13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T5fd,

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 $$$998244353$$$.

Input

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 $$$a$$$.

Zero-XOR Array

Examples