Problem: Ujan has finally cleaned up his house and now wants to decorate the interior. He decided to place a beautiful carpet that would really tie the guest room together.

He is interested in carpets that are made up of polygonal patches such that each side of a patch is either a side of another (different) patch, or is an exterior side of the whole carpet. In other words, the carpet can be represented as a planar graph, where each patch corresponds to a face of the graph, each face is a simple polygon. The perimeter of the carpet is the number of the exterior sides. 

Ujan considers a carpet beautiful if it consists of f patches, where the i-th patch has exactly a_i sides, and the perimeter is the smallest possible. Find an example of such a carpet, so that Ujan can order it!

Input

The first line of input contains a single integer f (1 ≤ f ≤ 10^5), the number of patches in the carpet. 

The next line contains f integers a_1, …, a_f (3 ≤ a_i ≤ 3⋅ 10^5), the number of sides of the patches. The total number of the sides of the patches a_1 + … + a_f does not exceed 3⋅10^5.

Output

Output the description of the carpet as a graph. 

First, output a single integer n (3 ≤ n ≤ 3 ⋅ 10^5), the total number of vertices in your graph (the vertices must be numbered from 1 to n). 

Then output f lines containing the description of the faces. The i-th line should describe the i-th face and contain a_i distinct integers v_{i,1}, …, v_{i,a_i} (1 ≤ v_{i,j} ≤ n), which means that the vertices v_{i,j} and v_{i,(j mod{a_i})+1} are connected by an edge for any 1 ≤ j ≤ a_i.

The graph should be planar and satisfy the restrictions described in the problem statement. Its perimeter should be the smallest possible. There should be no double edges or self-loops in the graph. The graph should be connected. Note that a solution always exists; if there are multiple solutions, output any of them.

Examples

Input


2
3 3


Output


4
2 1 4 
1 2 3 


Input


3
5 3 5


Output


6
1 2 3 4 5
4 5 6
1 3 4 6 5

Note

In the first sample, the two triangular faces are connected by a single edge, which results in the minimum perimeter 4.

The figure shows one possible configuration for the second sample. The minimum perimeter in this case is 3. 

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MAXF = 1.1e5;
int F;
pair<int, int> A[MAXF];
vector<int> ans[MAXF];
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  cin >> F;
  for (int i = 0; i < F; i++) {
    int a;
    cin >> a;
    A[i] = {a, i};
  }
  sort(A, A + F);
  int N = 2;
  deque<int> dq({1, 2});
  for (int i = F - 1; i >= 0; i--) {
    int v, f;
    tie(v, f) = A[i];
    int s = int(dq.size());
    int numMerge = min((s + v - (i ? A[i - 1].first : 3)) / 2, min(s, v) - 1);
    for (int z = 0; z < numMerge - 1; z++) {
      ans[f].push_back(dq.back());
      dq.pop_back();
    }
    ans[f].push_back(dq.back());
    for (int z = numMerge; z < v - 1; z++) {
      ++N;
      ans[f].push_back(N);
      dq.push_back(N);
    }
    ans[f].push_back(dq.front());
    dq.push_back(dq.front());
    dq.pop_front();
  }
  cout << N << '\n';
  for (int i = 0; i < F; i++) {
    for (int v : ans[i]) {
      cout << v << ' ';
    }
    cout << '\n';
  }
  return 0;
}