# Original solution
import base64

exec(base64.b64decode(b'import subprocess
import sys

code = r"""#pragma GCC optimize("unroll-loops")

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cctype>
#include <chrono>
#include <cmath>
#include <complex>
#include <cstring>
#include <deque>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <utility>
#include <vector>

using namespace std;

using int64 = long long;

#define all(_) begin(_), end(_)
#define rall(_) rbegin(_), rend(_)

int64 dp[3000][3000][4];

namespace FastIO {
class Scanner {
  static constexpr int buf_size = (1 << 18);
  static constexpr int integer_size = 20;
  static constexpr int string_size = 1000; // default
  char buf[buf_size] = {};
  char *cur = buf, *ed = buf;

 public:
  Scanner() {}

  template <class T>
  inline Scanner& operator>>(T& val) {
    read(val);
    return *this;
  }

 private:
  inline void reload() {
    size_t len = ed - cur;
    memmove(buf, cur, len);
    char* tmp = buf + len;
    ed = tmp + fread(tmp, 1, buf_size - len, stdin);
    *ed = 0;
    cur = buf;
  }

  inline void skip_space() {
    while (true) {
      if (cur == ed) reload();
      while (*cur == ' ' || *cur == '\n') ++cur;
      if (__builtin_expect(cur != ed, 1)) return;
    }
  }

  template <class T, std::enable_if_t<std::is_same<T, int>::value, int> = 0>
  inline void read(T& num) {
    skip_space();
    if (cur + integer_size >= ed) reload();
    bool neg = false;
    num = 0;
    if (*cur == '-') neg = true, ++cur;
    while (*cur >= '0') num = num * 10 + (*cur ^ 48), ++cur;
    if (neg) num = -num;
  }

  template <class T, std::enable_if_t<std::is_same<T, int64>::value, int> = 0>
  inline void read(T& num) {
    skip_space();
    if (cur + integer_size >= ed) reload();
    bool neg = false;
    num = 0;
    if (*cur == '-') neg = true, ++cur;
    while (*cur >= '0') num = num * 10 + (*cur ^ 48), ++cur;
    if (neg) num = -num;
  }

  template <class T,
            std::enable_if_t<std::is_same<T, std::string>::value, int> = 0>
  inline void read(T& str) {
    skip_space();
    if (cur + str.size() >= ed) reload();
    auto it = cur;
    while (!(*cur == ' ' || *cur == '\n')) ++cur;
    str = std::string(it, cur);
  }

  template <class T, std::enable_if_t<std::is_same<T, char>::value, int> = 0>
  inline void read(T& c) {
    skip_space();
    if (cur + 1 >= ed) reload();
    c = *cur, ++cur;
  }

  template <class T, std::enable_if_t<std::is_same<T, double>::value, int> = 0>
  inline void read(T& num) {
    skip_space();
    if (cur + integer_size >= ed) reload();
    bool neg = false;
    num = 0;
    if (*cur == '-') neg = true, ++cur;
    while (*cur >= '0' && *cur <= '9') num = num * 10 + (*cur ^ 48), ++cur;
    if (*cur != '.') return;
    ++cur;
    T base = 0.1;
    while (*cur >= '0' && *cur <= '9') {
      num += base * (*cur ^ 48);
      ++cur;
      base *= 0.1;
    }
    if (neg) num = -num;
  }

  template <class T,
            std::enable_if_t<std::is_same<T, long double>::value, int> = 0>
  inline void read(T& num) {
    skip_space();
    if (cur + integer_size >= ed) reload();
    bool neg = false;
    num = 0;
    if (*cur == '-') neg = true, ++cur;
    while (*cur >= '0' && *cur <= '9') num = num * 10 + (*cur ^ 48), ++cur;
    if (*cur != '.') return;
    ++cur;
    T base = 0.1;
    while (*cur >= '0' && *cur <= '9') {
      num += base * (*cur ^ 48);
      ++cur;
      base *= 0.1;
    }
    if (neg) num = -num;
  }

