You are given an undirected graph of N nodes and M edges, E_1, E_2, ... E_M.

A connected graph is a cactus if each of it's edges belogs to at most one simple cycle. A graph is a desert if each of it's connected components is a cactus. 

Find the number of pairs (L, R), (1 ≤ L ≤ R ≤ M) such that, if we delete all the edges except for E_L, E_{L+1}, ... E_R, the graph is a desert. 

Input

The first line contains two integers N and M (2 ≤ N ≤ 2.5 × 10^5, 1 ≤ M ≤ 5 × 10^5). Each of the next M lines contains two integers. The i-th line describes the i-th edge. It contains integers U_i and V_i, the nodes connected by the i-th edge (E_i=(U_i, V_i)). It is guaranteed that 1 ≤ U_i, V_i ≤ N and U_i ≠ V_i. 

Output

The output contains one integer number – the answer.

Examples

Input


5 6
1 2
2 3
3 4
4 5
5 1
2 4


Output


20

Input


2 3
1 2
1 2
1 2


Output


5

Note

In the second example: Graphs for pairs (1, 1), (2, 2) and (3, 3) are deserts because they don't have any cycles. Graphs for pairs (1, 2) and (2, 3) have one cycle of length 2 so they are deserts.
5 10
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5
 4 5
1 2
2 3
2 4
3 4
4 1
 5 4
1 2
2 3
3 4
4 5
 3 6
1 2
2 3
3 1
1 2
2 3
3 1
 10 15
1 2
1 5
1 6
2 3
2 7
3 4
3 8
4 5
4 9
5 10
6 8
6 9
7 9
7 10
8 10
 8 11
1 2
2 3
2 4
3 4
4 1
5 6
6 8
6 7
7 8
7 5
8 5
 5 1
1 2
 5 8
1 2
2 3
3 1
2 5
3 4
4 5
5 3
1 4

38
 14
 10
 15
 99
 48
 1
 30

#include <bits/stdc++.h>
using namespace std;
const long long MaxN = 500005;
template <class T>
class BlockAllocator {
 private:
  static const long long BlockL = 10000;
  union TItem {
    char rt[sizeof(T)];
    TItem *next;
  };
  TItem *pool, *tail;
  TItem *unused;

