You're given a matrix *A* of size *n* × *n*.

Let's call the matrix with nonnegative elements magic if it is symmetric (so *a*<sub class="lower-index">*ij*</sub> = *a*<sub class="lower-index">*ji*</sub>), *a*<sub class="lower-index">*ii*</sub> = 0 and *a*<sub class="lower-index">*ij*</sub> ≤ *max*(*a*<sub class="lower-index">*ik*</sub>, *a*<sub class="lower-index">*jk*</sub>) for all triples *i*, *j*, *k*. Note that *i*, *j*, *k* do not need to be distinct.

Determine if the matrix is magic.

As the input/output can reach very huge size it is recommended to use fast input/output methods: for example, prefer to use scanf/printf instead of cin/cout in C++, prefer to use BufferedReader/PrintWriter instead of Scanner/System.out in Java.
The first line contains integer *n* (1 ≤ *n* ≤ 2500) — the size of the matrix *A*.

Each of the next *n* lines contains *n* integers *a*<sub class="lower-index">*ij*</sub> (0 ≤ *a*<sub class="lower-index">*ij*</sub> &lt; 10<sup class="upper-index">9</sup>) — the elements of the matrix *A*.

Note that the given matrix not necessarily is symmetric and can be arbitrary.
none
3
0 1 2
1 0 2
2 2 0
MAGIC
2
0 1
2 3
NOT MAGIC
4
0 1 2 3
1 0 3 4
2 3 0 5
3 4 5 0
NOT MAGIC
5
0 2 5 9 5
2 0 5 9 5
5 5 0 9 4
9 9 9 0 9
5 5 4 9 0
MAGIC
10
0 16 5 14 14 17 14 14 9 14
16 0 16 16 16 17 16 16 16 16
5 16 0 14 14 17 14 14 9 14
14 16 14 0 7 17 3 8 14 12
14 16 14 7 0 17 7 8 14 12
17 17 17 17 17 0 17 17 17 17
14 16 14 3 7 17 0 8 14 12
14 16 14 8 8 17 8 0 14 12
9 16 9 14 14 17 14 14 0 14
14 16 14 12 12 17 12 12 14 0
MAGIC
5
0 2 9 10 10
2 0 5 2 3
9 5 0 1 1
10 2 1 0 7
10 3 1 7 0
NOT MAGIC
10
0 18 0 12 20 3 14 12 13 2
18 0 6 12 7 20 1 9 13 10
0 6 0 15 17 9 16 15 1 0
12 12 15 0 0 8 19 20 11 11
20 7 17 0 0 3 5 14 8 3
3 20 9 8 3 0 7 16 20 17
14 1 16 19 5 7 0 14 18 14
12 9 15 20 14 16 14 0 6 19
13 13 1 11 8 20 18 6 0 13
2 10 0 11 3 17 14 19 13 0
NOT MAGIC
2
1 1
1 1
NOT MAGIC
3
0 999999998 999999998
999999998 0 999999999
999999998 999999999 0
NOT MAGIC
5
0 3 7 1 1
3 0 7 1 1
7 7 0 7 7
1 1 7 0 1
1 1 7 1 0
NOT MAGIC
5
0 2 9 1 1
2 0 9 1 1
9 9 0 9 9
1 1 9 0 1
1 1 9 1 0
NOT MAGIC
3
0 1 2
0 0 2
2 2 0
NOT MAGIC
3
1 2 3
2 1 3
3 3 1
NOT MAGIC
4
0 9 9 9
9 0 1 2
9 1 0 3
9 2 3 0
NOT MAGIC
2
2 2
2 2
NOT MAGIC
4
0 1 2 9
1 0 3 9
2 3 0 9
9 9 9 0
NOT MAGIC
4
0 0 0 4
0 0 3 4
0 3 0 4
4 4 4 0
NOT MAGIC
import sys
readline=sys.stdin.readline

class UnionFind:
    def __init__(self,N,label=None,f=None,weighted=False):
        self.N=N
        self.parents=[None]*self.N
        self.size=[1]*self.N
        self.roots={i for i in range(self.N)}
        self.label=label
        if self.label!=None:
            self.label=[x for x in label]
        self.f=f
        self.weighted=weighted
        if self.weighted:
            self.weight=[0]*self.N

