The following terms in the partition
Partitions of n into summands - a set of positive integers whose sum is n. At the same partition, differing only in the order of terms are identical, so we can assume that the terms in the partition in order of non-decreasing.
For example, there are 7 partitions of 5 in terms:
5=1+1+1+1+15=1+1+1+25=1+1+35=1+2+25=1+45=2+35=5
In the example of the partition are ordered lexicographically - first by the first term in the partition, then the second, and so on. In this task you will need for a given partition on the terms to find the next partition in lexicographic order.
Input
The input file contains one line - a partition of n in terms of (1 ≤ n ≤ 100 000). The terms in the partition followed in nondecreasing order.
Output
Derive the output file one line - a partition of n into summands, the next in the lexicographical order after the above in the input file. If the input file is given the last partition of n into summands, output "No solution".