K-equivalence

Time Limit: 2000MS

Memory Limit: 65536K

Description

Consider a set K of positive integers. Let p and q be two non-zero decimal digits. Call them K-equivalent if the following condition applies: For every n \in K, if you replace one digit p with q or one digit q with p in the decimal notation of n then the resulting number will be an element of K. For example, when K is the set of integers divisible by 3, the digits 1, 4, and 7 are K-equivalent. Indeed, replacing a 1 with a 4 in the decimal notation of a number never changes its divisibility by 3. It can be seen that K-equivalence is an equivalence relation (it is reflexive, symmetric and transitive). You are given a finite set K in form of a union of disjoint finite intervals of positive integers. Your task is to find the equivalence classes of digits 1 to 9.

Input

The first line contains n, the number of intervals composing the set K (1 <= n <= 10 000). Each of the next n lines contains two positive integers ai and bi that describe the interval [ai, bi] (i. e. the set of positive integers between ai and bi, inclusive), where 1 <= ai <= bi <= 1018. Also, for i \in [2..n]: ai >= b(i-1) + 2.

Output

Represent each equivalence class as a concatenation of its elements, in ascending order. Output all the equivalence classes of digits 1 to 9, one at a line, sorted lexicographically.

Sample Input

Sample Input #1:
1
1 566

Sample Input #2:
1
30 75

Sample Output

Sample Output #1:
1234
5
6
789

Sample Output #2:
12
345
6
7
89

Hint

Source

Northeastern Europe 2009

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