N,M = map(int,input().split())

cost_s = [[0 for i in range(N)] for j in range(N)]
cost_e = [[0 for i in range(N)] for j in range(N)]
memo = []
for _ in range(M):
    h,w,c = map(int,input().split())
    cost_s[h-1][w-1] = c
    cost_e[h-1][w-1] = c
    memo.append((h-1,w-1,c))

for i in range(N):
    for j in range(N):
        if i==0 and j==0:
            continue

        tmp = 10**18
        if i!=0:
            tmp = cost_s[i-1][j] + 1
        if j!=0:
            tmp = min(cost_s[i][j-1] + 1,tmp)
        cost_s[i][j] += tmp

for i in range(N-1,-1,-1):
    for j in range(N-1,-1,-1):
        if i==N-1 and j==N-1:
            continue

        tmp = 10**18
        if i!=N-1:
            tmp = cost_e[i+1][j] + 1
        if j!=N-1:
            tmp = min(cost_e[i][j+1] + 1,tmp)
        cost_e[i][j] += tmp

res = cost_s[N-1][N-1]
for h,w,c in memo:
    tmp = cost_s[h][w] + cost_e[h][w] - 2*c
    res = min(res,tmp)

print(res)