    def Find(self,x):
        stack=[]
        while self.parents[x]!=None:
            stack.append(x)
            x=self.parents[x]
        if self.weighted:
            w=0
            for y in stack[::-1]:
                self.parents[y]=x
                w+=self.weight[y]
                self.weight[y]=w
        else:
            for y in stack[::-1]:
                self.parents[y]=x
        return x

    def Union(self,x,y,w=None):
        root_x=self.Find(x)
        root_y=self.Find(y)
        if root_x==root_y:
            if self.weighted:
                if self.weight[y]-self.weight[x]==w:
                    return True
                else:
                    return False
        else:
            if self.size[root_x]<self.size[root_y]:
                x,y=y,x
                root_x,root_y=root_y,root_x
                if self.weighted:
                    w=-w
            self.parents[root_y]=root_x
            self.size[root_x]+=self.size[root_y]
            self.roots.remove(root_y)
            if self.label!=None:
                self.label[root_x]=self.f(self.label[root_x],self.label[root_y])
            if self.weighted:
                self.weight[root_y]=w+self.weight[x]-self.weight[y]

    def Size(self,x):
        return self.size[self.Find(x)]

    def Same(self,x,y):
        return self.Find(x)==self.Find(y)

    def Label(self,x):
        return self.label[self.Find(x)]

    def Weight(self,x,y):
        root_x=self.Find(x)
        root_y=self.Find(y)
        if root_x!=root_y:
            return None
        return self.weight[y]-self.weight[x]

    def Roots(self):
        return list(self.roots)

    def Linked_Components_Count(self):
        return len(self.roots)

    def Linked_Components(self):
        linked_components=defaultdict(list)
        for x in range(self.N):
            linked_components[self.Find(x)].append(x)
        return linked_components

    def __str__(self):
        linked_components=defaultdict(list)
        for x in range(self.N):
            linked_components[self.Find(x)].append(x)
        return "\n".join(f"{r}: {m}" for r,m in linked_components.items())

class Graph:
    def __init__(self,V,edges=None,graph=None,directed=False,weighted=False,inf=float("inf")):
        self.V=V
        self.directed=directed
        self.weighted=weighted
        self.inf=inf
        if graph!=None:
            self.graph=graph
            self.edges=[]
            for i in range(self.V):
                if self.weighted:
                    for j,d in self.graph[i]:
                        if self.directed or not self.directed and i<=j:
                            self.edges.append((i,j,d))
                else:
                    for j in self.graph[i]:
                        if self.directed or not self.directed and i<=j:
                            self.edges.append((i,j))
        else:
            self.edges=edges
            self.graph=[[] for i in range(self.V)]
            if weighted:
                for i,j,d in self.edges:
                    self.graph[i].append((j,d))
                    if not self.directed:
                        self.graph[j].append((i,d))
            else:
                for i,j in self.edges:
                    self.graph[i].append(j)
                    if not self.directed:
                        self.graph[j].append(i)

