import sys
readline = sys.stdin.readline

N, M = map(int, readline().split())
inf = 10 ** 18
dp0 = [[inf] * N for i in range(N)]
dp1 = [[inf] * N for i in range(N)]
cost = [[0] * N for i in range(N)]
dp0[0][0] = 0

for i in range(M):
    h, w, c = map(int, readline().split())
    h, w = h - 1, w - 1
    cost[h][w] = c
    
for i in range(N):
    for j in range(N):
        if i - 1 >= 0:
            dp0[i][j] = min(dp0[i][j], dp0[i - 1][j] + cost[i][j])
            dp1[i][j] = min(dp1[i][j], dp1[i - 1][j] + cost[i][j])
            dp1[i][j] = min(dp1[i][j], dp0[i - 1][j])
        if j - 1 >= 0:
            dp0[i][j] = min(dp0[i][j], dp0[i][j - 1] + cost[i][j])
            dp1[i][j] = min(dp1[i][j], dp1[i][j - 1] + cost[i][j])
            dp1[i][j] = min(dp1[i][j], dp0[i][j - 1])
            
print(min(dp0[-1][-1], dp1[-1][-1]) + 2 * (N - 1))