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: $[\underline{3}, \underline{4}, 3, 4, \underline{5}]$, $[\underline{3}, 4, 3, \underline{4}, \underline{5}]$, $[3, 4, \underline{3}, \underline{4}, \underline{5}]$.