  template <class T>
  inline void read(std::vector<T>& vec) {
    for (T& e : vec) read(e);
  }

  template <class T, class U>
  inline void read(std::pair<T, U>& p) {
    read(p.first, p.second);
  }

  template <class Tuple, std::size_t... Is>
  inline void tuple_scan(Tuple& tp, std::index_sequence<Is...>) {
    (read(std::get<Is>(tp)), ...);
  }

  template <class... Args>
  inline void read(std::tuple<Args...>& tp) {
    tuple_scan(tp, std::index_sequence_for<Args...>{});
  }

  inline void read() {}

  template <class Head, class... Tail>
  inline void read(Head&& head, Tail&&... tail) {
    read(head);
    read(std::forward<Tail>(tail)...);
  }
};

class Printer {
  static constexpr int buf_size = (1 << 18);
  static constexpr int integer_size = 20;
  static constexpr int string_size = (1 << 6);
  static constexpr int margin = 1;
  static constexpr int n = 10000;
  char buf[buf_size + margin] = {};
  char table[n * 4] = {};
  char* cur = buf;

 public:
  constexpr Printer() { build(); }

  ~Printer() { flush(); }

  template <class T>
  inline Printer& operator<<(T val) {
    write(val);
    return *this;
  }

  template<class T>
  inline void println(T val) {
    write(val);
    write('\n');
  }

 private:
  constexpr void build() {
    for (int i = 0; i < 10000; ++i) {
      int tmp = i;
      for (int j = 3; j >= 0; --j) {
        table[i * 4 + j] = tmp % 10 + '0';
        tmp /= 10;
      }
    }
  }

  inline void flush() {
    fwrite(buf, 1, cur - buf, stdout);
    cur = buf;
  }

  template <class T, std::enable_if_t<std::is_same<T, int>::value, int> = 0>
  inline int get_digit(T n) {
    if (n >= (int)1e5) {
      if (n >= (int)1e8) return 9;
      if (n >= (int)1e7) return 8;
      if (n >= (int)1e6) return 7;
      return 6;
    } else {
      if (n >= (int)1e4) return 5;
      if (n >= (int)1e3) return 4;
      if (n >= (int)1e2) return 3;
      if (n >= (int)1e1) return 2;
      return 1;
    }
  }

  template <class T, std::enable_if_t<std::is_same<T, int64>::value, int> = 0>
  inline int get_digit(T n) {
    if (n >= (int64)1e10) {
      if (n >= (int64)1e14) {
        if (n >= (int64)1e18) return 19;
        if (n >= (int64)1e17) return 18;
        if (n >= (int64)1e16) return 17;
        if (n >= (int64)1e15) return 16;
        return 15;
      } else {
        if (n >= (int64)1e14) return 15;
        if (n >= (int64)1e13) return 14;
        if (n >= (int64)1e12) return 13;
        if (n >= (int64)1e11) return 12;
        return 11;
      }
    } else {
      if (n >= (int64)1e5) {
        if (n >= (int64)1e9) return 10;
        if (n >= (int64)1e8) return 9;
        if (n >= (int64)1e7) return 8;
        if (n >= (int64)1e6) return 7;
        return 6;
      } else {
        if (n >= (int64)1e4) return 5;
        if (n >= (int64)1e3) return 4;
        if (n >= (int64)1e2) return 3;
        if (n >= (int64)1e1) return 2;
        return 1;
      }
    }
  }

  template <class T, std::enable_if_t<std::is_same<T, int>::value, int> = 0>
  inline void write(T num) {
    if (__builtin_expect(cur + integer_size >= buf + buf_size, 0)) flush();
    if (num == 0) {
      write('0');
      return;
    }
    if (num < 0) {
      write('-');
      num = -num;
    }
    int len = get_digit(num);
    int digits = len;
    while (num >= 10000) {
      memcpy(cur + len - 4, table + (num % 10000) * 4, 4);
      num /= 10000;
      len -= 4;
    }
    memcpy(cur, table + num * 4 + (4 - len), len);
    cur += digits;
  }

