Description:
There is a string $$$s$$$ of lowercase English letters. A cursor is positioned on one of the characters. The cursor can be moved with the following operation: choose a letter $$$c$$$ and a direction (left or right). The cursor is then moved to the closest occurence of $$$c$$$ in the chosen direction. If there is no letter $$$c$$$ in that direction, the cursor stays in place. For example, if $$$s = \mathtt{abaab}$$$ with the cursor on the second character ($$$\mathtt{a[b]aab}$$$), then:
- moving to the closest letter $$$\mathtt{a}$$$ to the left places the cursor on the first character ($$$\mathtt{[a]baab}$$$);
- moving to the closest letter $$$\mathtt{a}$$$ to the right places the cursor the third character ($$$\mathtt{ab[a]ab}$$$);
- moving to the closest letter $$$\mathtt{b}$$$ to the right places the cursor on the fifth character ($$$\mathtt{abaa[b]}$$$);
- any other operation leaves the cursor in place.
Let $$$\mathrm{dist}(i, j)$$$ be the smallest number of operations needed to move the cursor from the $$$i$$$-th character to the $$$j$$$-th character. Compute $$$\displaystyle \sum_{i = 1}^n \sum_{j = 1}^n \mathrm{dist}(i, j)$$$.
Input Format:
The only line contains a non-empty string $$$s$$$ of at most $$$10^5$$$ lowercase English letters.
Output Format:
Print a single integer $$$\displaystyle \sum_{i = 1}^n \sum_{j = 1}^n \mathrm{dist}(i, j)$$$.
Note:
In the first sample case, $$$\mathrm{dist}(i, j) = 0$$$ for any pair $$$i = j$$$, and $$$1$$$ for all other pairs.