#include <algorithm>
#include <vector>
using namespace std;class MissingLCM {public:int getMin(int N) {if (N == 1) {return 2;}long long result = 0;std::vector<bool> tags(N + 1, false);for (int i = 2; i <= N; ++i) {if (!tags[i]) {for (int j = i + i; j <= N; j += i) {tags[j] = true;}long long t = 1;while (t <= N / i) {t *= i;}result = std::max(result, N % t == 0 ? N + t : N / t * t + t);}}return static_cast<int>(result);}
};

class ColorfulLineGraphs {public:int countWays(long long N, long long K, int M) {long long result = 1;for (int i = 0; i < M && i < N; ++i) {long long x = K + (K - 1) * i;long long y = (N - 1 - i) / M + 1;result = result * Pow(x, y, M) % M;}return static_cast<int>(result);}private:long long Pow(long long x, long long y, int M) {x %= M;long long result = 1;while (y != 0) {if (y % 2 == 1) {result = result * x % M;}x = x * x % M;y /= 2;}return result;}
};

#include <algorithm>
#include <cstring>
#include <vector>constexpr int kMaxN = 200;
int L[kMaxN][kMaxN];
int R[kMaxN][kMaxN];
int S[kMaxN][kMaxN];
int D[kMaxN][kMaxN];
int dp[kMaxN][kMaxN + 1];class BridgeBuilding {public:int minDiameter(const std::vector<int> &a, const std::vector<int> &b, int K) {int n = static_cast<int>(a.size()) + 1;std::vector<int> prefix_a(n);std::vector<int> prefix_b(n);for (int i = 1; i < n; ++i) {prefix_a[i] = prefix_a[i - 1] + a[i - 1];prefix_b[i] = prefix_b[i - 1] + b[i - 1];}auto Dist = [&](int a, int b, int t) {if (a >= b) {return 0;}return t == 0 ? prefix_a[b] - prefix_a[a] : prefix_b[b] - prefix_b[a];};auto GetMax = [&](int left, int right) {int number = right - left;auto Get = [&](int k) {if (k <= number) {return Dist(left, left + k, 0);}return Dist(left, right, 0) + Dist(right - (k - number), right, 1);};int total = Dist(left, right, 0) + Dist(left, right, 1);int tmax = 0;for (int L = 0, R = 0; L < number * 2; ++L) {if (R <= L) {R = L + 1;}int t = Get(L);while (R < number * 2 && Get(R) - t < total / 2) {int p = Get(R) - t;tmax = std::max(tmax, std::min(p, total - p));++R;}int p = Get(R) - t;tmax = std::max(tmax, std::min(p, total - p));}return tmax;};for (int i = 0; i < n; ++i) {for (int j = i + 1; j < n; ++j) {int s0 = Dist(i, j, 0);int s1 = Dist(i, j, 1);D[i][j] = std::min(s0, s1);S[i][j] = GetMax(i, j);L[i][j] = R[i][j] = 0;for (int k = i; k <= j; ++k) {L[i][j] =std::max(L[i][j], std::min(Dist(i, k, 0), Dist(k, j, 0) + s1));L[i][j] =std::max(L[i][j], std::min(Dist(i, k, 1), Dist(k, j, 1) + s0));R[i][j] =std::max(R[i][j], std::min(Dist(k, j, 0), Dist(i, k, 0) + s1));R[i][j] =std::max(R[i][j], std::min(Dist(k, j, 1), Dist(i, k, 1) + s0));}}}auto Check = [&](int mid) {memset(dp, -1, sizeof(dp));for (int i = 0; i < n; ++i) {if (prefix_a[i] + prefix_b[i] <= mid) {dp[i][1] = std::max(prefix_a[i], prefix_b[i]);}}for (int i = 0; i < n; ++i) {for (int j = 1; j < K; ++j) {if (dp[i][j] != -1) {for (int k = i + 1; k < n; ++k) {if (S[i][k] <= mid && dp[i][j] + L[i][k] <= mid) {int v = std::max(R[i][k], dp[i][j] + D[i][k]);if (dp[k][j + 1] == -1 || dp[k][j + 1] > v) {dp[k][j + 1] = v;}}}}}}int result = std::numeric_limits<int>::max();for (int i = K - 1; i < n; ++i) {if (dp[i][K] != -1 && Dist(i, n - 1, 0) + Dist(i, n - 1, 1) <= mid) {result = std::min(result, dp[i][K] + std::max(Dist(i, n - 1, 0),Dist(i, n - 1, 1)));}}return result <= mid;};int result = std::numeric_limits<int>::max();int left = 0, right = result;while (left <= right) {int mid = (left + right) >> 1;if (Check(mid)) {result = std::min(result, mid);right = mid - 1;} else {left = mid + 1;}}return result;}
};