CF134A.Average Numbers

You are given a sequence of positive integers _a_1, _a_2, ..., a__n. Find all such indices i, that the i-th element equals the arithmetic mean of all other elements (that is all elements except for this one).

给你一个正整数序列 $a_1,\,a_2,\,...,\,a_n$。请找出所有满足如下条件的下标 $i$：第 $i$ 个元素等于其余所有元素（即除该元素外的所有元素）的算术平均值。

The first line contains the integer n (2 ≤ n ≤ 2·105). The second line contains elements of the sequence _a_1, _a_2, ..., a__n (1 ≤ a__i ≤ 1000). All the elements are positive integers.

第一行包含整数 $n$（$2 \leq n \leq 2\cdot10^5$）。第二行包含序列 $a_1, a_2, ..., a_n$ 的元素（$1 \leq a_i \leq 1000$）。所有元素均为正整数。

Print on the first line the number of the sought indices. Print on the second line the sought indices in the increasing order. All indices are integers from 1 to n.

If the sought elements do not exist, then the first output line should contain number 0. In this case you may either not print the second line or print an empty line.

第一行输出所求索引的个数。第二行按升序输出所求索引。所有索引均为从 $1$ 到 $n$ 的整数。

若不存在所求元素，则第一行输出数字 $0$。此时，第二行可不输出，也可输出一个空行。