F. 1 2 3 4 ...time limit per test5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputIgor had a sequence d_1, d_2, \dots, d_n of integers. When Igor entered the classroom there was an integer x written on the blackboard.Igor generated sequence p using the following algorithm:   initially, p = [x];  for each 1 \leq i \leq n he did the following operation |d_i| times:   if d_i \geq 0, then he looked at the last element of p (let it be y) and appended y + 1 to the end of p;  if d_i < 0, then he looked at the last element of p (let it be y) and appended y - 1 to the end of p.  For example, if x = 3, and d = [1, -1, 2], p will be equal [3, 4, 3, 4, 5].Igor decided to calculate the length of the longest increasing subsequence of p and the number of them.A sequence a is a subsequence of a sequence b if a can be obtained from b by deletion of several (possibly, zero or all) elements.A sequence a is an increasing sequence if each element of a (except the first one) is strictly greater than the previous element.For p = [3, 4, 3, 4, 5], the length of longest increasing subsequence is 3 and there are 3 of them: [\underline{3}, \underline{4}, 3, 4, \underline{5}], [\underline{3}, 4, 3, \underline{4}, \underline{5}], [3, 4, \underline{3}, \underline{4}, \underline{5}].InputThe first line contains a single integer n (1 \leq n \leq 50) — the length of the sequence d.The second line contains a single integer x (-10^9 \leq x \leq 10^9) — the integer on the blackboard.The third line contains n integers d_1, d_2, \ldots, d_n (-10^9 \leq d_i \leq 10^9).OutputPrint two integers:   the first integer should be equal to the length of the longest increasing subsequence of p;  the second should be equal to the number of them modulo 998244353. You should print only the second number modulo 998244353.ExamplesInput
3
3
1 -1 2
Output
3 3
Input
3
100
5 -3 6
Output
9 7
Input
3
1
999999999 0 1000000000
Output
2000000000 1
Input
5
34
1337 -146 42 -69 228
Output
1393 3876
NoteThe first test case was explained in the statement.In the second test case p = [100, 101, 102, 103, 104, 105, 104, 103, 102, 103, 104, 105, 106, 107, 108].In the third test case p = [1, 2, \ldots, 2000000000].
3
3
1 -1 2

3 3 
['dp', 'math', 'matrices', '*3000']