 public:
  BlockAllocator() {
    pool = NULL;
    unused = NULL;
  }
  T *allocate() {
    TItem *p;
    if (unused) {
      p = unused;
      unused = unused->next;
    } else {
      if (pool == NULL) pool = new TItem[BlockL], tail = pool;
      p = tail++;
      if (tail == pool + BlockL) pool = NULL;
    }
    return (T *)p;
  }
  void deallocate(T *pt) {
    TItem *p = (TItem *)pt;
    p->next = unused, unused = p;
  }
};
struct edgeWeight;
struct path_message;
struct lcc_circle;
struct lcc_edge;
struct lcc_message;
struct lcc_node;
struct edgeWeight {
  long long wA, wB;
  edgeWeight() {}
  edgeWeight(const long long &_wA, const long long &_wB) : wA(_wA), wB(_wB) {}
  friend inline bool operator==(const edgeWeight &lhs, const edgeWeight &rhs) {
    return lhs.wA == rhs.wA && lhs.wB == rhs.wB;
  }
  friend inline bool operator!=(const edgeWeight &lhs, const edgeWeight &rhs) {
    return lhs.wA != rhs.wA || lhs.wB != rhs.wB;
  }
};
struct path_message {
  long long minLA;
  long long minWB;
  path_message() {}
  path_message(const edgeWeight &ew) : minLA(ew.wA), minWB(ew.wB) {}
  path_message(const long long &_minLA, const long long &_minWB)
      : minLA(_minLA), minWB(_minWB) {}
  void setEmpty() {
    minLA = 0;
    minWB = 1000000000000000000;
  }
  void setInvalid() {
    minLA = -1;
    minWB = -1;
  }
  bool valid() const { return minLA != -1; }
  void setMultiple() { minWB = -1; }
  friend inline path_message operator+(const path_message &lhs,
                                       const path_message &rhs) {
    if (lhs.minLA < rhs.minLA)
      return lhs;
    else if (rhs.minLA < lhs.minLA)
      return rhs;
    else
      return path_message(lhs.minLA, -1);
  }
  friend inline path_message operator*(const path_message &lhs,
                                       const path_message &rhs) {
    return path_message(lhs.minLA + rhs.minLA, min(lhs.minWB, rhs.minWB));
  }
};
struct lcc_circle {
  lcc_node *pA, *pB;
  lcc_node *pEx;
  lcc_edge *missingE;
  bool equalL;
};
struct lcc_edge {
  edgeWeight ew;
  lcc_circle *cir;
  inline lcc_circle *getCir() { return this ? this->cir : NULL; }
};
struct lcc_message {
  path_message pathMsg;
  lcc_edge *firstE, *lastE;
  bool hasCir;
  bool hasMultiplePath;
  void rev() { swap(firstE, lastE); }
  void coverCir(lcc_circle *cir, bool isSingle) {
    hasCir = !isSingle && cir != NULL;
    hasMultiplePath = false;
    if (cir && firstE->getCir() != cir && lastE->getCir() != cir) {
      if (cir->equalL) hasMultiplePath = true;
    }
  }
  void addWB(long long delta, bool isSingle) {
    if (!isSingle) pathMsg.minWB += delta;
  }
  friend inline lcc_message operator+(const lcc_message &lhs,
                                      const lcc_message &rhs) {
    lcc_message res;
    assert(lhs.lastE == rhs.firstE);
    lcc_edge *e = lhs.lastE;
    res.pathMsg = lhs.pathMsg * path_message(e->ew) * rhs.pathMsg;
    res.hasMultiplePath = lhs.hasMultiplePath || rhs.hasMultiplePath;
    if (e->cir && lhs.firstE->getCir() != e->cir &&
        rhs.lastE->getCir() != e->cir) {
      if (e->cir->equalL) res.hasMultiplePath = true;
    }
    res.firstE = lhs.firstE, res.lastE = rhs.lastE;
    res.hasCir = lhs.hasCir || e->cir || rhs.hasCir;
    return res;
  }
};
struct lcc_node {
  lcc_node *fa, *lc, *rc;
  lcc_edge *prevE, *nextE;
  lcc_message msg;
  bool hasRev;
  bool hasCoveredCir;
  lcc_circle *coveredCir;
  long long wBDelta;
  bool isRoot() { return !fa || (fa->lc != this && fa->rc != this); }
  void rotate() {
    lcc_node *x = this, *y = x->fa, *z = y->fa;
    lcc_node *b = x == y->lc ? x->rc : x->lc;
    x->fa = z, y->fa = x;
    if (b) b->fa = y;
    if (z) {
      if (z->lc == y)
        z->lc = x;
