Problem Statement

You are given a sequence of positive integers $A=(A_1,A_2,\ldots,A_N)$.

There are $2^N$ subsequences of $A$ when distinguishing subsequences by the indices of their elements. Let $S_1, S_2, \ldots, S_{2^N}$ be the sums of these subsequences, enumerated in ascending order.

For all integers $k$ ($1\leq k\leq 2^N-1$) that satisfy $1.01 \times S_k\leq S_{k+1}$, output $S_k, S_{k+1}, (k\bmod 998244353)$.

What is a subsequence A subsequence of a sequence $A$ is a sequence obtained by removing zero or more elements from $A$ and arranging the remaining elements in their original order.

Constraints

• $2\leq N\leq 5000$
• $1\leq A_i\leq 10^{13}$

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 \ldots A_N

Output

On the first line, output the number of integers $k$ that satisfy the condition.

From the second line onwards, for each integer $k$ that satisfies the condition, output $S_k, S_{k+1}, (k\bmod 998244353)$ separated by spaces on each line.

Output in ascending order of $k$.