You are given an array of integers (a) of size (n). This array is non-decreasing, i. e. (a_1 \le a_2 \le \dots \le a_n). You have to find arrays of integers (b) of size (2n - 1), such that: (b_{2i-1} = a_i) ((1 \le i \le n)); array (b) is non-decreasing; (b_1 \oplus b_2 \oplus \dots \oplus b_{2n-1} = 0) ((\oplus) denotes bitwise XOR operation: https://en.wikipedia.org/wiki/Exclusive_or . In Kotlin, it is xor function). Calculate the number of arrays that meet all the above conditions, modulo (998244353). The first line contains a single integer (n) ((2 \le n \le 17)) — the size of the array (a). The second line contains (n) integers ((0 \le a_i \le 2^{60} - 1; a_i \le a_{i+1})) — elements of the array (a). Print a single integer — the number of arrays that meet all the above conditions, modulo (998244353).