import sys
import heapq
def MI(): return map(int,sys.stdin.readline().rstrip().split())


N,M = MI()
HWC = [tuple(MI()) for _ in range(M)]

Graph = [[] for _ in range(N**2)]
for i in range(N):
    for j in range(N-1):
        a,b = N*i+j,N*i+j+1
        Graph[a].append([b,1])
        Graph[b].append([a,1])
for i in range(N-1):
    for j in range(N):
        a,b = N*i+j,N*(i+1)+j
        Graph[a].append([b,1])
        Graph[b].append([a,1])

for h,w,c in HWC:
    h -= 1
    w -= 1
    b = N*h+w
    if h >= 1:
        a = N*(h-1)+w
        Graph[a] = [x for x in Graph[a] if x[0] != b]+[[b,c+1]]
    if h <= N-2:
        a = N*(h+1)+w
        Graph[a] = [x for x in Graph[a] if x[0] != b]+[[b,c+1]]
    if w >= 1:
        a = N*h+w-1
        Graph[a] = [x for x in Graph[a] if x[0] != b]+[[b,c+1]]
    if w <= N-2:
        a = N*h+w+1
        Graph[a] = [x for x in Graph[a] if x[0] != b]+[[b,c+1]]

inf = 10**18

dist0 = [inf]*(N**2)  # (1,1)からの最短距離
dist0[0] = 0
q0 = []
heapq.heappush(q0,(0,0))
v0 = [0]*(N**2)
while q0:
    k,u = heapq.heappop(q0)
    if v0[u]:
        continue
    v0[u] = True
    for x in Graph[u]:
        uv,ud = x
        if v0[uv]:
            continue
        vd = k + ud
        if dist0[uv] > vd:
            dist0[uv] = vd
            heapq.heappush(q0,(vd,uv))

dist1 = [inf]*(N**2)  # (N,N)からの最短距離
dist1[N**2-1] = 0
q1 = []
heapq.heappush(q1,(0,N**2-1))
v1 = [0]*(N**2)
while q1:
    k,u = heapq.heappop(q1)
    if v1[u]:
        continue
    v1[u] = True
    for x in Graph[u]:
        uv,ud = x
        if v1[uv]:
            continue
        vd = k + ud
        if dist1[uv] > vd:
            dist1[uv] = vd
            heapq.heappush(q1,(vd,uv))

ans = dist0[-1]
for h,w,c in HWC:
    h -= 1
    w -= 1
    a = N*h+w
    ans = min(ans,dist0[a]+dist1[a]-2*c)
print(ans)