  template <class T, std::enable_if_t<std::is_same<T, int64>::value, int> = 0>
  inline void write(T num) {
    if (__builtin_expect(cur + integer_size >= buf + buf_size, 0)) flush();
    if (num == 0) {
      write('0');
      return;
    }
    if (num < 0) {
      write('-');
      num = -num;
    }
    int len = get_digit(num);
    int digits = len;
    while (num >= 10000) {
      memcpy(cur + len - 4, table + (num % 10000) * 4, 4);
      num /= 10000;
      len -= 4;
    }
    memcpy(cur, table + num * 4 + (4 - len), len);
    cur += digits;
  }

  template <class T, std::enable_if_t<std::is_same<T, char>::value, int> = 0>
  inline void write(T c) {
    if (__builtin_expect(cur + 1 >= buf + buf_size, 0)) flush();
    *cur = c;
    ++cur;
  }

  template <class T,
            std::enable_if_t<std::is_same<T, std::string>::value, int> = 0>
  inline void write(T str) {
    if (__builtin_expect(cur + str.size() >= buf + buf_size, 0)) flush();
    for (char c : str) write(c);
  }

  template <class T,
            std::enable_if_t<std::is_same<T, const char*>::value, int> = 0>
  inline void write(T str) {
    if (__builtin_expect(cur + string_size >= buf + buf_size, 0)) flush();
    for (int i = 0; str[i]; ++i) write(str[i]);
  }
};
}  // namespace FastIO

FastIO::Scanner fin;
FastIO::Printer fout;


int main() {
  int r, c, k; fin >> r >> c >> k;
  int val[r][c];
  fill(val[0], val[r], 0);
  for (int i = 0; i < k; ++i) {
    int x, y, z; fin >> x >> y >> z;
    --x; --y;
    val[x][y] = z;
  }

  if (val[0][0] != 0) dp[0][0][1] = val[0][0];

  for (int i = 0; i < r; ++i) {
    for (int j = 0; j < c; ++j) {
      if (i == 0 && j == 0) continue;

      if (val[i][j] != 0) {
        if (i > 0) {
          for (int l = 0; l < 4; ++l) dp[i][j][0] = max(dp[i][j][0], dp[i - 1][j][l]);
          for (int l = 0; l < 4; ++l) dp[i][j][1] = max(dp[i][j][1], dp[i - 1][j][l] + val[i][j]);
        }
        if (j > 0) {
          dp[i][j][0] = max(dp[i][j][0], dp[i][j - 1][0]);
          for (int l = 1; l < 4; ++l) {
            dp[i][j][l] = max({dp[i][j][l], dp[i][j - 1][l], dp[i][j - 1][l - 1] + val[i][j]});
          }
        }
      } else {
        if (i > 0) {
          for (int l = 0; l < 4; ++l) dp[i][j][0] = max(dp[i][j][0], dp[i - 1][j][l]);
        }
        if (j > 0) {
          for (int l = 0; l < 4; ++l) dp[i][j][l] = max(dp[i][j][l], dp[i][j - 1][l]);
        }
      }
    }
  }

  int64 ans = 0;
  for (int i = 0; i < 4; ++i) ans = max(ans, dp[r - 1][c - 1][i]);
  fout.println(ans);

  return 0;
}
"""

with open('sol.cpp', 'w') as f:
    f.write(code)

subprocess.Popen(['g++', '-std=c++17', '-O2', 'sol.cpp']).communicate()
subprocess.Popen(['./a.out'], stdin=sys.stdin, stdout=sys.stdout).communicate()'))

# Optimized solution
import base64

exec(base64.b64decode(b'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'))