      else if (z->rc == y)
        z->rc = x;
    }
    if (y->lc == x)
      x->rc = y, y->lc = b;
    else
      x->lc = y, y->rc = b;
    y->update();
  }
  void allFaTagDown() {
    long long anc_n = 0;
    static lcc_node *anc[MaxN];
    anc[anc_n++] = this;
    for (long long i = 0; !anc[i]->isRoot(); i++) anc[anc_n++] = anc[i]->fa;
    for (long long i = anc_n - 1; i >= 0; i--) anc[i]->tag_down();
  }
  void splay() {
    allFaTagDown();
    while (!this->isRoot()) {
      if (!fa->isRoot()) {
        if ((fa->lc == this) == (fa->fa->lc == fa))
          fa->rotate();
        else
          this->rotate();
      }
      this->rotate();
    }
    this->update();
  }
  void splay_until(lcc_node *target) {
    allFaTagDown();
    while (this->fa != target) {
      if (fa->fa != target) {
        if ((fa->lc == this) == (fa->fa->lc == fa))
          fa->rotate();
        else
          this->rotate();
      }
      this->rotate();
    }
    this->update();
  }
  long long getLcTotL() {
    if (!prevE) return 0;
    long long totL = prevE->ew.wA;
    if (lc) totL += lc->msg.pathMsg.minLA + msg.firstE->ew.wA;
    return totL;
  }
  long long getRcTotL() {
    if (!nextE) return 0;
    long long totL = nextE->ew.wA;
    if (rc) totL += rc->msg.pathMsg.minLA + msg.lastE->ew.wA;
    return totL;
  }
  void access() {
    for (lcc_node *p = this, *q = NULL; p; q = p, p = p->fa) {
      p->splay();
      if (p->prevE && p->prevE->cir) {
        bool isTogether = false;
        lcc_circle *cir = p->prevE->cir;
        if (cir->pEx && !cir->pEx->isRoot()) cir->pEx = p;
        cir->pB->splay(), cir->pA->splay();
        if (cir->pB->isRoot()) {
          if (cir->pB->fa != cir->pA) {
            swap(cir->pA, cir->pB);
            if (cir->pEx) cir->pEx->tag_rev();
          }
        } else {
          isTogether = true;
          cir->pB->splay_until(cir->pA);
          if (cir->pA->lc == cir->pB) {
            cir->pB->rotate();
            swap(cir->pA, cir->pB);
            if (cir->pEx) cir->pEx->tag_rev();
          }
          cir->pA->rc = NULL, cir->pA->nextE = NULL;
        }
        cir->pB->rc = cir->pEx,
        cir->pB->nextE = cir->pEx ? cir->pEx->msg.firstE : cir->missingE;
        if (cir->pEx) cir->pEx->fa = cir->pB;
        p->splay();
        if (p->getLcTotL() > p->getRcTotL()) p->tag_rev(), p->tag_down();
        cir->pB = p;
        cir->pEx = p->rc, cir->missingE = p->rc ? NULL : p->nextE;
        cir->equalL = p->getLcTotL() == p->getRcTotL();
        if (cir->pEx) cir->pEx->fa = NULL;
        p->rc = q, p->nextE = q ? q->msg.firstE : NULL;
        p->update();
        if (isTogether) {
          cir->pA->rc = p, cir->pA->nextE = p->msg.firstE;
          p->splay();
        }
      } else {
        p->rc = q, p->nextE = q ? q->msg.firstE : NULL;
        p->update();
      }
    }
    this->splay();
  }
  void makeRoot() {
    this->access();
    this->tag_rev(), this->tag_down();
  }
  lcc_node *findRoot() {
    lcc_node *p = this;
    p->access();
    while (p->tag_down(), p->lc) p = p->lc;
    p->splay();
    return p;
  }
  void tag_rev() {
    hasRev = !hasRev;
    msg.rev();
  }
  void tag_coverCir(lcc_circle *cir) {
    hasCoveredCir = true;
    coveredCir = cir;
    msg.coverCir(cir, !lc && !rc);
  }
  void tag_addWB(long long delta) {
    wBDelta += delta;
    msg.addWB(delta, !lc && !rc);
  }
  void tag_down() {
    if (hasRev) {
      swap(lc, rc);
      swap(prevE, nextE);
      if (lc) lc->tag_rev();
      if (rc) rc->tag_rev();
      hasRev = false;
    }
    if (hasCoveredCir) {
      if (lc) {
        prevE->cir = coveredCir;
        lc->tag_coverCir(coveredCir);
      }
      if (rc) {
