
• 每种运算可以使用任意多次，也可以不用。
• 禁止使用负号
• 可以使用（甚至嵌套使用）任意数量的括号以规定运算顺序。