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Igor 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:

1. initially, $$$p = [x]$$$;
2. 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: $$$[\underline{3}, \underline{4}, 3, 4, \underline{5}]$$$, $$$[\underline{3}, 4, 3, \underline{4}, \underline{5}]$$$, $$$[3, 4, \underline{3}, \underline{4}, \underline{5}]$$$.