Next partition into terms

A partition of a number $n$ into terms is a multiset of positive integers whose sum is $n$. Partitions that differ only in the order of their terms are considered the same, so we may assume the terms of a partition are sorted in nondecreasing order.

For example, there are 7 partitions of 5 into terms:

\begin{align*} 5&=1+1+1+1+1\\ 5&=1+1+1+2\\ 5&=1+1+3\\ 5&=1+2+2\\ 5&=1+4\\ 5&=2+3\\ 5&=5 \end{align*}

In the example above the partitions are ordered lexicographically: first by the first term of the partition, then by the second term, and so on. In this problem you are given a partition into terms and must find the next partition in lexicographic order.

The input file contains one line, a partition of the number $n$ into terms ($1 \le n \le 100\,000$). The terms of the partition are given in nondecreasing order.

Print to the output file one line, the partition of $n$ into terms that comes next in lexicographic order after the one in the input file. If the input file contains the last partition of $n$ into terms, print <<No solution>>.