    def SIV_DFS(self,s,bipartite_graph=False,cycle_detection=False,directed_acyclic=False,euler_tour=False,linked_components=False,lowlink=False,parents=False,postorder=False,preorder=False,subtree_size=False,topological_sort=False,unweighted_dist=False,weighted_dist=False):
        seen=[False]*self.V
        finished=[False]*self.V
        if directed_acyclic or cycle_detection or topological_sort:
            dag=True
        if euler_tour:
            et=[]
        if linked_components:
            lc=[]
        if lowlink:
            order=[None]*self.V
            ll=[None]*self.V
            idx=0
        if parents or cycle_detection or lowlink or subtree_size:
            ps=[None]*self.V
        if postorder or topological_sort:
            post=[]
        if preorder:
            pre=[]
        if subtree_size:
            ss=[1]*self.V
        if unweighted_dist or bipartite_graph:
            uwd=[self.inf]*self.V
            uwd[s]=0
        if weighted_dist:
            wd=[self.inf]*self.V
            wd[s]=0
        stack=[(s,0)] if self.weighted else [s]
        while stack:
            if self.weighted:
                x,d=stack.pop()
            else:
                x=stack.pop()
            if not seen[x]:
                seen[x]=True
                stack.append((x,d) if self.weighted else x)
                if euler_tour:
                    et.append(x)
                if linked_components:
                    lc.append(x)
                if lowlink:
                    order[x]=idx
                    ll[x]=idx
                    idx+=1
                if preorder:
                    pre.append(x)
                for y in self.graph[x]:
                    if self.weighted:
                        y,d=y
                    if not seen[y]:
                        stack.append((y,d) if self.weighted else y)
                        if parents or cycle_detection or lowlink or subtree_size:
                            ps[y]=x
                        if unweighted_dist or bipartite_graph:
                            uwd[y]=uwd[x]+1
                        if weighted_dist:
                            wd[y]=wd[x]+d
                    elif not finished[y]:
                        if (directed_acyclic or cycle_detection or topological_sort) and dag:
                            dag=False
                            if cycle_detection:
                                cd=(y,x)
            elif not finished[x]:
                finished[x]=True
                if euler_tour:
                    et.append(~x)
                if lowlink:
                    bl=True
                    for y in self.graph[x]:
                        if self.weighted:
                            y,d=y
                        if ps[x]==y and bl:
                            bl=False
                            continue
                        ll[x]=min(ll[x],order[y])
                    if x!=s:
                        ll[ps[x]]=min(ll[ps[x]],ll[x])
                if postorder or topological_sort:
                    post.append(x)
                if subtree_size:
                    for y in self.graph[x]:
                        if self.weighted:
                            y,d=y
                        if y==ps[x]:
                            continue
                        ss[x]+=ss[y]
        if bipartite_graph:
            bg=[[],[]]
            for tpl in self.edges:
                x,y=tpl[:2] if self.weighted else tpl
                if uwd[x]==self.inf or uwd[y]==self.inf:
                    continue
                if not uwd[x]%2^uwd[y]%2:
                    bg=False
                    break
            else:
                for x in range(self.V):
                    if uwd[x]==self.inf:
                        continue
                    bg[uwd[x]%2].append(x)
        retu=()
        if bipartite_graph:
            retu+=(bg,)
        if cycle_detection:
            if dag:
                cd=[]
            else:
                y,x=cd
                cd=self.Route_Restoration(y,x,ps)
            retu+=(cd,)
        if directed_acyclic:
            retu+=(dag,)
        if euler_tour:
            retu+=(et,)
        if linked_components:
            retu+=(lc,)
        if lowlink:
            retu=(ll,)
        if parents:
            retu+=(ps,)
        if postorder:
            retu+=(post,)
        if preorder:
            retu+=(pre,)
        if subtree_size:
            retu+=(ss,)
        if topological_sort:
            if dag:
                tp_sort=post[::-1]
            else:
                tp_sort=[]
            retu+=(tp_sort,)
        if unweighted_dist:
            retu+=(uwd,)
        if weighted_dist:
            retu+=(wd,)
        if len(retu)==1:
            retu=retu[0]
        return retu

N=int(readline())
A=[list(map(int,readline().split())) for i in range(N)]
for i in range(N):
    for j in range(i+1,N):
        ma=max(A[i][j],A[j][i])
        A[i][j]=ma
        A[j][i]=ma
idx=[(i,j) for i in range(N) for j in range(N)]
idx.sort(key=lambda tpl:A[tpl[0]][tpl[1]])
UF=UnionFind(N)
edges=[]
for i,j in idx:
    if not UF.Same(i,j):
        UF.Union(i,j)
        edges.append((i,j,A[i][j]))
ans="MAGIC"
G=Graph(N,edges=edges,weighted=True)
for i in range(N):
    parents,tour=G.SIV_DFS(i,parents=True,preorder=True)
    dist=[0]*N
    for x in tour:
        for y,a in G.graph[x]:
            if y==parents[x]:
                continue
            dist[y]=max(dist[x],a)
    for j in range(N):
        if i==j:
            continue
        if dist[j]<A[i][j]:
            ans="NOT MAGIC"
for i in range(N):
    if A[i][i]>min(A[i]):
        ans="NOT MAGIC"
print(ans)