        nextE->cir = coveredCir;
        rc->tag_coverCir(coveredCir);
      }
      hasCoveredCir = false;
    }
    if (wBDelta != 0) {
      if (lc) {
        prevE->ew.wB += wBDelta;
        lc->tag_addWB(wBDelta);
      }
      if (rc) {
        nextE->ew.wB += wBDelta;
        rc->tag_addWB(wBDelta);
      }
      wBDelta = 0;
    }
  }
  void update() {
    msg.pathMsg.setEmpty();
    msg.firstE = prevE, msg.lastE = nextE;
    msg.hasCir = false;
    msg.hasMultiplePath = false;
    if (lc) msg = lc->msg + msg;
    if (rc) msg = msg + rc->msg;
  }
};
long long n;
lcc_node lccVer[MaxN + 1];
BlockAllocator<lcc_edge> lccEAllocator;
BlockAllocator<lcc_circle> lccCirAllocator;
void cactus_init() {
  for (long long v = 1; v <= 250000; v++) {
    lcc_node *x = lccVer + v;
    x->fa = x->lc = x->rc = NULL;
    x->prevE = x->nextE = NULL;
    x->hasRev = false;
    x->hasCoveredCir = false;
    x->wBDelta = 0;
    x->update();
  }
}
bool cactus_link(long long v, long long u, long long wA, long long wB) {
  if (v == u) return false;
  edgeWeight ew(wA, wB);
  lcc_node *x = lccVer + v, *y = lccVer + u;
  x->makeRoot(), y->makeRoot();
  if (x->fa) {
    x->access();
    if (x->msg.hasCir) return false;
    lcc_circle *cir = lccCirAllocator.allocate();
    lcc_edge *e = lccEAllocator.allocate();
    e->ew = ew, e->cir = cir;
    cir->pA = y, cir->pB = x, cir->pEx = NULL;
    cir->missingE = e;
    x->tag_coverCir(cir);
    x->access();
  } else {
    lcc_edge *e = lccEAllocator.allocate();
    e->ew = ew, e->cir = NULL;
    x->fa = y, x->prevE = e, x->update();
  }
  return true;
}
bool cactus_cut(long long v, long long u, long long wA, long long wB) {
  if (v == u) return false;
  edgeWeight ew(wA, wB);
  lcc_node *x = lccVer + v, *y = lccVer + u;
  if (x->findRoot() != y->findRoot()) return false;
  y->makeRoot(), x->access();
  y->splay_until(x);
  lcc_circle *cir = x->prevE->cir;
  if (cir && cir->pA == y && !cir->pEx && cir->missingE->ew == ew) {
    lcc_edge *e = cir->missingE;
    x->tag_coverCir(NULL);
    lccCirAllocator.deallocate(cir);
    lccEAllocator.deallocate(e);
    return true;
  }
  if (!y->rc && x->prevE->ew == ew) {
    lcc_edge *e = x->prevE;
    lccEAllocator.deallocate(e);
    if (cir) {
      if (cir->pEx) {
        cir->pEx->tag_rev();
        cir->pEx->fa = y, y->rc = cir->pEx;
        y->nextE = cir->pEx->msg.firstE;
        x->prevE = cir->pEx->msg.lastE;
      } else
        y->nextE = x->prevE = cir->missingE;
      y->update(), x->update();
      x->tag_coverCir(NULL);
      lccCirAllocator.deallocate(cir);
    } else {
      y->fa = NULL, y->nextE = NULL, y->update();
      x->lc = NULL, x->prevE = NULL, x->update();
    }
    return true;
  }
  return false;
}
bool cactus_add(long long qv, long long qu, long long delta) {
  lcc_node *x = lccVer + qv, *y = lccVer + qu;
  if (x->findRoot() != y->findRoot()) return false;
  x->makeRoot(), y->access();
  if (y->msg.hasMultiplePath) return false;
  y->tag_addWB(delta);
  return true;
}
path_message cactus_query(long long qv, long long qu) {
  path_message res;
  lcc_node *x = lccVer + qv, *y = lccVer + qu;
  if (x->findRoot() != y->findRoot()) {
    res.setInvalid();
    return res;
  }
  x->makeRoot(), y->access();
  res = y->msg.pathMsg;
  if (y->msg.hasMultiplePath) res.setMultiple();
  return res;
}
long long m, res;
long long a[500005], b[500005];
signed main() {
  scanf("%lld %lld", &n, &m);
  for (long long i = 1; i <= m; i++) scanf("%lld %lld", &a[i], &b[i]);
  cactus_init();
  long long j = 1;
  for (long long i = 1; i <= m; i++) {
    while (j <= m && cactus_link(a[j], b[j], 0, 0)) j++;
    res += j - i;
    cactus_cut(a[i], b[i], 0, 0);
  }
  printf("%lld", res);
}
