A12029. Linear Congruential Generator

You are given a tuple generator $f^{(k)} = (f_1^{(k)}, f_2^{(k)}, \dots, f_n^{(k)})$ , where $f_i^{(k)} = (a_i \cdot f_i^{(k - 1)} + b_i) \bmod p_i$ and $f^{(0)} = (x_1, x_2, \dots, x_n)$ . Here $x \bmod y$ denotes the remainder of $x$ when divided by $y$ . All $p_i$ are primes.

One can see that with fixed sequences $x_i$ , $y_i$ , $a_i$ the tuples $f^{(k)}$ starting from some index will repeat tuples with smaller indices. Calculate the maximum number of different tuples (from all $f^{(k)}$ for $k \ge 0$ ) that can be produced by this generator, if $x_i$ , $a_i$ , $b_i$ are integers in the range $[0, p_i - 1]$ and can be chosen arbitrary. The answer can be large, so print the remainder it gives when divided by $10^9 + 7$

The first line contains one integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the number of elements in the tuple.

The second line contains $n$ space separated prime numbers — the modules $p_1, p_2, \ldots, p_n$ ( $2 \le p_i \le 2 \cdot 10^6$ ).

Print one integer — the maximum number of different tuples modulo $10^9 + 7$ .

In the first example we can choose next parameters: $a = [1, 1, 1, 1]$ , $b = [1, 1, 1, 1]$ , $x = [0, 0, 0, 0]$ , then $f_i^{(k)} = k \bmod p_i$ .

In the second example we can choose next parameters: $a = [1, 1, 2]$ , $b = [1, 1, 0]$ , $x = [0, 0, 1]$ .