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To find the next permutation of an array ar:
- Find the highest index, i1 such that ar[i1] is the first of a pair of elements in ascending order. If there isn't one, the sequence is the highest permutation, so reverse the whole thing to begin again.
- Find the highest index i2, such that i2 > i1 and ar[i2] > ar[i1].
- Swap ar[i1] and ar[i2].
- The elements from ar[i1 + 1] to the end are now in descending order (a later permutation), so reverse them.
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